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By Prof. K C Sarangi, Prof. Amber Srivastava, Monika Malhotra, Prof. Rohit Mukherjee, Dr. Vivek Kr Sharma

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- 978-81-88870-60-8
- English
- 2008, 2009, 2010, 2011, 2012, 2013, 2014
- Paper Back
- 602

**1. Laplace Transform**

Introduction, Laplace Transform, Piecewise Continuous Function, Functions of Exponential Order, Sufficient Conditions for the Existence of Laplace Transform, Laplace Transform of Some Elementary Functions, Properties of Laplace Transform, Linearity Property, First Shifting (or First Translation) Theorem, Second Shifting (or Second Translation) Theorem, Change of Scale Property, Laplace Transform of Derivatives, Laplace Transform of Integrals, Laplace Transform of f(t) Multiplied by Some Positive Integral Power of t, Laplace Transform of f(t)/t, Unit Step Function, Properties of Unit Step Function Related to Laplace Transform, Laplace Transform of Periodic Functions, Laplace Transform of Bessel Function, Illustrative Examples, Exercise 1 (A), Inverse Laplace Transform, Table of Inverse Laplace Transform, Properties of Inverse Laplace Transform, Linearity Property, First Shifting (or First Translation) Theorem, Second Shifting (or Second Translation) Theorem, Change of Scale Property, Inverse Laplace Transform of Derivatives, Inverse Laplace Transform of Integrals, Inverse Laplace Transform of F(s) Multiplied by Powers of s, Inverse Laplace Transform of f s s ( ), Convolution Theorem For Laplace Transform, Partial Fraction Method to find Inverse Laplace Transform, Illustrative Examples, Exercise 1 (B), Application of Laplace Transform to Ordinary Differential Equations with Constant Coefficients, Application of Laplace Transform to the System of Simultaneous Differential Equations, Application of Laplace Transform to Electrical Circuits, Illustrative Examples, Exercise 1(C), Application of Laplace Transform to Partial Differential Equations, The Complex Inversion Formula, Illustrative Examples, Exercise 1 (D).**2. Fourier Series**

Introduction, Fourier Series, Dirichlet’s Conditions, Even and Odd Functions, Fourier Series for Even and Odd Functions, Illustrative Examples, Exercise 2(A), Fourier Series in Arbitrary Interval (0, 2?) or (–?, ?), Half-Range Series, Illustrative Examples, Exercise 2 (B), Harmonic Analysis, Illustrative Examples, Exercise 2 (C).**3. Z-Transforms (Not For III Semester Electrical Engineering)**

Introduction, Definition, Properties of Z-Transforms, Linearity, Change of Scale or Damping Rule, Shifting Property, Multiplication by n, Division by n, Initial Value Theorem, Final Value Theorem, Illustrative Examples, Exercise 3 (A), Region of Convergence (R.O.C.), Inverse Z-Transform, Partial Fraction Method, Convolution Property for Z-Transform, Convolution Theorem for Casual Sequence, Solution of Difference Equations, Illustrative Examples, Exercise 3 (B).**4. Fourier Transform**

Introduction, Fourier Integral, Fourier Integral Theorem, Equivalent Complex form or Exponential Form of Fourier Integral Theorem, Particular Cases of Fourier Integral Theorem, Fourier Transform Pairs, Fourier Transform or Complex Fourier Transform, Fourier Cosine Transform (FCT), Fourier Sine Transform (FST), Relationship Between Fourier and Laplace Transforms, Illustrative Examples, Exercise 4 (A), Properties of Fourier Transform, Convolution, Convolution Theorem for Fourier Transforms, Parseval’s Identity for Fourier Transforms, Applications of Fourier Transforms to Boundary Value Problems, Illustrative Examples, Exercise 4 (B), Finite Fourier Sine and Cosine Transforms, Finite Fourier Sine Transform, Finite Fourier Cosine Transform, Applications of Finite Fourier Sine and Cosine Transforms in Boundary Value Problems, Illustrative Examples, Exercise 4 (C), Discrete Fourier Transform (DFT), Discrete Inverse Fourier Transform, Properties of Discrete Fourier Transform, Fast Fourier Transform Method, Fast Fourier Transform Algorithm, Fast Fourier Algorithm for n when n is Product of Three Integers, Discrete Fourier Cosine Transform, Exercise 4 (D).**5. Complex Variables: Differentiation & Integration**

Introduction, Analytic Function, Necessary and Sufficient Conditions for Analyticity, Cauchy-Riemann Equations, Theorem 1, Milne Thomson’s Method, Orthogonality of u and v, Illustrative Examples, Exercise 5 (A), Mappings or Transformations, Conformal Transformation, Necessary and Sufficient Condition for w = f(z) to Represent a Conformal Mapping, Some Standard Transformations, Bilinear Transformation, Some Special Transformations, Illustrative Examples, Exercise 5 (B), Complex Integration, Cauchy’s Integral Theorem, Some Basic Definitions, Extension of Cauchy Integral Theorem, Cauchy’s Integral Formula, Illustrative Examples, Exercises 5 (C).**6. Complex Variables: Power Series and Contour Integration**

Introduction, Absolute Convergence, Taylor’s Series, Laurent’s Series, Illustrative Examples, Exercise 6 (A), Zero of an Analytic Function, Singularity of a Function, Residue of a Complex Function, Residue Theorem, Illustrative Examples, Exercise 6 (B), Evaluation of Real Definite Integrals, Illustrative Examples, Exercise 6 (C).**7. Calculus of Variations (Only For III Semester Electrical Engineering)**

Introduction, Definitions, Euler’s Equation, Isoperimetric Problems, Illustrative Examples, Exercise 7 (A).**A. Appendix**(List of Important Formulae)**P. Papers**