Physics

(1)

abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbc d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d

H

ARMONIZED

C

URRICULUM

FOR

BS

C

D

EGREE

P

ROGRAM

IN

P

HYSICS

ETHIOPIA

Curriculum Harmonization Team:

1. Hagos Woldeghebriel (PhD),

Assistant Professor of Physics, Mekele University, Chairman 2. Sintayehu Tesfa, (PhD),

Assistant Professor of Physics, Dilla University, Secretary 3. Tilahun Tesfaye, (PhD),

Assistant Professor of Physics, Addis Ababa University, Member 4. Alem Mebratu, (PhD),

Assistant Professor of Physics, Mekele University, Member

August 2009

Addis Ababa

Ethiopia

e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e fgggggggggggggggggggggggggggggggggggggggggggggh

(2)

3 Objectives 3 4 Graduate Profile 4 5 Grading System 5 6 Program Requirements 5 6.1 Admission Requirements . . . 5 6.2 Graduation Requirements . . . 5 6.3 Degree Nomenclature . . . 6 7 Teaching-Learning Methods 6 8 Course Selection & Sequencing 6 8.1 Course Coding/Numbering . . . 6 8.2 Course Selection . . . 7 8.2.1 Compulsory Courses: . . . 7 8.2.2 Elective Courses: . . . 8 8.2.3 Service Courses: . . . 8 8.2.4 Supportive Courses: . . . 8

8.2.5 General Education Courses: . . . 8

8.2.6 Summary of Course Requirements . . . 9

8.3 Sequencing . . . 9

8.3.1 Course Schedule . . . 9

9 Course Details 10 9.1 PHYSICS COMPULSORY COURSES . . . 10

Mechanics (Phys 201 ) . . . 11

Electromagnetism (Phys 202 ) . . . 15

Wave and Optics (Phys 203) . . . 19

Experimental Physics I (Phys 211 ) . . . 22

Experimental Physics II (Phys 212 ) . . . 25

Modern Physics (Phys 242 ) . . . 28

Mathematical Methods of Physics I (Phys 301) . . . 31

(3)

Curriculum for BSc Program in Physics

Experimental Physics III (Phys 312 ) . . . 39

Statistical Physics I (Phys 321) . . . 42

Classical Mechanics I (Phys 331) . . . 45

Quantum Mechanics I (Phys 342 ) . . . 48

Electronics I (Phys 353) . . . 51

Modern Optics (Phys 371 ) . . . 55

Electrodynamics I (Phys 376) . . . 59

Nuclear Physics I (Phys 382) . . . 62

Introduction to Computational Physics (Phys 402) . . . 65

Experimental Physics IV (Phys 411 ) . . . 67

Statistical Physics II (Phys 422) . . . 69

Classical Mechanics II (Phys 431) . . . 72

Quantum Mechanics II (Phys 441 ) . . . 75

Solid State Physics I (Phys 451 ) . . . 78

Sustainable Sources of Energy (Phys 461) . . . 81

Electrodynamics II (Phys 476) . . . 84

Research Methods and Senior Project (Phys 492) . . . 87

9.2 PHYSICS ELECTIVE COURSES . . . 90

Metrology I (Phys 316) . . . 91

Environmental Physics (Phys 367) . . . 94

General Geophysics (Phys 368) . . . 97

Introduction to Medical Physics (Phys 384) . . . 100

Astronomy I (Phys 437) . . . 103

Astronomy II (Phys 438) . . . 105

Physics Teaching (Phys 409 ) . . . 107

Metrology II (Phys 415) . . . 109

Metrology III (Phys 416) . . . 112

Stellar Physics I (Phys 434) . . . 114

Stellar Physics II (Phys 435) . . . 117

Introduction to Plasma Physics (Phys 436) . . . 120

Space Physics (Phys 439 ) . . . 123

Solid State Physics II (Phys 452) . . . 126

Introduction to Atmospheric Physics (Phys 463) . . . 129

Physics of Electronic Devices (Phys 456 ) . . . 132

Electronics II (Phys 454 ) . . . 135

Exploration Geophysics (Phys 468) . . . 138

Introduction to Laser Physics (Phys 471) . . . 141

(4)

Nuclear Physics II (Phys 482) . . . 144

Radiation Physics (Phys 484) . . . 147

9.3 PHYSICS SERVICE COURSES . . . 149

Mechanics and Heat for Chemists (Phys 205) . . . 150

Electricity and Magnetism (Phys 206) . . . 153

Mechanics and Heat (Phys 207) . . . 157

9.4 Supportive Courses . . . 160

Introduction to Computer Applications (Comp 201 ) . . . 161

Introduction to Programming (Comp 271 ) . . . 164

Calculus I (Math 261) . . . 167

Calculus II (Math 262 ) . . . 170

Linear Algebra (Math 325 ) . . . 173

9.5 General Education Courses . . . 175

Communicative Skill English . . . 175

Writing Skills English . . . 175

Civics and Ethical Studies . . . 175

10 Quality Assurance 175

(5)

1 Introduction

Physics, as one of the fundamental sciences, is concerned with the observation, un-derstanding and prediction of natural phenomena and the behavior of man-made systems. It deals with profound questions about the nature of the universe and with some of the most important practical, environmental and technological issues of our time. The scope of Physics is broad and encompasses mathematical and theoretical investigation, experimental observation, computing technique, technological applica-tion, material manipulation and information processing. Physics seeks simple expla-nations of physical phenomena based on universal principles stated in concise and powerful language of mathematics. The principles form a coherent unity, applicable to objects as diverse as DNA molecules, neutron stars, super-fluids, and liquid crys-tals. Findings in Physics have implications in all walks of life ranging from the way we perceive reality to gadgets of everyday use.

Physicists constantly test the basic laws of nature by probing the unknown, the mys-terious and the complex. They also search for new laws at the frontiers of knowledge, systematically seek novel properties of matter. They are alert to the possibility of applying physical idea and processes to new situations, and often the realization of these possibilities has had revolutionary consequences. It is with the intention of producing such physicists for the country that this curriculum has been developed and is currently under a harmonization process.

The Physics departments throughout the country have different backgrounds with the Physics Department at AAU being the pioneer. Most of the others are opened during the last two decades. Some of these Universities have been offering BSc, others BEd while the rest both. Currently there are 22 Physics Departments offering a BSc degree program in the country. It was evident that the previous curriculum, where ever it has been applied in the country, had a number of limitations. In order to find out the limitations of the previous curriculum and develop a better and new curriculum based on the new 70:30 enrolment and program mix policy, all Universities were requested, by the Ministry of Education, to carry out needs assessment.

Based on the findings of the needs assessment, most of the universities have con-ducted a consultative meeting at cluster levels, and then a national conference has been conducted where representatives from almost all Ethiopian Universities offering a degree program in Physics have actively participated. The conference has clearly indicated that the previous curriculum has significant limitations, and hence, in or-der to alleviate these shortcomings, a new and dynamic approach was required. It is indicated that the new curriculum should be prepared taking into account that the limitations of the previous curriculum should be critically addressed. It should aim for a comprehensive curriculum that contributes significantly towards the development of our country in a way that this important field plays a vital role for the advancement of science and technology. In light of these recommendations, all universities came together for the second time to finalize and harmonize a common curriculum. In that conference, a national three years curriculum has been developed which was later endorsed by the National Advisory Committee and consequently by the Ministry of Education.

