**SECTION A: DEFINITIVE**

*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:

1.5

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.

5.2

**CLO**

**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

**SECTION B: NON-DEFINITIVE**

**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)

**CLOs**

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**

**19-23**

**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**

(tentative)

**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:**