HIGHER ENGINEERING MATHEMATICS By: B.S.GREWAL
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.
- Calculus: Differential calculus, Partial differentiation, Integral calculus, Multiple integrals, Vector calculus.
- Series: Infinite Series and Fourier Series.
- 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
- Linear Programming
Unit VIII: Special Topics
- Calculus of Variations
- Integral Equations
- Discrete Mathematics
- Tensor Analysis
- Useful Information
- Tables
- Answers to Problems
- Index
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