A consensus has been reached by the Universities that at present our country is lacking the necessary expertise in Physics. It has become very evident to start a

(6)

Bachelor of Science (BSc) Degree Program in Physics for the following main reasons: • there is a growing need, from the learners’ side, to maximize the stability of their

skills in the ever increasing competition in the job market;

• as the result of the graduate expansion program, new study areas that absorb Physics graduates in their post graduate programmes are emerging in various faculties/colleges of different universities throughout the country

• the need for educated manpower in the country itself is increasing in diversity. Professions like teaching, medicine, radiation protection, meteorology, quality and standards control, geoPhysics among others absorb graduates of Physics. A Physics student should nurture strong analytical, experimental and computing skills as well as mathematical abilities.Students should also be able to work with mechanical, optical and electronic equipments, to design projects and synthesize and summarize data that compliment theoretical and experimental skills to enhance ca-reer opportunity. Taking this into account the Ethiopian Higher Education Strategic Center (HESC), has initiated an idea of further harmonizing the national curricu-lum taking the experience of the last one year in implementing the new curricucurricu-lum. On Hamle 12, 2001 EC, HESC has formed group of consultants from the existing universities in the respective fields. The Physics curriculum harmonizing team is es-tablished accordingly. The team has consulted many curriculum documents relevant for its work. Particularly, it has critically evaluated the newly implemented Physics curricula of almost all the Ethiopian universities. It has also looked at the Physics curricula from the European Union which are developed on the so called Bologna Pro-cess. In addition, the team has consulted the Ethiopian Physics curriculum for the preparatory schools. It is based on these accounts that the team has come up with the current harmonized curriculum for BSc Degree program in Physics. The team has found out that there is a smooth coherence between the preparatory curricula and the harmonized Physics Curricula for the Ethiopian Universities.

2 Rationale of the Curriculum

There is a high demand in the country for graduates with a good background in Physics. It is evident that earlier efforts to improve the national curriculum were not successful enough. It is hence found essential to harmonize and improve the BSc Physics curriculum in the country so as to meet the required demand of the country. Particularly, on the basis that the graduates of earlier curricula are content defi-cient and lacked depth to understand their environment, there has been an attempt of designing a curriculum aimed at producing graduates who are capable of solving the problems of the society. Despite such efforts, the curricula designed by respective universities are found to be virtually different and dealing with concepts which are not coherent enough. The current harmonization effort has also taken an easy transfer of students from university to university into account, and it has given due emphasis to maintain the graduate profile fairly uniform. The issue of quality controlling mecha-nism at national level has got also the necessary attention. In addition to this, taking experience from foreign Universities especially from Bologna process is considered as an essential component in enriching the course objectives (out puts) content and the method of presentation and evaluation. Besides, the BSc curriculum:

(7)

• aims to cultivate physicists who combine a high level of numeracy with the ability to apply their skills and experience.

• is designed to develop students awareness of the role of Physics in contempo-rary applications, together with the skills of logical thought and a flexibility of mind that will help them continue their personal development throughout their subsequent career.

• lays emphasis on the fundamentals of Physics, whilst offering students a wide range of final year options that are intended to stimulate the versatility, knowl-edge and skills that employers look for in a Physics graduate.

3 Objectives

The BSc Physics curriculum has the following general objectives:

• to provide a broad knowledge and understanding of the basic principles of Physics and the ability to apply that knowledge and understanding to solve physical problems;

• to enable students express their ideas clearly and cogently in both written and verbal form;

• to insure high quality education in Physics within a stimulating and support-ive environment committed to excellence in Physics (theoretical, experimental, computational, research and community services);

• to educate students the core of Physics areas at the necessary depth, while they are encouraged to be critically receptive to new ideas and to attain their full academic potential;

• to equip students with a sound base of knowledge and understanding in Physics; • to expose students to the applications of physical principles in various branches

of Physics;

• to support students develop the ability to carry out experimental or/and other investigations, analyze their results critically, draw valid conclusions, and com-municate their findings both verbally and in writing;

• to lay the foundations and transferable skills essential for further training and for the development of skills and knowledge;

• to render public consultations in areas closely related to Physics;

• to create an environment that gives students opportunities to develop personal confidence, self-reliance and career aspirations.

• to train students with a basic courses in Physics that will enable them to be academically and professionally qualified to solve physical problems;

• to develop the students ability to work independently and in groups or coopera-tively;

• to equip students with necessary confidence, understanding and skills that he/she needs to take up his/her civic responsibilities;

• to enhance the capability of the students to work as professional physicists in industries, research and other institutions/organizations;

(8)

• to have enhanced skills in mathematics; problem solving; experimental tech-niques; scientific report writing; collecting, analyzing and presenting informa-tion; use of information technology and self-educainforma-tion;

4 Graduate Profile

The Physics graduates are expected to acquire problem solving and abstract thinking skills. This makes Physics graduates very desirable employees in a wide variety of areas like Education, Research, Medicine, Consulting, Defense, Industry, and Jour-nalism and other governmental and non governmental organizations. These funda-mental skills as well as training in practical subjects such as optics, lasers, computer interfacing, image processing, geophysical and space exploration, weather forecast-ing and electronics also make them very desirable employees in high tech companies, industries and research centers.

Having completed a BSc curriculum in Physics, students should be able to:

• have a solid knowledge and understanding of modern and classical Physics; along with the associated mathematics and experimental techniques to become instructors at educational institutions;

• have preparedness to undertake a postgraduate program in Physics and other related multidisciplinary postgraduate programs that require BSc in Physics; • have the capability to work as professional physicists in scientific research;

Physics-related careers in industry, public service or the media;

• be prepared to enter a wide range of professional careers that require and values the analytical, mathematical and computational skills of a well-trained Physics graduate;

• have acquired an insight into, and have practice in basic methods of independent research;

• have developed the following discipline-specific skills:

– investigative skills, to design, carry out, analyze and evaluate experiments; – experimental skills, to use equipment safely; carry out measurements with

desired degree of accuracy in laboratories;

– mathematical skills appropriate to the subject;

– readiness to be trained in specific professions like Physics teaching, Physics

curriculum design and implementation • have developed the following transferable skills:

– information retrieval skills, to gather and extract relevant information from

books, journals and other data sources;

– information technology skills, to collect, order, analyze and present data

using computers and other electronic systems;

– interpersonal skills, to communicate effectively with others, both in writing

and orally, and to work as part of a team;

– the ability to work independently and organize work to meet desired

require-ments;

– in developing local technologies and adapting technologies for local needs;

(9)

• have capacity for logical, critical, and objective thinking;

• develop interest to work in group, make reliable decisions, have personal confi-dence, have sense of responsibility and have the commitment to serve the com-munity

• have personal confidence and prepared for life.

