- Course Outline
- Laplace Transforms: Definition and properties, Sufficient condition of Existence, Transforms of derivatives and integrals, Derivatives and integrals of transforms, Inverse Laplace Transforms, Exponential shifts, Convolutions, Applications: Differential and Integral Equations.
- Fourier Series: Periodic functions, fundamental period, Trigonometric series, Fourier series, Bessel's inequality, Orthonormal and orthogonal set, Euler formulas, Functions with arbitrary periods, Even and odd functions , Half range expansions, Fourier coefficients without integration, Approximation by trigonometric polynomials, Application to differential equation.
- Fourier Transforms: Fourier integral theorem, Sine and Cosine Integrals, Inverse Transforms, Transforms of Elementary Functions, Properties, Convolution, Parseval’s relation, Transform of Dirac Delta Function, Multiple Fourier transform, Finite Fourier transform.
- Z Transforms: Z-transforms, properties, Inverse Z- transforms, relationship with Fourier transforms.
- Complex Analysis: Complex numbers, Modulus, Argument, Curves and regions in complex plane, Functions, Limits, Derivatives, Analytic functions, Cauchy-Riemann equations, Complex exponential logarithms and trigonometric function, General powers, Line integrals, Cauchy's theorem, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor and Laurent series , Zeros and singularities, Residues, Residues theorem, Evaluation of real improper integrals.
- Text Book
- E. Kreyszig, Advanced Engineering Mathematics, Wiley.
- Reference Books
- M. Braun, Differential Equations and Their Applications, Springer-Verlag, New York.
- W. Trench, Elementary Differential Equations.
- J. Schiff, The Laplace Transform: Theory and Applications, Springer.
- J. Brown and R. Churchill, Complex Variables and Application, McGraw-Hill.
- G. F. Simmons, Differential Equations, Tata Mcgraw Hill.
- R. Jain and S. Iyenger, Advanced Engineering Mathematics, Narosa.
- Lecture Notes on Complex Analysis by Prof. Shunmugaraj
- Problem Set
- Questions and Marking Schemes
|Nov 18, 2015||The problem set 6 has been uploaded. Try to solve the problems.|
|Nov 18, 2015||No more problem will be added to problem set 5.|
|Nov 02, 2015||The second quiz of the course will be held on Thursday, November 05, 2015. Timing: 18:30--19:00 IST. Venue for the RGIT students will be announced by Dr. Sanjai Singh and for IITA students will be announced by Dr. Abdullah. Syllabus: Complex exponential, logarithms, and trigonometric function; Complex integrals; Taylor and Laurent series; Fourier Series.|
|Oct 26, 2015||The problem set 5 has been uploaded. Try to solve the problems. Some new problems may be added to the problem set 5.|
|Oct 08, 2015||The problem set 4 has been uploaded. Try to solve the problems.|
|Sep 05, 2015||The problem set 3 has been uploaded. Try to solve the problems.|
|Sep 03, 2015||The problem set 2 has been uploaded. Try to solve the problems.|
|Aug 19, 2015||The first quiz of the course will be conducted on Monday, August 24, 2015. Timing: 7pm - 8pm. Venue for the RGIT students will be announced by Dr. Sanjai Singh and for IITA students will be announced by Dr. Abdullah.|
|Aug 19, 2015||No more question will be added to problem set 1.|
|Aug 09, 2015||The problem set 1 has been uploaded. Try to solve the problems. I will add some more questions to this problem set.|
|Jul 29, 2015||Grading Policy: Quiz I: 20 points, Mid-sem Exam: 30 points, Quiz II: 20 points, End-sem Exam: 75 points, Internal Assessment: 5 points, Total: 150 points|