Introduction:

Complex Variables and Transform provides sound knowledge of calculus in the complex domain with a detailed discussion oncomplex algebra, complex functions, analyticity and contour integration. It also covers Fourier Series, Fourier Integrals and Fourier Transforms to provide students strong mathematical tools to solve Engineering problems

Course pre-requisites:
As a pre-requisite to this course students are required to have a reasonable mastery of
multivariable calculus and differential equations. This includes being able to
• extensively understand algebraic and transcendental functions;
• describe and parameterize curves and regions in two-dimensional space;
• understand and evaluate partial derivatives and integrals of multivariable functions;
• understand and find Taylor series and determine their intervals of convergence;
• solve boundary value problems.

Course Learning Outcomes

• Demonstrate understanding of the basic concepts underlying complex analyis.

• Demonstrate familiarity with a range of examples of these concepts.

• Prove basic results in complex analysis.

• Apply the methods of complex analysis to evaluate definite integrals and infinite series.

• Demonstrate skills in communicating mathematics orally and in writing.

Course Outline:

Complex numbers and functions, complex integration, Power series, Taylor series, Laurents series , residu integration. Laplace transform, use of  Laplace transform in solving differential dequations. Fourier series, Fourier Transform, Fast Fourier transform , Z- transform.

Text BooK

Recommended  Book:

Erwin Kreyzing , "Advanced Engineering Mathematics", John Wiley. (latest Ed)

PPT/Handouts

https:/www.slideshare.net

ASSEMENT CRITERIA:

Sessional:20 %(Assignments 5% , Quiz 5% ,Class Attendance/Class Participation/Presentation  10%)

Mid Term Paper:30%

Final Term: 50 %

Key Dates and Time of Class Meeting

Thursday   8:00 AM - 9:30AM 

 Friday      10: 00 AM -11:30 AM

Commencement of Classes                                                   January 13, 2020

Mid Term Examination                                                            March 09-13, 2020

Final Term Examination                                                          May 04-08, 2020

Declaration of Result                                                              May 19, 2020