5 Grading System

One of the issue that need attention in harmonizing curricula is to have a similar grading system. Since maximum effort should be done to achieve the stated objectives of the curriculum, there is a need for a fixed scale grading system. In addition, in order to insure fair grading, a letter grading system needs to be adjusted and should be made uniform across Universities, subject to approval by respective Senates, as shown below:

Range of Marks 100%

Letter Grade Value Interpretation

≥ 75 A 4.00 [70 − 75) A− 3.67 Excellent [65 − 70) B+ 3.33 [60 − 65) B 3.00 Very Good [55 − 60) B− 2.67 [50 − 55) C+ 2.33 [40 − 50) C 2.00 Satisfactory [35 − 40) C− 1.67 Fair [30 − 35) D+ 1.33 [20 − 30) D 1.00 Unsatisfactory < 20) F 0.00 Failure

6 Program Requirements

6.1 Admission Requirements

To be admitted to the BSc program in Physics, a candidate should satisfy the general admission requirements of the Universities and must have at least a pass grade in Physics and mathematics in the College Entrance Examination.

6.2 Graduation Requirements

i) A student is required to take a minimum of 107 credit hours:

Compulsory 71 Cr. Hrs Elective 9 Cr. Hrs Supportive 18 Cr. Hrs General Education 9 Cr. Hrs Total 107 Cr. Hrs Page 5 of 176

(10)

ii) The Maximum total credit hours taken by a student shall not exceed 113. iii) The Minimum Cumulative Grade Points Average (CGPA) at the end should meet

the value as specified below:

Physics Cumulative Grade Point Average 2.00 Overall Cumulative Grade Point Average 2.00 No F in any of the courses

6.3 Degree Nomenclature

English: Bachelor of Science in Physics

Amharic:

yúYNS ÆClR Ä!G¶ bðz!KS

7 Teaching-Learning Methods

Method of Teaching:

Presentation of courses is through lectures, tutorials, self-study (project works), problem solving, class and group discussions, assignments, laboratory demon-strations and hands-on exercises as well as quizzes and tests to insure continu-ous assessment and student/learner centered approach.

Attendance Policy:

Regular, punctual class attendance is essential for the satisfactory completion of a course. Each student is expected to attend all sessions, complete all assigned work, and take all examinations.

Assessment:

Assignments, report, end-of-semester examinations, dissertations, projects, etc. with their percentage contribution to the final assessment will be provided by the instructor with a course outline (which will be available to students before the course begins).

8 Course Selection & Sequencing

8.1 Course Coding/Numbering

All Physics courses are coded “Phys” followed by three digits:

The first digit indicate the level of the course: , i.e.,

2 for first year courses 3 for second year courses 4 for third year courses.

The middle digits indicate the various streams of Physics Courses, i.e.,

(11)

0 General Physics

1 Laboratory/Technical Courses 2 Statistical Physics

3 Classical Mechanics, Astronomy, Astro, Space, Plasma & Stelar Physics 4 Modern Physics, Quantum Mechanics

5 Solid State Physics, Electronics, Semiconductor Devices

6 Atmospheric, Environmental, Sustainable Source of Energy, GeoPhysics 7 Electrodynamics, Modern Optics, Laser Physics

8 Nuclear, Medical & Radiation Physics 9 Senior Project

The last digits stand for semester in which the course is offered i.e.

ODD last digit courses are offered during the first semester. EVEN last digit courses are offered during the second semester

8.2 Course Selection

8.2.1 Compulsory Courses:

Course Title Course Code Credits

Mechanics Phys 201 4 Electromagnetism Phys 202 4 Wave and Optics Phys 203 2 Experimental Physics I Phys 211 2 Experimental Physics II Phys 212 2 Modern Physics Phys 242 3 Mathematical Methods of Physics I Phys 301 3 Mathematical Methods of Physics II Phys 302 3 Experimental Physics III Phys 312 2 Statistical Physics I Phys 321 3 Classical Mechanics I Phys 331 3 Quantum Mechanics I Phys 342 3 Electronics I Phys 353 3 Modern Optics Phys 371 3 Electrodynamics I Phys 376 3 Nuclear Physics I Phys 382 3 Introduction to Computational Physics Phys 402 3 Experimental Physics IV Phys 411 2 Statistical Physics II Phys 422 3 Classical Mechanics II Phys 432 3 Quantum Mechanics II Phys 441 3 Solid State Physics I Phys 451 3 Sustainable Sources of Energy Phys 461 2 Electrodynamics II Phys 476 3 Research Methods and Senior Project Phys 492 3

Total 71

(12)

8.2.2 Elective Courses:

Metrology I Phys 316 3 Environmental Physics Phys 367 3 General Geophysics Phys 369 3 Introduction to Medical Physics Phys 384 3 Physics Teaching Phys 409 3 Metrology II Phys 415 3 Metrology III Phys 416 3 Stelar Physics I Phys 434 3 Stelar Physics II Phys 435 3 Introduction to Plasma Physics Phys 436 3 Astronomy I Phys 437 3 Astronomy II Phys 438 3 Space Physics Phys 439 3 Solid State Physics II Phys 452 3 Electronics II Phys 454 3 Physics of Electronic Devices Phys 456 3 Atmospheric Physics Phys 463 3 Exploration Geophysics Phys 468 3 Introduction to Laser Physics Phys 471 3 Nuclear Physics II Phys 482 3 Radiation Physics Phys 484 3

A minimum of 9 Crhrs from a total of 63

8.2.3 Service Courses:

Mechanics and Heat for Chemists/Geologists Phys 205 3 Electricity and Magnetism Phys 206 3 Mechanics and Heat Phys 207 4

8.2.4 Supportive Courses:

Calculus I Math 261 4

Calculus II Math 262 4

Linear Algebra Math 325 3

Introduction to Computer Applications Comp 201 3

Introduction to Programming Comp 271 4

Total Credit Hours 18 8.2.5 General Education Courses:

Communicative Skill English EnLa 201 3

Writing Skill EnLa 202 3

Civics and Ethical Studies CvEt 202 3

Total Credit Hours 9

(13)

8.2.6 Summary of Course Requirements

Min. Cr.hrs. Max. Cr.hrs.

Compulsory Physics Courses 71 71

Elective Physics Courses 9 15

Supportive Courses 18 18

General Education Courses 9 9

Total 107 113

8.3 Sequencing

8.3.1 Course Schedule

Year I

Semester I Semester II

Course Code Cr.hr. Course Code Cr.hr.

Phys 201 4 Phys 202 4 Phys 211 2 Phys 212 2 Math 261 4 Phys 242 3 EnLa 201 3 CvEt 202 3 Phys 203 2 Math 262 4 Comp 201 3 EnLa 202 3 Total 18 Total 19 Year II Semester I Semester II

Phys 321 3 Phys 382 3

Phys 331 3 Physics Elective I 3

Phys 371 3 Phys 342 3 Phys 353 3 Phys 312 2 Math 325 3 Phys 376 3 Phys 301 3 Phys 302 3 Total 18 Total 17 Page 9 of 176

(14)

Year III

Semester I Semester II

Phys 411 2 Phys 492 3

Phys 451 3 Phys 402 3

Comp 271 4 Phys Elective III 3

Phys 461 2 Phys 476 3

Phys Elective II 3 Phys 432 3

Phys 441 3 Phys 422 3

Total 17 Total 18

9 Course Details

All Compulsory courses offered in the program are described and detailed outline is given with approximate allotted time. The various entries for a given course descrip-tion are as follows:

Title: The descriptive title of the course.

