## Teaching >> SMAT330

**Announcements****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**- Quiz I: Question Paper Marking Scheme
- Mid-term: Question Paper Marking Scheme
- Quiz II: Question Paper Marking Scheme
- End-term: Question Paper Marking Scheme

Date | Announcement |
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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 |