Advanced Engineering Mathematics and Analysis

Preface
Acknowledgments
Chapter 1
Linear Algebra and Matrices
	1.1. Introduction
	1.2. Motivation
	1.3. Basics and Definitions of Matrices
	1.4. Computation by Elementary Operations
	1.5. The Solution of Linear Algebraic Systems
	1.6. Basics of Linear Algebra
	1.7. Linear Transformations
	1.8. Eigenvalue and Eigenvector Problems
	1.9. Cayley-Hamilton Theorem and Minimum Polynomial of a Matrix
	1.10. Symmetric and Orthogonal Matrices
	1.11. Singular Values, Singular Vectors, and Norms of Matrices
	1.12. Matrix Factorizations
	Exercises
		Sections 1.1-1.5
		Sections 1.6-1.7
		Sections 1.8-1.9
		Sections 1.10-1.12
Chapter 2
Differential Equations – Part I
	2.1. Introduction
	2.2. Classification of Differential Equations
	2.3. Ordinary Differential Equations in Engineering Problems
	2.4. Solution Concepts
	2.5. First-Order Ordinary Differential Equations
	2.6. Second-Order Ordinary Differential Equations
	2.7. High-Order Ordinary Differential Equations
	2.8. The Solution of a First-Order System of Differential Equations
	Exercises
		Sections 2.1-2.4
		Section 2.5
		Section 2.6
		Sections 2.7-2.8
Chapter 3
Differential Equations – Part II
	3.1. Introduction
	3.2. Second-Order Variable-Coefficients Ordinary Differential Equations
	3.3. Special Second-Order Ordinary Differential Equations
	3.4. Nonlinear Second-Order Differential Equations
	3.5. Method of a Parameter
	3.6. Solution Method Based on Jacobi Elliptic Functions
	Exercises
		Section 3.2
		Section 3.3
		Section 3.4-3.6
Chapter 4
Laplace Transforms
	4.1. Introduction
	4.2. Definitions and Theorems
	4.3. Laplace Inverse
	4.4. The Solution of Differential Equations Using Laplace Transformation
	4.5. Laplace Transform of Especial Functions
	4.6. Convolution Theorem
	4.7. Advanced Applications
	Exercises
		Section 4.2
		Section 4.3-4.4
		Section 4.5
		Section 4.6-4.7
Chapter 5
Numerical Methods
	5.1. Introduction
	5.2. Definitions and Concepts
	5.3. The Solution of Nonlinear Algebraic Equations
		5.3.1. The Solution of Transcendental Equations
		5.3.2. The Solution of Polynomial Equations
		5.3.3. The Solution of Nonlinear Systems
		5.3.4. Solutions by MATLAB
	5.4. Polynomial Approximation and Interpolation
		5.4.1. Approximation Based on Least-Squares Error Method
		5.4.2. Linear and Quadratic Regressions
		5.4.3. Interpolation and Finite Differences
		5.4.4. Lagrange Interpolation Formula
	5.5. Numerical Differentiation
	5.6. Numerical Integration
	5.7. Numerical Methods for Solving Ordinary Differential Equations
		5.7.1. Euler’s Method
		5.7.2. Heun’s Method – Predictor Corrector Approach
		5.7.3. Runge – Kutta Methods
		5.7.4. Numerical Solution of Higher-Order Differential Equations
	5.8. Numerical Solution of Boundary Value Problem
		5.8.1. Shooting Method
		5.8.2. Finite Difference Method
	Exercises
		Section 5.3
		Section 5.4
		Sections 5.5-5.6
		Sections 5.7-5.8
Answers to Selected Exercises
	Sections 1.1–1.5
	Sections 1.6–1.7
	Sections 1.8–1.9
	Section 1.10–1.12
	Section 2.1–2.4
	Section 2.5
	Section 2.6
	Sections 2.7-2.8
	Section 3.2
	Section 3.3
	Section 4.2
	Section 4.3–4.4
	Section 5.3
	Section 5.4
	Section 5.5–5.6
	Section 5.7–5.8
References
About the Author
Index
Blank Page
Blank Page