Credits: The break down of the credit in terms of Lecture, Tutorial or Laboratory

hours.

Prerequisite: The course that must be taken prior to the course. Co-requisite: The course that must be taken along with the course.

Learning Outcome/Objective: What a student will be expected to have learned, as

a result of successful completion of a course.

Course Outline: The description of the minimum content to be covered during the

course delivery.

Course Description: Describes the course coverage hrs: Equivalent to contact hours

9.1 PHYSICS COMPULSORY COURSES

(15)

Mechanics (Phys 201 )

Course Title and Code: Mechanics (Phys 201 )

Credits 4 Cr.hrs ≡ Lecture: (4 hrs) + Tutor: (2 hrs)

Prerequisite(s): Co-requisite(s):

Academic Year: 20 / Semester: I / II

Students’ Faculty: Science Department: Physics

Program: Undergraduate Enrollment: Regular

Instructor’s Name

Address: Block No. Rm. No.

Class Hours:

Course Rationale

The aim of this course is to develop a sound understanding of the central concepts of mechanics at the conceptual level so that solving relevant practical problems is possible. A first-principle approach is adopted, as most students have not studied calculus based treatment of the topics previously. Emphasis will be given to basic understanding rather than the development of mathematical theory. It also describes the fundamental concepts of fluid behavior under both static and dynamic conditions to enable the learner to analyze many practical problems in which fluid is the working medium.

Learning Outcomes

Upon completion of this course students should be able to:

• discuss the graphical and analytical methods of vector addition, subtraction and multiplication,

• compute average and instantaneous values of velocity, speed and acceleration, • derive the kinematic equations for uniformly accelerated motion,

• solve problems involving bodies moving in one and two dimensional space using concepts in calculus and trigonometry,

• explain some implications of Newton’s laws of motion, • derive and apply work-energy theorem,

• apply the law of conservation of linear momentum to collisions,

• repeat the procedures followed to solve problems in rectilinear motion for rota-tional motion,

(16)

Curriculum for BSc Program in Physics Mechanics (Phys 201 )

• demonstrate understanding of Newton’s law of gravitation,

• describe simple harmonic motion and the corresponding problems, • explain how external forces act on fluids in equilibrium,

• work out problems applying Pascal’s principle, Archimedes’ principle and Bernoulli’s equation in various situations,

Course Description

The main topics to be covered are Vector Algebra, Particle Kinematics and Dynamics, Work and Energy, Conservative Forces and Potential Energy, Dynamics of a System of Particles, Linear Momentum, Collisions, Rotational Kinematics, Dynamics and Statics of a Rigid Body, Gravitation and Planetary Motion, Oscillatory Motion, Fluid Mechan-ics. Course Outline 1) Vectors (4 hrs) 1.1) Representation of vectors 1.2) Vector addition 1.3) Vector multiplication 1.3.1) Dot (Scalar ) product 1.3.2) Cross (Vector) product 1.3.3) Triple scalar product 1.3.4) Triple vector product

2) One and Two Dimensional Motions (6 hrs) 2.1) Average and instantaneous velocity 2.2) Average and instantaneous acceleration 2.3) Motion with constant acceleration 2.4) Projectile motion

2.5) Uniform circular motion 3) Particle Dynamics (7 hrs)

3.1) Newton’s laws of motion 3.2) Friction force

3.3) Application of Newton’s laws 4) Work and Energy (5 hrs)

4.1) Work done by a constant force 4.2) Work done by a variable force

4.3) Kinetic energy and work-energy theorem 4.4) Elastic potential energy

4.5) Conservative and nonconservative forces 5) Impulse and Momentum (10 hrs)

5.1) Linear momentum and impulse 5.2) Conservation of momentum

(17)

5.3) system of particles 5.3.1) Center of mass

5.3.2) Center of mass of a rigid body 5.3.3) Motion of system of particles 5.4) Elastic and inelastic collision

5.4.1) Elastic collisions in one-dimension 5.4.2) Two-dimensional elastic collisions 5.4.3) Inelastic collisions

5.4.4) Systems of variable mass 6) Rotation of Rigid Bodies (9 hrs)

6.1) Rotational kinematics

6.1.1) Rotational motion with constant and variable angular accelerations 6.1.2) Rotational kinetic energy

6.1.3) Moment of inertia 6.2) Rotational dynamics

6.2.1) Torque and angular momentum 6.2.2) Work and power in rotational motion 6.2.3) Conservation of angular momentum

6.2.4) Relation between linear and angular motions 7) Gravitation (5 hrs)

7.1) Newton’s law of gravitation

7.2) Gravitational field and gravitational potential energy 7.3) Kepler’s law of planetary motion

8) Simple harmonic motion (6 hrs) 8.1) Energy in simple harmonic motion 8.2) Equations of simple harmonic motion 8.3) Pendulum

8.4) Damped and forced oscillations 8.5) Resonance

9) Fluid Mechanics (8 hrs) 9.1) Internal forces in fluids 9.2) Pressure in a fluid 9.3) Pascal’s principle 9.4) Archimedes’ principle 9.5) Continuity equation

9.6) Bernoulli’s equation and its applications

Method of Teaching

Lecture, discussion, homework, tutorial and project. Online learning resources are also employed.

(18)

Assessment

• Homework will consist of selected end of chapter problems: 20%

• In-class participation (asking questions, discussing homework, answering ques-tions): 5%

• quizzes and Tests (25%),

• All in all the continuous assessment covers 50 % • Final Semester Examination (50%)

Recommended References

Course Textbook

Raymond A. Serway, Physics: For Scientists & Engineers, 6th _{ed., Thomson Bruke,}

2004

References

1. Hugh D. Young and Roger A. Freedmann, University Physics with Modern Physics 12th _{ed., 2008}

2. Douglas C. Giancoli, Physics for scientists and engineers, Printice Hall, 4th_{, 2005}

3. Robert Resnick and David Halliday, Fundamentals of Physics Extended, HRW 8thed., 2008

4. Paul M. Fishbane, Stephene Gasiorowicz, Stephen T. Thoronton, Physics for Sci-entists and Engineers, 3rd _{ed., 2005}

(19)

Electromagnetism (Phys 202 )

Course Title and Code: Electromagnetism (Phys 202 )

Prerequisite(s): —- Co-requisite(s):

Class Hours:

This course is designed to introduce concepts of classical electrodynamics with the aid of calculus. It also emphasizes on establishing a strong foundation of the re-lation between electric and magnetic phenomena; a concept that turns out to be a fundamental basis for many technological advances.

