**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