• No results found

5. Course learning outcomes (CLOs) 5.1 By the end of the course the student will be expected to be able to:


Academic year: 2021

Share "5. Course learning outcomes (CLOs) 5.1 By the end of the course the student will be expected to be able to:"

Show more ( Page)

Full text



Items in this section may be reviewed and developed within Schools as part of the Annual Program Monitoring Process and in line with the Guidelines to Modifications to Programs and Courses. 1. General course information

1.1 School: Engineering 1.6 Credits (ECTS):6

1.2 Course Title: Engineering Mathematics II 1.7 Course Code: BENG225 1.3 Pre-requisites: Engineering Mathematics I

1.8 Effective from:2018(year) 1.4 Co-requisites:


Programs: (in which the course is offered)

2. Course description (max.150 words)

This module will deepen and extend the first year engineering mathematics program with a more mature look at the fundamental mathematical techniques and tools that concern multivariate and vector-valued functions, complex functions, multiple integrals, differential equations, Fourier series/trns and Laplace transformations. In particular, many of the most important mathematical methods and techniques that occur frequently in engineering and industrial applications will be developed and explored.

3. Summative assessment methods (tick if applicable):

3.1 Examination X 3.5 Presentation

3.2 Term paper 3.6 Peer-assessment X

3.3 Project 3.7 Essay

3.4 Laboratory Practicum X 3.8 Other (specify) ____________ 4. Course aims

1. Thorough presentation of multivariate calculus 2. Description of Vector fields calculus

3. Analysis of Multiple integrals

4. Introduction to complex numbers and functions 5. Introduction to ordinary differential equations 6. Fourier Series/transformations

7. Laplace Transformations

8. Use of Mathematical software package for relevant to the course problems 5. Course learning outcomes (CLOs)

5.1 By the end of the course the student will be expected to be able to:

1. Articulate scientific reasoning utilizing the formalism of differential calculus of several variable functions.

2. Analyze fundamental scientific problems with vector field calculus. 3. Demonstrate advanced skills on multiple integral calculus.

4. Develop analytical skills on problems with complex numbers and functions 5. Exhibit ability to solve fundamental differential equations

6. Assemble mathematical techniques concerning Fourier series transformations and _______________________________________


Laplace transformations

7. Compute analytically all mathematical objects of the content of Eng Maths II with the help of mathematical software.

8. Appraise numerically mathematical tasks regarding the content of Eng Maths II using mathematical software.



ref # Program Learning Outcome(s) towhich CLO is linked Graduate Attribute(s) to whichCLO is linked

1 Common course 1,2,3,6,7 2 Common course 1,2,3,6,7 3 Common course 1,2,3,6,7 4 Common course 1,2,3,6,7 5 Common course 1,2,3,6,7 6 Common course 1,2,3,6,7 7 Common course 1,2,3,6,7 8 Common course 1,2,3,6,7 2



Course Syllabus Template

Details of teaching, learning and assessment

Items in this Section should be considered annually (or each time a course is delivered) and amended as appropriate, in conjunction with the Annual Program Monitoring Process. The template can be adapted by Schools to meet the necessary accreditation requirements.

6. Detailed course information

6.1 Academic Year: 2017 6.3 Schedule (class days, time): 6.2 Semester:Spring 6.4 Location (building, room): 7. Course leader and teaching staff

Position Name Office


Contact information Office hours/or by appointment


Course Leader Vasileios Zarikas 3e528 vasileios.zarikas

@nu.edu.kz everyday

Course Instructor(s) Vasileios Zarikas 3e528 vasileios.zarikas

@nu.edu.kz everyday

Teaching Assistant(s) Damira Perebayeva Ulanbek Auyeskhan Aslzhan Kunakbayev anytime 8. Course Outline Session Date (tentative)

Topics and Assignments Course Aims

(ref. # only, see item 4)


1 Functions of two, three or more variables..

Planes. Level curves and surfaces. Limits

1 1

2 Partial derivatives. Approximating surfaces

using tangent plane. The differential and its application. Directional derivative. The various chain rules for multivariate functions. Second-order partial derivatives. Taylor series for functions of two or more variables.

