Engineering Mathematics III : For GTU

✍ Scribed by Babu Ram

• Publisher: Pearson Education
• Year: 2010
• Tongue: English
• Leaves: 401
• Category: Library

✦ Table of Contents

Cover
Engineering Mathematics-III
Copyright
Contents
Preface
Symbols and Basic Formulae
1 Ordinary Differential Equations
1.1 Definitions and Examples
1.2 Formulation of Differential Equation
1.3 Solution of Differential Equation
1.4 Differential Equations of First order
1.5 Separable Equations
1.6 Homogeneous Equations
1.7 Equations Reducible to Homogeneous Form
1.8 Linear Differential Equations
1.9 Equations Reducible to Linear Differential Equations
1.10 Exact Differential Equation
1.11 The Solution of Exact Differential Equation
1.12 Equations Reducible to Exact Equation
1.13 Applications of First Order and First Degree Equations
1.14 Linear Differential Equations
1.15 Solution of Homogeneous Linear Differential Equation with Constant Coefficients
1.16 Complete Solution of Linear Differential Equation with Constant Coefficients
1.17 Method of Variation of Parameters to Find Particular Integral
1.18 Differential Equations with Variable Coefficients
1.19 Simultaneous Linear Differential Equations with Constant Coefficients
1.20 Applications of Linear Differential Equations
1.21 Mass-Spring System
1.22 Simple Pendulum
1.23 Solution in Series
1.24 Bessel’s Equation and Bessel’s Function
1.25 Fourier–Bessel Expansion of a Continuous Function
1.26 Legendre’s Equation and Legendre’s Polynomial
1.27 Fourier–Legendre Expansion of a Function
1.28 Miscellaneous Examples
Exercises
2 Beta and Gamma Functions
2.1 Beta Function
2.2 Properties of Beta Function
2.3 Gamma Function
2.4 Properties of Gamma Function
2.5 Relation Between Beta and Gamma Functions
2.6 Dirichlet’s and Liouville’s Theorems
2.7 Miscellaneous Examples
Exercises
3 Fourier Series
3.1 Trigonometric Series
3.2 Fourier (or Euler) Formulae
3.3 Periodic Extension of a Function
3.4 Fourier Cosine and Sine Series
3.5 Complex Fourier Series
3.6 Spectrum of Periodic Functions
3.7 Properties of Fourier Coefficients
3.8 Dirichlet’s Kernel
3.9 Integral Expression for Partial Sums of a Fourier Series
3.10 Fundamental Theorem (Convergence Theorem) of Fourier Series
3.11 Applications of Fundamental Theorem of Fourier Series
3.12 Convolution Theorem for Fourier Series
3.13 Integration of Fourier Series
3.14 Diferentiation of Fourier Series
3.15 Examples of Expansions of Functions in Fourier Series
3.16 Method to Find Harmonics of Fourier Series of a Function from Tabular Values
3.17 Signals and Systems
3.18 Classification of Signals
3.19 Classification of Systems
3.20 Response of a Stable Linear Time-Invariant Continuous Time System (LTC System) to a Piecewise Smooth and Periodic Input
3.21 Application to Differential Equations 3.37
3.22 Application to Partial Differential Equations 3.39
3.23 Miscellaneous Examples
Exercises
4 Fourier Transform
4.1 Fourier Integral Theorem
4.2 Fourier Transforms
4.3 Fourier Cosine and Sine Transforms
4.4 Properties of Fourier Transforms
4.5 Solved Examples
4.6 Complex Fourier Transforms
4.7 Convolution Theorem
4.8 Parseval’s Identities
4.9 Fourier Integral Representation of a Function
4.10 Finite Fourier Transforms
4.11 Applications of Fourier Transforms
4.12 Application to Differential Equations
4.13 Application to Partial Differential Equations
Exercises
5 Laplace Transform
5.1 Definition and Examples of Laplace Transform
5.2 Properties of Laplace Transforms
5.3 Limiting Theorems
5.4 Miscellaneous Examples
Exercises
6 Inverse Laplace Transform
6.1 Definition and Examples of Inverse Laplace Transform
6.2 Properties of Inverse Laplace Transform
6.3 Partial Fractions Method to Find Inverse Laplace Transform
6.4 Heaviside’s Expansion Theorem
6.5 Series Method to Determine Inverse Laplace Transform
6.6 Convolution Theorem
6.7 Complex Inversion Formula
6.8 Miscellaneous Examples
Exercises
7 Applications of Laplace Transform
7.1 Ordinary Differential Equations
7.2 Simultaneous Differential Equations
7.3 Difference Equations
7.4 Integral Equations
7.5 Integro-Differntial Equations
7.6 Solution of Partial Differential Equation
7.7 Evaluation of Integrals
7.8 Miscellaneous Examples
Exercises
8 Partial Differential Equations
8.1 Formation of Partial Differential Equation
8.2 Solutions of a Partial Differential Equation
8.3 Classification of Second Order Linear Partial Differential Equations
8.4 The Method of Separation of Variables
8.5 Basic Partial Differential Equations
8.6 Solutions of Laplace Equation
8.7 Miscellaneous Examples
Exercises
Examination Papers with Solutions
Index