• explain the basic concepts of electric charge, electric field and electric potential, • apply vector algebra and calculus in solving different problems in

electromag-netism,

• analyze direct and alternating current circuits containing different electric ele-ments and solve circuit problems,

• describe properties of capacitors and dielectrics,

• describe the magnetic field and solve problems related to the magnetic field and magnetic forces,

• discuss about electromagnetic induction, • state Maxwell’s equation in free space,

• describe some applications of Maxwell’s equations,

(20)

Curriculum for BSc Program in Physics Electromagnetism (Phys 202 )

The topics to be included are: Coulomb’s Law, Electric Field, Gauss’ Law, Electric Potential, Electric Potential Energy, Capacitors and Dielectric, Electric Circuits, Mag-netic Field, Bio-Savart’s Law, Ampere’s Law, ElectromagMag-netic Induction, Inductance, Circuits with Time Dependent Currents, Maxwell’s Equations, Electromagnetic Wave.

Course Outline

1) Electric Field (8 hrs)

1.1) Properties of electric charges 1.2) Coulomb’s law

1.3) Electric field due to point charge 1.4) Electric dipole

1.5) Electric field due to continuous charge distribution 1.6) Motion of charged particles in electric field

2) Gauss’s Law ( 4 hrs) 2.1) Electric flux 2.2) Gauss’s Law

2.3) Applications of Gauss’s Law 3) Electric Potential ( 7 hrs)

3.1) Electric potential energy

3.2) Electric potential due to point charges

3.3) Electric potential due to continuous charge distribution 3.4) Relations between potential and electric field

3.5) Equi-potential surfaces

4) Capacitance and Dielectrics (5 hrs) 4.1) Capacitance

4.2) Combination of capacitors 4.3) Capacitors with dielectrics 4.4) Electric dipole in external field 4.5) Electric field energy

5) Direct Current Circuits (7 hrs)

5.1) Electric current and current density 5.2) Resistance and Ohm’s law

5.3) Resistivity of conductors

5.4) Electrical energy, work and power 5.5) Electromotive force

5.6) Combinations of resistors 5.7) Kirchhoff’s rules

5.8) RC circuits

6) Magnetic Force (6 hrs)

6.1) Properties of magnetic field

6.2) Magnetic force on a current carrying conductor 6.3) Torque on a current loop in uniform magnetic field

(21)

6.4) Motion of charged particles in magnetic field 6.5) Hall effect

7) Calculation of Magnetic Field (4 hrs) 7.1) Source of magnetic field

7.2) Biot-Savart’s law

7.3) The force between two parallel conductors 7.4) Ampere’s law and its application

8) Electromagnetic Induction (6 hrs) 8.1) Magnetic flux

8.2) Gauss’s law in magnetism 8.3) Faraday’s Law of induction 8.4) Lenz’z law

8.5) Induced Emf (including motional Emf) 8.6) Induced electric field

8.7) Displacement current 9) Inductance (4 hrs)

9.1) Self inductance and mutual inductance 9.2) RL circuits

9.3) Energy in magnetic field 9.4) Oscillations in an LC circuits 10) AC Circuits (6 hrs)

10.1) AC sources and phasors 10.2) Resistors in an AC circuits 10.3) Inductors in an AC circuits 10.4) Capacitors in an AC circuits 10.5) The RLC series circuits 10.6) Power in an AC circuits 11) Maxwell’s Equations (3 hrs)

11.1) Maxwell’s equations 11.2) Electromagnetic waves

Assessment

(22)

Course Textbook

Raymond A. Serway, Physics: For Scientists & Engineers, 6th _{ed., Thomson Bruke,}

2004

References

1. Hugh D. Young and Roger A. Freedmann, University Physics with Modern Physics 12th _{ed., 2008}

3. Robert Resnick and David Halliday, Fundamentals of Physics Extended, HRW 8th

ed., 2008

4. Paul M. Fishbane, Stephene Gasiorowicz, Stephen T. Thoronton, Physics for Sci-entists and Engineers, 3rd ed., 2005

(23)

Wave and Optics (Phys 203)

Course Title and Code: Wave and Optics (Phys 203)

Prerequisite(s): —- Co-requisite(s):

Class Hours:

This course is mainly aimed at introducing concepts of waves. Emphasis is given to distinguish various types of waves which paves a way for in depth understanding of sound, optics and the corresponding applications.

• describe basic laws and principles of mechanical and electromagnetic waves, • associate vibrations with the creation of mechanical waves,

• distinguish different types of waves,

• demonstrate the application of Physics laws in music and musical instrument, • demonstrate understanding of the superposition principle,

• exhibit understanding of the geometrical description of different properties of light,

• describe the interference and diffraction phenomena,

Vibrations, Periodic Motions, Resonance, Coupled Oscillation, Types of Waves, Me-chanical Wave, Sound, Music and Musical Instruments, Superposition of Waves, Standing Waves, Group and Phase Velocities, Nature of Light, Electromagnetic Spec-trum, Geometric Optics, Reflection, Refraction, Dispersion, Fermat’s Principle, Inter-ference, Diffraction, Optical Devices.

(24)

Curriculum for BSc Program in Physics Wave and Optics (Phys 203) Course Outline 1) Vibrations (4 hrs) 1.1) Periodic motion 1.2) Types of vibrations 1.3) Sound

1.4) Music and musical instruments 1.5) Resonance

1.6) Coupled Oscillation 2) Types of Waves (4 hrs)

2.1) Mechanical waves

2.2) Transverse and longitudinal waves 2.3) Phase velocity and group velocity 2.4) Amplitude and intensity of Waves 2.5) Frequency and wavelength

2.6) Wave packets

2.7) Many dimensional waves 3) Superposition of Waves (4 hrs)

3.1) Vector addition of amplitudes

3.2) Superposition of two wave trains of the same frequency 3.3) Superposition of many waves with random phases 3.4) Complex waves

3.5) Addition of simple harmonic motions 4) Nature of Light ( 6 hrs)

4.1) Electromagnetic spectrum 4.2) Propagation and speed of light 4.3) Reflection and refraction

4.4) Refractive index and optical path 4.5) Reversibility principle

4.6) Fermat’s principle

4.7) Propagation of light in material medium 5) Interference and Diffraction of Light (9 hrs)

5.1) Types of interference 5.2) Huygen’s principle 5.3) Young’s experiment

5.4) Interference fringes from a double source 5.5) Index of refraction by interference method 5.6) Types of diffraction

5.7) Diffraction by a single slit 5.8) Resolving power

5.9) Intensity function

5.10) Distinction between interference and diffraction 5.11) Diffraction grating

6) Optical Devices (3 hrs) 6.1) Human eye

6.2) Cameras and photographic objectives 6.3) Types and properties of lenses

6.4) Types of magnifiers

6.5) Microscopes and Telescopes

(25)

Curriculum for BSc Program in Physics Wave and Optics (Phys 203)

Assessment

Course Textbook

1. F. A. Jenkins and H. A. White, Fundamentals of Optics, McGraw Hill, 4th ed., 2001

2. Raymond A. Serway, Physics: For Scientists & Engineers, 6th _{ed., Thomson}

Bruke, 2004

References

1. H. J. Pain, The Physics of Vibrations and Waves, John Wiley and Sons, 5th _ed.,

1999.