1 1

3 Optimization. Local extrema. Critical points and

stationary values. Second-derivative test. Global extrema. Constrained optimisation. Lagrange multipliers. Problems with one and two constraints. Vector-valued functions. Space curves, limits, derivatives, and integrals of vector-valued functions

1 1

4 Scalar and vector fields. Line integrals.

Calculating line integrals using parametrisation. Independence of path, conservative fields, and potential functions. Green’s theorem in the plane. Flux integrals over arbitrary curves in the plane.

2 2

5 The gradient of a scalar field, and the divergence

and curl of a vector field. The Laplacian. Conservative vector fields and scalar potentials, Green’s theorem, surface integrals.

2 2

6 Parametric surfaces. Surface integrals with

parametrised surfaces. Stokes’ theorem, Gauss’ divergence theorem.

2 2

7 Double integration. Rectangular and

non-rectangular regions, limits of integration. Fubini’s theorem and change of variables. Applications to area, centre of mass, and centroid. The use of double integrals to find single variable definite integrals. Triple

3 3


integration. Limits of integration. Cylindrical and spherical coordinates. Change of variable. Applications to volume, centre of mass, and centroid.


8 Complex numbers, Argand diagram,

modulus-argument and polar forms, de Moivre’s theorem, exponential form, nth roots of a complex number and the nth roots of unity. Complex functions and their properties, evaluating the elementary functions given complex arguments,

4 4

9 Intro to differential equations. First Order

differential equations 5 5

10 Intro to differential equations. Second order

differential equations 5 5


march Break Big mid semester assignment

11 Fourier series Functions with period two pi. The

Euler formulae for coefficients. Functions of arbitrary period. Fourier sine and cosine series. Parseval’s theorem.Fourier transforms

6 6

12 Laplace transformation of basic functions 6 7

13 Laplace transformation of rational

functions/applications to differential equations

6 7

14 Revision lecture

9. Learning and Teaching Methods (briefly describe the approaches to teaching and learning to be employed in the course)

1 Lectures 2h/week

2 Tutorials 10h/second week 3 Labs 10h / second week

Coursework: one homework 4

10. Summative Assessments

# Activity Date


Weighting (%) CLOs

Final written exam 50% 1,2,3,4,5,6

Labs 40% 7,8

Course work (1 assignment) 10% 1,2,3,4,5,6

11. Grading

Letter Grade Percent range Grade description (where applicable)

A ≥95% Excellent, exceeds the highest standards in the assignment or course. A- 90.0 – 94.9% Excellent, meets the highest standards for the assignments or course. B+ 85.0 – 89.9% Very good, meets high standards for the assignment or course. B 80.0 – 84.9% Good; meets most of the standards for the assignment or course. B- 75.0 – 79.9% More than adequate; shows some reasonable command of the material. C+ 70.0 – 74.9% Acceptable, meets basic standards for the assignment or course.

C 65.0 – 69.9% Acceptable, meets some of the basic standards for the assignment or course. C- 60.0 – 64.9% Acceptable, while failing short of meeting basic standards in several ways. D+ 55.0 – 59.9% Minimally acceptable, failing sort of the meeting many basic standards.


D 50.0 – 54.9% Minimally acceptable, lowest passing grade. F ≤49.9% Failing, very poor performance.

12. Learning resources (use a full citation and where the texts/materials can be accessed) E-resources, including,

but not limited to: databases, animations, simulations, professional blogs, websites, other e-reference materials (e.g. video, audio, digests)

Lectures notes Lab notes Tutorial notes uploaded in Moodle E-textbooks Laboratory physical resources

Special software programs mathematica Journals (inc. e-journals)

Text books 1. Seán Dineen, Functions of Two Variable, 2nd Edition, (Chapman & Hall/CRC, 2000).

2. Paul C. Matthews, Vector Calculus, (Springer, 2005).

3. Erwin Kreyszig, Advanced Engineering Mathematics, 10th edition (John Wiley & Sons, Inc., 2011).

4. Boris Demidovich (Editor), Problems in Mathematical Analysis (MIR Publishers, 1989).

13. Course expectations

List the expectations of students for the course regarding the course attendance, class participation, group work, late/missed submission of assignments.

