Book description
Mathematics lays the basic foundation for engineering students to pursue their core subjects. Mathematical Methodscovers topics on matrices, linear systems of equations, eigen values, eigenvectors, quadratic forms, Fourier series, partial differential equations, Ztransforms, numerical methods of solutions of equation, differentiation, integration and numerical solutions of ordinary differential equations. The book features numerical solutions of algebraic and transcendental equations by iteration, bisection, Newton  Raphson methods; the numerical methods include cubic spline method, RungeKutta methods and AdamsBashforth  Moulton methods; applications to onedimensional heat equations, wave equations and Laplace equations; clear concepts of classifiable functions—even and odd functions—in Fourier series; exhaustive coverage of LU decomposition—tridiagonal systems in solutions of linear systems of equations; over 900 objectivetype questions that include multiple choice questions fill in the blanks match the following and true or false statements and the atest University model question papers with solutions.
Table of contents
 Cover
 Title page
 Contents
 About the Author
 Dedication
 Preface

Chapter 1. Matrices and Linear Systems of Equations
 1.1 Introduction
 1.2 Algebra of Matrices
 1.3 Matrix Multiplication
 1.4 Determinant of a Square Matrix
 1.5 Related Matrices
 1.6 DeterminantRelated Matrices
 1.7 Special Matrices
 Exercise 1.1
 1.8 Linear Systems of Equations
 1.9 Homogeneous (H) and Nonhomogeneous (NH) Systems of Equations
 1.10 Elementary Row and Column Operations (Transformations) for Matrices
 Exercise 1.2
 1.11 Inversion of a Nonsingular Matrix
 Exercise 1.3
 1.12 Rank of a Matrix
 1.13 Methods for Finding the Rank of a Matrix
 Exercise 1.4
 1.14 Existence and Uniqueness of Solutions of a System of Linear Equations
 1.15 Methods of Solution of NH and H Equations
 1.16 Homogeneous System of Equations (H)
 Exercise 1.5

Chapter 2. Eigenvalues and Eigenvectors
 2.1 Introduction
 2.2 Linear Transformation
 2.3 Characteristic Value Problem
 Exercise 2.1
 2.4 Properties of Eigenvalues and Eigenvectors
 2.5 Cayley–Hamilton Theorem
 Exercise 2.2
 2.6 Reduction of a Square Matrix to Diagonal Form
 2.7 Powers of a Square Matrix A—Finding of Modal Matrix P and Inverse Matrix A−1
 Exercise 2.3
 Chapter 3. Real and Complex Matrices
 Chapter 4. Quadratic Forms
 Chapter 5. Solution of Algebraic and Transcendental Equations

Chapter 6. Interpolation
 6.1 Introduction
 6.2 Interpolation with Equal Intervals
 6.3 Symbolic Relations and Separation of Symbols
 Exercise 6.1
 6.4 Interpolation
 6.5 Interpolation Formulas For Equal Intervals
 Exercise 6.2
 6.6 Interpolation with Unequal Intervals
 6.7 Properties Satisfied by ∆'
 6.8 Divided Difference Interpolation Formula
 6.9 Inverse Interpolation Using Lagrange's Interpolation Formula
 6.10 Central Difference Formulas
 Exercise 6.3
 Chapter 7. Curve Fitting
 Chapter 8. Numerical Differentiation and Integration
 Chapter 9. Numerical Solution of Ordinary Differential Equations

Chapter 10. Fourier Series
 10.1 Introduction
 10.2 Periodic Functions, Properties
 10.3 Classifiable Functions—Even and Odd Functions
 10.4 Fourier Series, Fourier Coefficients and Euler's Formulae in (α, α + 2π)
 10.5 Dirichlet's Conditions for Fourier Series Expansion of a Function
 10.6 Fourier Series Expansions: Even/Odd Functions
 10.7 SimplyDefined and Multiply(Piecewise) Defined Functions
 Exercise 10.1
 10.8 Change of Interval: Fourier Series in Interval (α, α + 2l)
 Exercise 10.2
 10.9 Fourier Series Expansions of Even and Odd Functions in (–l, l)
 Exercise 10.3
 10.10 HalfRange Fourier Sine/Cosine Series: Odd and Even Periodic Continuations
 Exercise 10.4
 10.11 Root Mean Square (RMS) Value of a Function
 Exercise 10.5

Chapter 11. Fourier Integral Transforms
 11.1 Introduction
 11.2 Integral Transforms
 11.3 Fourier Integral Theorem
 11.4 Fourier Integral in Complex Form
 11.5 Fourier Transform of f(x)
 11.6 Finite Fourier Sine Transform and Finite Fourier Cosine Transform (FFCT)
 11.7 Convolution Theorem for Fourier Transforms
 11.8 Properties of Fourier Transform
 Exercise 11.1
 11.9 Parseval's Identity for Fourier Transforms
 11.10 Parseval's Identities for Fourier Sine and Cosine Transforms
 Exercise 11.2

Chapter 12. Partial Differential Equations
 12.1 Introduction
 12.2 Order, Linearity and Homogeneity of a Partial Differential Equation
 12.3 Origin of Partial Differential Equation
 12.4 Formation of Partial Differential Equation by Elimination of Two Arbitrary Constants
 Exercise 12.1
 12.5 Formation of Partial Differential Equations by Elimination of Arbitrary Functions
 Exercise 12.2
 12.6 Classification of FirstOrder Partial Differential Equations
 12.7 Classification of Solutions of FirstOrder Partial Differential Equation
 12.8 Equations Solvable by Direct Integration
 Exercise 12.3
 12.9 QuasiLinear Equations of First Order
 12.10 Solution of Linear, SemiLinear and QuasiLinear Equations
 Exercise 12.4
 12.11 Nonlinear Equations of First Order
 Exercise 12.5
 12.12 Euler's Method of Separation of Variables
 Exercise 12.6
 12.13 Classification of Secondorder Partial Differential Equations
 Exercise 12.7
 Exercise 12.8
 Exercise 12.9

Chapter 13. ZTransforms and Solution of Difference Equations
 13.1 Introduction
 13.2 ZTransform: Definition
 13.3 ZTransforms of Some Standard Functions (Special Sequences)
 13.4 Recurrence Formula for the Sequence of a Power of Natural Numbers
 13.5 Properties of ZTransforms
 Exercise 13.1
 13.6 Inverse ZTransform
 Exercise 13.2
 13.7 Application of ZTransforms: Solution of a Difference Equation; by ZTransform
 13.8 Method for Solving a Linear Difference Equation with Constant Coefficients
 Exercise 13.3
 Question Bank
 Solved Question Papers
 Bibliography
 Notes
 Acknowledgements
 Copyright
Product information
 Title: Mathematical Methods
 Author(s):
 Release date: September 2009
 Publisher(s): Pearson India
 ISBN: 9788131725986
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