2. Hugh D. Young and Roger A. Freedmann, University Physics with Modern Physics 12th ed., 2008

4. Robert Resnick and David Halliday, Fundamentals of Physics Extended, HRW 8th

ed., 2008

5. Paul M. Fishbane, Stephene Gasiorowicz, Stephen T. Thoronton, Physics for Sci-entists and Engineers, 3rd _{ed., 2005}

(26)

Experimental Physics I (Phys 211 )

Course Title and Code: Experimental Physics I (Phys 211 )

Credits 2 Cr.hrs ≡ Tutor: (1 hrs) + Lab: (3 hrs)

Academic Year: 20 / Semester: _{I / II} Students’ Faculty: Science Department: Physics

Address: Block No. Room No. —–

Class Hours:

Experimental observations form the basis for new hypotheses, and also test scientific theories. It is therefore essential that all Physicists understand the experimental method and develop the ability to make reliable measurements. This course provides a broad foundation in experimental physics.

Upon completion of this course students should be able to: • plan and execute experimental investigations;

• apply and describe a variety of experimental techniques; • identify, estimate, combine and quote experimental errors; • keep accurate and thorough records;

• discuss and analyze critically results of investigations, including the use of com-puters for data analysis;

• minimize experimental errors;

• demonstrate awareness of the importance of safety within the laboratory context; • identify the hazards associated with specific experimental apparatus, and

com-ply with the safety precautions required;

• delivery of written and oral presentations (experiment write-ups, formal report, group talk);

• work in team; • manage time;

• use computers (for data analysis and collection), if possible;

Selected experiments from topics of mechanics and heat, at least 12 experiments to be performed.

(27)

Curriculum for BSc Program in Physics Experimental Physics I (Phys 211 )

Recommended List of Experiments

1) Mechanics

1.1) Measurements of Mass, Volume, Density 1.2) Local Value of Acceleration Due to Gravity 1.3) Translational Equilibrium / Vector Forces

1.4) Determination of the static and kinetic coefficients of friction. 1.5) Rotational Equilibrium / Torque

1.6) Work and Energy / A Model Pile Driver 1.7) Collisions / Conservation of Momentum 1.8) Projectile Motion / The Ballistic Pendulum 1.9) Centripetal Force

1.10) Archimedes Principle

To verify Archimedes Principle and use it for the determination of the density of an object more dense than water.

1.11) Elastic Forces/Hooke’s Law

1.12) Simple Harmonic Motion of a Spring-Mass System 1.13) The Simple Pendulum

2) Heat

2.1) Thermal / Linear Expansion

2.2) Calorimetry and the Specific Heat of a Metal 2.3) Heat of Fusion of Ice

2.4) Heat of Vaporization of Water 3) Waves and Sound

3.1) Wave Motion / Vibrating Strings

3.2) To study longitudinal sound waves created in an air column of variable

length.

The apparatus is a modified Kundts tube with a movable water reservoir, and a tuning fork.

Laboratory classes should be conducted in groups, with background material pre-sented in the form of handouts (manuals) and with necessary support from the in-structor. Tutor sessions should be supplemented with (on-line) notes, error analysis and graph plotting elaborations. Private study and preparing formal experimental reports. Group work in preparing and delivering oral presentation.

Simulation experiments from the Internet can be used to supplement laboratory ac-tivities whenever possible.

Assessment

• Pre-Lab Questions: 25%

• In-Lab questions (answering questions during lab sessions and preparedness): 20%

• Lab-Reports: (20%)

• Examination (oral, practical or/and written): (35%)

It is recommended that the number of students per laboratory session to be between 20 and 30.

(28)

Curriculum for BSc Program in Physics Experimental Physics I (Phys 211 )

1.1) David C. Baird, Experimentation: An Introduction to Measurement, Theory and Experimental Design, Benjamin Cummings, 3rd _{ed., (1994).}

2.2) Andrian C. Melisinos and Jim Napolitano, Experiments in Modern Physics Aca-demic Press, 2nd _{ed., (2003).}

(29)

Experimental Physics II (Phys 212 )

Course Title and Code: Experimental Physics II (Phys 212 )

Credits 2 Cr.hrs ≡ Tutor: (1 hrs) + Lab: (3 hrs)

Class Hours:

Experimental observations form the basis for new hypotheses, and also test scientific theories. It is therefore essential that all Physicists understand the experimental method and develop the ability to make reliable measurements. This course provides a broad foundation in experimental physics.

Upon completion of this course students should be able to: • plan and execute experimental investigations;

• apply and describe a variety of experimental techniques; • identify, estimate, combine and quote experimental errors; • keep accurate and thorough records;

• discuss and analyze critically results of investigations, including the use of com-puters for data analysis;

• minimize experimental errors;

• demonstrate awareness of the importance of safety within the laboratory context; • identify the hazards associated with specific experimental apparatus, and

com-ply with the safety precautions required;

• delivery of written and oral presentations (experiment write-ups, formal report, group talk);

• work in team; • manage time;

• use computers (for data analysis and collection), if possible;

Selected experiments from topics of Electricity and Magnetism. 25

(30)

Curriculum for BSc Program in Physics Experimental Physics II (Phys 212 )

Recommended List of Experiments

1) Direct Current Circuits

1.1) Calibration of a Voltmeter and an Ammeter from a Galvanometer

1.2) Study of the phase change of ice into water and understand how to work

with phase changes in materials.

1.3) Investigation of the variation of magnetic field, due to a current carrying

conductor, with distance and current

1.4) Verification of Ohm’s law and the law of combination of resistors 1.5) Determination of internal resistance of a cell

1.6) Verification of Kirchohoff’s Law 2) Alternating Current Circuits

2.1) Study the electrical characteristics of an ac circuit containing a resistor, an

inductor, and a capacitor in series

2.2) Study of AC circuits using oscilloscope.

2.3) Determination of unknown resistance using Wheatstone bridge

2.4) Determination of capacitance and inductance with wheatstone bridge. 2.5) To investigate how the number of turns (n), the diameter of a coil (d), the

frequency (f ), and the magnetic field strength (B) are related to the induced voltage (V ) in a coil.

3) Magnetism

3.1) To measure the horizontal component of the earth’s magnetic field strength 3.2) To measure the magnetic dipole moment of a bar magnet by the method of

Gauss

Laboratory classes should be conducted in groups, with background material pre-sented in the form of handouts (manuals) and with necessary support from the in-structor. Tutor sessions should be supplemented with (on-line) notes, error analysis and graph plotting elaborations. Private study and preparing formal experimental reports. Group work in preparing and delivering oral presentation.

Simulation experiments from the Internet can be used to supplement laboratory ac-tivities whenever possible.

Assessment

• Pre-Lab Questions: 25%

• In-Lab questions (answering questions during lab sessions and preparedness): 20%

• Lab-Reports: (20%)

• Examination (oral, practical or/and written): (35%)

It is recommended that the number of students per laboratory session to be between 20 and 30.