1. Minimum 80% attendance in lectures otherwise they will be marked with “fail”

2. Minimum 75% attendance in labs otherwise they will be marked with “fail” (absence in a lab for a non medical reason means zero mark in this particular lab)

3. Individual work for assessments/coursework

4. Discovered plagiarism/cheating results to zero mark for this particular test plus serious penalties.

5. No late submission, penalty will be imposed. 14. Academic Integrity Statement

Any case of cheating, or plagiarism or copying of course work or laboratories tasks, will be associated with serious penalties.

Student Code of Conduct and Disciplinary Procedures (approved by the AC on 05.02.2014), specifically, paragraphs 13-16 (plagiarism and cheating) will be applied .

15. E-Learning

If the content of the course and instruction will be delivered (or partially delivered) via digital and online media, consult with the Head of Instructional Technology to complete this section and/or provide a separate document complementary to this Template.

16. Approval and review

Date of Approval: Minutes #: Committee:



Related documents

b In cell B11, write a formula to find Condobolin’s total rainfall for the week.. Use Fill Right to copy the formula into cells C11

○ If BP elevated, think primary aldosteronism, Cushing’s, renal artery stenosis, ○ If BP normal, think hypomagnesemia, severe hypoK, Bartter’s, NaHCO3,

We use dis-aggregated unemployment rate data corresponding to six demographic groups: White Total, White Males, White Females, Black Total, Black Males, and Black Females.. To

TV industry players are beginning to respond to the challenge of digital competitors with early partnerships and efforts to generate sharper insights that will allow them to

The stew The Irishman one welcome the breast's most anticipated titles comes out on Nov 1 Though that movie character a Netflix project the streaming.. Media Limited or its

With all four financing mechanisms, price control results in a price decrease in both the monopolistic and the competitive region due to the incumbent ’s strong market power.. There

22) K. Zeeberg “Stromal Composition And Hypoxia Modulate Pancreatic Ductal Adenocarcinoma Pdac Cancer Stem Cell Behavior And Plasticity By Controlling The Angiogenic Secretome”. 23)

The 18 interdisciplinary doctoral students interviewed in this study discussed their socialization experiences as occurring across several major themes: (a) their

While not seeking to ignore the scale of the problems in Gaza, we were concerned that immediate exposure to the full scale of the challenges facing the country would prove

Located 5 minutes from I-75 in the City of Alachua, this private Park has easy access to the University of Florida (UF) in Gainesville and the Gainesville Regional Airport.. It

The existing system uses a method called Global Registration to align the different matching images which are retrieved from the image database. This method

CFPP shared ILS will be required to support current and future standards and frameworks for all record and data types including, but not limited to, licensing, electronic

In the future, when we put part X in the machine, sensors in the optics will immediately identify the type of part, material, position and welding points, and the laser will make

In response to the increasing malnutrition levels and decreased purchasing power of the drought affected households, nutrition sensitive activities such as, vegetable and

For the group of firms with expected SEOs, larger firms experienced a significant lower negative abnormal return on both the expectation- and announcement date.. This coincides

The finance department were not involved – S&OP should be about matching the medium term sales and operations plans to the financial numbers in the budget and the business

As was mentioned in Section 1, in the existing multi- camera image fusion techniques, calibration and regis- tration of dierent images, taken from variant view- points of a scene,

For "dot" classification, the same fields are extracted from each packet and used to compute a hash value that points to the bucket used to store the connection state.. In

The broadcast count is defined as the number of transmissions (time-slots) re- quired to make a broadcast in a frame (to reach all the nodes if possible, or at least the maximum

In addition, if I marked "Yes" to any of the above questions, I hereby authorize release of information from my Department of Transportation regulated drug and alcohol

The title document (e.g. a builder's certificate or a bill of sale) together with an acceptance of transfer or acceptance of sale signed by the buyer both need to be translated

An analysis of the economic contribution of the software industry examined the effect of software activity on the Lebanese economy by measuring it in terms of output and value