The book provides a clear exposition of essential tools of applied mathematics from a modern point of view and meets complete requirements of engineering and computer science students. Every effort has been made to keep the presentation at once simple and lucid. It is written with the firm conviction that a good book is one that can be read with minimum guidance from the instructor. To achieve this, more than the usual number of solved examples, followed by properly graded problems have been given. Many of the examples and problems have been selected from recent papers of various university and other engineering examinations. Basic Concepts and Useful Information has been given in an Appendix. However, the subject matter has been set in eight main units:
Algebra & Geometry: Solution of equations, Linear algebra: Determinants, Matrices, Vector algebra and Solid geometry.
Differential Equations: Differential equations of first order and their applications, Linear differential equations and their applications, Differential equations of different types, Series solution of differential equations and special functions, Partial differential equations and their applications.
Complex Analysisc: Complex numbers and functions, Calculus of complex functions.
Transforms: Laplace Transforms, Fourier transforms and Z-transforms.
Numerical Techniques: Empirical Laws and Curve fitting, Statistical methods, Probability and Distributions, Sampling and Inference, Numerical methods, Finite differences and Interpolation, Difference equations, Numerical solution of Ordinary and Partial differential equations, Linear programming.
Special Topics: Calculus of variations, Integral equations, Discrete mathematics, Tensors.
An exhaustive list of 'Objective Type of Questions' has been given at the end of each chapter. Standard Tables, Answers to Problems, and a fairly comprehensive Index is given at the end.
Table of Contents
Unit I: Algebra, Vectors and Geometry
Solution of Equations
Linear Algebra: Determinants, Matrices
Vector Algebra and Solid Geometry
Unit II: Calculus
Differential Calculus & Its Applications
Partial Differentiation & Its Applications
Integral Calculus & Its Applications
Multiple Integrals & Beta, Gamma Functions
Vector Calculus & Its Applications
Univ III: Series
Infinite Series
Fourier Series & Harmonic Anslysis
Unit IV: Differential Equations
Differential Equations of First Order
Applications of Differential Equations of First Order
Linear Differential Equations
Applications of Linear Differential Equations
Differential Equations of Other Types
Series Solution of Differential Equations and Special Functions
Partial Differential Equations
Applications of Partial Differential Equations
Unit V: Complex Analysis
Complex Numbers and Functions
Calculus of Complex Functions
Unit VI: Transforms
Laplace Transforms
Fourier Transforms
Z-Transforms
Unit VII: Numerical Techniques
Empirical Laws and Curve-fitting
Statistical Methods
Probability and Distributions
Sampling and Inference
Numerical Solution of Equations
Finite Differences and Interpolation
Numerical Differentiation and Integration
Difference Equations
Numerical Solution of Ordinary Differential Equations
Numerical Solution of Partial Differential Equations