(31)

Curriculum for BSc Program in Physics Experimental Physics II (Phys 212 )

1.1) David C. Baird, Experimentation: An Introduction to Measurement, Theory and Experimental Design, Benjamin Cummings, 3rd _{ed., 1994.}

2.2) Andrian C. Melisinos and Jim Napolitano, Experiments in Modern Physics Aca-demic Press, 2nd _{ed., 2003.}

(32)

Modern Physics (Phys 242 )

Course Title and Code: Modern Physics (Phys 242 )

Prerequisite(s): Phys 201 Co-requisite(s):

Students’ Faculty: Science/——– Department: Physics

Class Hours:

The rationale of this course is to introduce students to the basic ideas of modern physics with emphasis on the Theory of Special Relativity, identification of the limi-tations of classical mechanics and the development of quantum mechanics, the wave particle duality and the atomic structure.

At the end of this course students will be able to:

• verify the basic principles of the Special Theory of Relativity and its mathematical methods with application relevant to problems in modern physics;

• state basic explanations of modern theories of atomic and nuclear structure; • provide an understanding of how and why Einstein’s theory of Special Relativity

replaces the Newtonian concepts;

• familiarize with the Galilean and Lorenz transformations and their consequences; • develop the knowledge and skills required to perform simple relativistic

calcula-tions and to appreciate their consequences;

• describe wave-particle duality and the uncertainty principle;

• calculate and verify the behavior of matter traveling at speeds approaching the speed of light;

• describe the radiative behavior of black bodies;

• solve problems using both wave and particle mathematical models; • verify, measure, and predict the atomic spectra

Principle of Special Theory of Relativity, Michelson-Morley Experiment, Galilean Trans-formation, Lorentz TransTrans-formation, Length contraction, Time Dilation, Relativistic Momentum and Energy, Black-Body Radiation, Photoelectric Effect, Compton Effect,

(33)

Curriculum for BSc Program in Physics Modern Physics (Phys 242 )

X-Ray Diffraction, Matter Waves, Phase and Group Velocities, Uncertainty Principle, Rutherford Scattering, Bohr Theory of the Hydrogen Atom.

Course Outline

1) Special Theory of Relativity (15 hrs) 1.1) Relativity of Orientation and Origin

1.2) Inertial and Non inertial Reference Frames 1.3) Galilian Transformation

1.4) Michlson Morley Experiment 1.5) Postulates of Special Relativity 1.6) Lorenz Transformation

1.7) Applications of the Lorentz Transformation 1.8) Velocity - Addition Formula

1.9) Doppler Effect 1.10) Time Dilation 1.11) Length Contraction 1.12) Relativity of Mass 1.13) Relativistic Momentum 1.14) Relativistic Mass and Energy

2) Development of Quantum Mechanics ( 3 hrs) 2.1) Limitations of Classical Physics

2.2) Development of Quantum Mechanics

2.3) Uniqueness and role of Quantum Mechanics 3) Particle Properties of Waves ( 9 hrs)

3.1) Wave Particle Dualism 3.2) Photoelectric Effect 3.3) Quantum Theory of Light 3.4) Compton Effect/Scattering 3.5) X-ray diffraction and Bragg’s law 3.6) Black Body Radiation

3.7) Derivation of Plank’s Distribution Law 4) Wave Properties of Particles ( 9 hrs)

4.1) De Broglie waves

4.2) Wave function and its Interpretation 4.3) De Broglie wave velocity

4.4) Phase and Group velocities 4.5) Particle Diffraction

4.6) Uncertainty Principle and its Application 4.7) Gedanken Experiment

5) Atomic Structure ( 9 hrs)

5.1) Atomic Models (Thomson and Rutherford Models) 5.2) Scattering Cross Section

5.3) Alpha Particle Scattering 5.4) Rutherford Scattering Formula 5.5) Electron Orbits

5.6) Atomic Spectra

5.7) Bohr Atom his Explanation of Atomic Spectra 5.8) Quantization of Atomic Energy Levels

5.9) Atomic Excitations

(34)

Curriculum for BSc Program in Physics Modern Physics (Phys 242 )

Assessment

Course Textbook

Arthur Beiser, Concepts of Modern Physics, 6th _{ed., (2002).}

References

1. Raymond A. Serway, Physics: For Scientists & Engineers, 6th _{ed., Thomson}

Bruke, (2004).

2. Hugh D. Young and Roger A. Freedmann, University Physics with Modern Physics 12th ed., (2008).

3. Douglas C. Giancoli, Physics for scientists and engineers, Printice Hall, 4th_,

(2005).

4. Robert Resnick and David Halliday, Fundamentals of Physics Extended, HRW 8th ed., (2008).

5. Hugh Young, University Phyiscs with Modern Physics with Mastering Physics: International edition 12th _{ed., Pearson Education, (2006).}

6. Paul Hewitt, Conceptual Physics: International Edition, Pearson Education, (2005). 7. John Taylor, Modern Physics for Scientists and Engineers, Pearson Education,

(2003).

(35)

Mathematical Methods of Physics I (Phys 301)

Course Title and Code: Mathematical Methods of Physics I (Phys 301)

Prerequisite(s): Math 262 Co-requisite(s):

Class Hours:

This course aims to introduce students to some of the mathematical techniques that are most frequently used in Physics, and to give students experience in their use and application. The course is offered in Semester I of their second year so that Physics students will have an opportunity to develop all the mathematical skills required for core Physics courses. Emphasis is placed on the use of mathematical techniques rather than their rigorous proof.

• make series expansions of simple functions and determine their asymptotic be-haviour;

• perform basic arithmetic and algebra with complex numbers;

• manipulate vectors and matrices and solve systems of simultaneous linear equa-tions;

• calculate partial and total derivatives of functions of more than one variable; • evaluate single, double and triple integrals using commonly occuring coordinate

systems;

• apply differential operators to vector functions; • apply Stokes’s and Gauss’s theorems;

• solve simple first-order differential equations and second-order differential equa-tions with constant coefficients;

• recognize the Dirac delta function and be aware of its properties; • make a Fourier-series expansion of a simple periodic function; • obtain the Fourier transform of a simple function;

• tackle, with facility, mathematically formed problems and their solution;

(36)

Curriculum for BSc Program in Physics Mathematical Methods of Physics I (Phys 301)

Distribution Functions, Graphs, and Approximations Averages and Distribution

Functions, Graphs and Least square fit, Power Series and Applications, Complex numbers and the Euler Identity, Errors and numverical Methods

First-Order Differential Equations: separable, exact, linear , numerical integration; Second-Order Differential Equations: homogenous, inhomogeneous, series

solu-tions of ODEs, numerical solution of DEs, the Laplace Transform Method;

Vectors and Matrices: algebra of vectors, basis vectors and components, vector

spaces, matrix algebra, numerical methods for matrices, coordinate transformations, four-vectors, the eigenvalue problem;

Waves and Fourier Analysis: The Wave equation and principle of superpositions,

Standing waves and harmonics, Fourier Series, Parseval’s theorem and Frequency spectra, Solutions of Inhomgenous DEs, Fourier Transform and the Dirac Delta Func-tion.

