8/12/2019 CVT syllabus NUST SEECS

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Complex Variables & Transforms Credit Hours: 3+0

Textbook: Advanced Engineering Mathematics 9th editionAuthor: Erwin Kreyszig

Reference book: Advanced Engineering MathematicsAuthor: Alan Jeffrey.Name of Faculty: Sajid Ali

Course Description: The course gives the students a sound knowledge of Fourier Transformsalong with Fourier Integrals, Partial Differential Equations, advancedvector analysis, complex variables and complex integrals.

Equipped with the Knowledge gained in this course, the studentswill be able to apply mathematics as a strong tool to model andsolve the practical problems they come across in engineering andtechnology.

Course Description:

The course comprises three parts. The first part consists of Fourier series, Fourier Transform and Fourier Integrals. Advanced topics onLaplace Transform not covered in the course of Multivariable and Vector Calculus, are covered in this course.

In the second part Partial Differential Equations are covered. This parthelps the students in mathematical modeling of engineering problemsdepending on more than one variable.

The Third part covers complex variable, complex integration, Harmonicfunctions, line integrals, poles residues and singularities.

Course Evaluation: There will be (at least) six quizzes, three assignments, two one hour tests (OHTs)and one end semester examination (ESE). Evaluation will be on the basis of following criteria:

Quizzes 10%Assignments 10%OHTs 30%ESE 50%Total 100

8/12/2019 CVT syllabus NUST SEECS

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Detailed Syllabus forComplex Variable & Transforms

Week Ch. Sect Topics

1NotesKreyszig Sec 11.1,11.2

Periodic function, Trigonometric Fourier Series, Functions of general period p

2

Notes

Kreyszig Sec 11.3

Even and odd functions, Periodic Extensions of functions, Fourier Sine and

Cosine series. Half range expansions

3NotesKreyszig Sec 11.4,11.7

Complex form of Fourier Series, The Fourier Integral representation, Fourier sineand Cosine integrals.

4NotesKreyszig Sec 11.8,11.9

The Fourier Transforms, Properties, Convolution in time and frequency domain,Fourier sine and cosine Transform.

5NotesKreyszig Sec 12.1

Partial differential Equations, Fundamental theorem, Solution of Partialdifferential equations by Operator Method.

6 1 st One Hour Test

7Notes

Kreyszig Sec 12.1

Solution of partial differential equations by the method of separating of

variables, initial & boundary value problems.

8NotesKreyszig Sec 12.5

Derivation of Wave equation and its solution by Fourier Series.

9Notes

Kreyszig Sec 12.2Derivation of heat equation and its solution by Fourier series. More initial andboundary value problems.

10NotesKreyszig Sec 12.4

D ‘Alembert’s solution of wave equation.

11Notes/HandoutsKreyszigSec 13.1, 13.2

Review of Complex algebra, Complex functions, Real and imaginary componentsof a function of a complex variable function, Limit and continuity.

12 2 nd One Hour Test

13Notes/HandoutsKreyszigSec 13.3, 13.4

Derivative, Cauchy Riemann Equations, Properties of uv- function , AnalyticFunctions, Harmonic functions.

14NotesKreyszigSec 14.2, 14.3

Cauchy Integral Theorem and formula, singularities, Poles, Classification of Polesand singularities.

15

NotesKreyszigSec 15.2,16.1, 16.2,

16.3

Power Series, Radius of Convergence, Laurent Series and Evaluation of residuesby Laurent Series, Residues, Residue Theorem.

16NotesKreyszigSec 16.1, 16.2, 16.4

Definite integrals of different forms by using contour integration.

17

NotesKreyszig12.10, 12.11

Laplacian in cylindrical coordinates, Laplacian in spherical coordinates, Solutionof partial differential equations by Laplace transforms.

18 End Semester Exam