## Teaching >> SMAT330

• Announcements
• Date Announcement
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

• 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