Course Outcomes

Upon completion of this course students should be able to: • interpret and use distribution functions;

• analyze sets of data using plots and determine the best “fit”;

• make series expansions of simple functions and determine their asymptotic be-haviour;

• use techniques for represent data sets by analytic functions;

• handle physical problems that involve the rate of change of one quantity with respect to another;

• solve ODEs numerically

• transform a differential equation into an algebraic equation using Laplace trans-form and transtrans-form back the solutions to get the solution of DEs;

• describe waves through the solution of the wave equation; • use Parseval’s theorem to solve problems

• tackle, with facility, mathematically formed problems and their solution;

Course Outline

1) Distribution Functions Graphs, and Approximations(10 hrs) 1.1) Averages and Deviations

1.2) Distribution Functions

1.3) Applications of Distribution Functions 1.4) Linear Graphs

1.5) Least-Square Fit

1.6) Power Series and Applications of Power Series 1.7) Complex Numbers and the Euler Identity 1.8) Errors and Introduction to Numerical Methods 2) First-Order Differential Equations(12 hrs)

2.1) First-order Equations: Separable 2.2) First-order Equations: Exact

(37)

2.3) First-order Equations: Linear 2.4) Numerical integration

3) Second Order Differential Equations(10 hrs) 3.1) Second-order Equations: Homogeneous 3.2) Second-order Equations: Inhomogeneous

3.3) Series Solution of Ordinary Differential Equations 3.4) Numerical solutions of Differential Equations 3.5) Laplace Transform Method

4) Waves and Fourier Analysis(15 hrs) 4.1) Waves

4.2) Partial Differentiation 4.3) Wave Equation

4.4) Principle of Superposition 4.5) Standing Waves and Harmonics 4.6) Fourier Series

4.7) Parseval’s Theorem and Frequency Spectra 4.8) Solution of Inhomogeneous DEs

4.9) Fourier Transforms and the Dirac Delta Function

Presentation of the course is through lecture, Each week there will be two lectures and a problems class in which homework will be reviewed. Students will also attempt simple exercises during the lectures.

Assessment

Course Textbook

Stroud K.A. and Booth D.J., Advanced Engineering Mathematics (4th ed.), Paulgrave, (2003).

References

1. Arfken G.B. and Weber H.J., Mathematical methods for physicists (6th ed.), Aca-demic Press, (2006).

2. Spiegel M.R., Advanced Mathematics for Engineers and Scientists, Schaum Out-line Series, McGraw-Hill, (1971).

(38)

3. Stroud K.A., Engineering Mathematics (5th _{ed.), Paulgrave, (2001).}

4. Donald A. McQuarric, Mathematical Methods for Scientists and Engineers, Uni-versity Science Books, (2003).

5. Lambourne R. and Tinker M. Further Mathematics for the Physical Sciences, Wi-ley, (2000).

6. Mathews J. and Walker R.L., Mathematical Methods of Physics, 2nd ed., (1970).

(39)

Mathematical Methods of Physics II (Phys 302)

Course Title and Code: Mathematical Methods of Physics II (Phys 302)

Prerequisite(s): Phys 301 Co-requisite(s):

Academic Year: 20 / Semester: II

Class Hours:

This course aims to to give learners a deeper understanding of and greater competence in some central mathematical ideas and techniques used in Physics with the emphasis on practical skills rather than formal proof. Students will acquire skills in some key techniques related directly to the advanced courses they will meet in their final year.

• solve partial differential equations by separation of variables;

• calculate eignvalues and eigenvectors and apply the the techniques to physical problems;

• use basis vectors to transform differential operator equations to matrix form and hence apply eigen equation techniques;

• obtain approximate solutions to differential equations through the use of per-turbation theory.

• develop analytical and numerical skills in mathematics; • formulate problems logically;

• present and justify mathematical techniques and methods;

Vectors and Matrices algebra of vectors, basis vectors and components, vector spaces,

matrix algebra, numerical methods for matrices, coordinate transformation, Four-vectors, eigen value problem

Vector Calculus time derivatives of vectors, fluid kinematics, fluid dynamics, fields

and the gradient, fluid flow and the divergence, circulation and the curl, conservative forces and the Laplacian, electric and magnetic fields, vector calculus expressions and identities. Waves and Fourier Analysis: waves, partial differentiation, the wave equation, principle of superposition, standing waves and harmonics fourier series,

(40)

Curriculum for BSc Program in Physics Mathematical Methods of Physics II (Phys 302)

Parseval’s theorem and frequency spectra, solution of inhomogeneous Des, Fourier Transforms and the Dirac Delta Function;

Complex Variables: functions of a complex variable, differentiation and integration,

cauchy integral formula and Laurent Expansion; Singularities, poles and residues, applications

Partial Differential Equations: introduction to PDEs, the wave equation, Laplace’s

equation, Orthogonal functions and the Sturm-Liouville problem; Special Functions: Legendre, Bessel and Hermite Equations

Course Outcomes

• manipulate vectors and matrices and solve systems of simultaneous linear equa-tions;

• perform basic arithmetic and algebra with complex numbers; • use the ideas of singularities and poles to evaluate line integrals. • apply differential operators to vector functions;

• apply Stokes’s and Gauss’s theorems;

• use basis vectors to transform differential operator equations to matrix form and hence apply eigen equation techniques;

• obtain approximate solutions to differential equations through the use of per-turbation theory.

• use the method os separation of variables to solve PDEs; • solve PDEs in various coordinate systems;

• use numerical techniques for solving Laplace’s equation • Analytical and numerical skills in mathematics;

• Logical formulation of problems;

• Presentation and justification of techniques and methods;

• Group work - students are encouraged to work co-operatively together and with the demonstrators to solve guided problems.

Course Outline

1) Vectors and Matrices(10 hrs) 1.1) Algebra of Vectors

1.2) Basis Vectors and Components 1.3) Vector Spaces

1.4) Matrix Algebra

1.5) Numerical Methods for Matrices 1.6) Coordinate Transformations 1.7) Four- Vectors

1.8) The Eigenvalue Problem 2) Vector Calculus(12 hrs)

2.1) Time derivatives of vectors 2.2) Fluid kinematics and dynamics

Physics

H

ARMONIZED

C

URRICULUM

FOR

BS

C

D

EGREE

P

ROGRAM

IN

P

HYSICS

ETHIOPIA

August 2009

Addis Ababa

Ethiopia

Contents

1

Introduction

2

Rationale of the Curriculum

3

Objectives

4

Graduate Profile

5

Grading System

6

Program Requirements

English: Bachelor of Science in Physics

Amharic:

yúYNS ÆClR Ä!G¶ bðz!KS

7

Teaching-Learning Methods

8

Course Selection & Sequencing

9

Course Details

Mechanics (Phys 201 )

Electromagnetism (Phys 202 )

Wave and Optics (Phys 203)

Experimental Physics I (Phys 211 )

Experimental Physics II (Phys 212 )

Modern Physics (Phys 242 )

Mathematical Methods of Physics I (Phys 301)

Mathematical Methods of Physics II (Phys 302)