Engineering Mathematics with Examples and Applications PDF

Engineering Mathematics with Examples and Applications provides a compact and concise primer in the field, starting with the foundations, and then gradually developing to the advanced level of mathematics that is necessary for all engineering disciplines. Therefore, this book's aim is to help undergraduates rapidly develop the fundamental knowledge of engineering mathematics.

The book can also be used by graduates to review and refresh their mathematical skills. Step-by-step worked examples will help the students gain more insights and build sufficient confidence in engineering mathematics and problem-solving. The main approach and style of this book is informal, theorem-free, and practical. By using an informal and theorem-free approach, all fundamental mathematics topics required for engineering are covered, and readers can gain such basic knowledge of all important topics without worrying about rigorous (often boring) proofs.

Certain rigorous proof and derivatives are presented in an informal way by direct, straightforward mathematical operations and calculations, giving students the same level of fundamental knowledge without any tedious steps. In ad.

Chapter List (261 chapters):

Chapter 1: Cover image
Chapter 2: Title page
Chapter 3: Table of Contents
Chapter 4: Copyright
Chapter 5: About the Author
Chapter 6: Preface
Chapter 7: Acknowledgment
Chapter 8: Part I: Fundamentals
Chapter 9: Chapter 1: Equations and Functions
Chapter 10: Abstract
Chapter 11: 1.1. Numbers and Real Numbers
Chapter 12: 1.2. Equations
Chapter 13: 1.3. Functions
Chapter 14: 1.4. Quadratic Equations
Chapter 15: 1.5. Simultaneous Equations
Chapter 16: Exercises
Chapter 17: Chapter 2: Polynomials and Roots
Chapter 18: 2.1. Index Notation
Chapter 19: 2.2. Floating Point Numbers
Chapter 20: 2.3. Polynomials
Chapter 21: 2.4. Roots
Chapter 22: Exercises
Chapter 23: Chapter 3: Binomial Theorem and Expansions
Chapter 24: Abstract
Chapter 25: 3.1. Binomial Expansions
Chapter 26: 3.2. Factorials
Chapter 27: 3.3. Binomial Theorem and Pascal's Triangle
Chapter 28: Exercises
Chapter 29: Chapter 4: Sequences
Chapter 30: Abstract
Chapter 31: 4.1. Simple Sequences
Chapter 32: 4.2. Fibonacci Sequence
Chapter 33: 4.3. Sum of a Series
Chapter 34: 4.4. Infinite Series
Chapter 35: Exercises
Chapter 36: Chapter 5: Exponentials and Logarithms
Chapter 37: Abstract
Chapter 38: 5.1. Exponential Function
Chapter 39: 5.2. Logarithm
Chapter 40: 5.3. Change of Base for Logarithm
Chapter 41: Exercises
Chapter 42: Chapter 6: Trigonometry
Chapter 43: Abstract
Chapter 44: 6.1. Angle
Chapter 45: 6.2. Trigonometrical Functions
Chapter 46: 6.3. Sine Rule
Chapter 47: 6.4. Cosine Rule
Chapter 48: Exercises
Chapter 49: Part II: Complex Numbers
Chapter 50: Chapter 7: Complex Numbers
Chapter 51: Abstract
Chapter 52: 7.1. Why Do Need Complex Numbers?
Chapter 53: 7.2. Complex Numbers
Chapter 54: 7.3. Complex Algebra
Chapter 55: 7.4. Euler's Formula
Chapter 56: 7.5. Hyperbolic Functions
Chapter 57: Exercises
Chapter 58: Part III: Vectors and Matrices
Chapter 59: Chapter 8: Vectors and Vector Algebra
Chapter 60: Abstract
Chapter 61: 8.1. Vectors
Chapter 62: 8.2. Vector Algebra
Chapter 63: 8.3. Vector Products
Chapter 64: 8.4. Triple Product of Vectors
Chapter 65: Exercises
Chapter 66: Chapter 9: Matrices
Chapter 67: Abstract
Chapter 68: 9.1. Matrices
Chapter 69: 9.2. Matrix Addition and Multiplication
Chapter 70: 9.3. Transformation and Inverse
Chapter 71: 9.4. System of Linear Equations
Chapter 72: 9.5. Eigenvalues and Eigenvectors
Chapter 73: Exercises
Chapter 74: Part IV: Calculus
Chapter 75: Chapter 10: Differentiation
Chapter 76: 10.1. Gradient and Derivative
Chapter 77: 10.2. Differentiation Rules
Chapter 78: 10.3. Series Expansions and Taylor Series
Chapter 79: Exercises
Chapter 80: Chapter 11: Integration
Chapter 81: Abstract
Chapter 82: 11.1. Integration
Chapter 83: 11.2. Integration by Parts
Chapter 84: 11.3. Integration by Substitution
Chapter 85: Exercises
Chapter 86: Chapter 12: Ordinary Differential Equations
Chapter 87: Abstract
Chapter 88: 12.1. Differential Equations
Chapter 89: 12.2. First-Order Equations
Chapter 90: 12.3. Second-Order Equations
Chapter 91: 12.4. Higher-Order ODEs
Chapter 92: 12.5. System of Linear ODEs
Chapter 93: Exercises
Chapter 94: Chapter 13: Partial Differentiation
Chapter 95: Abstract
Chapter 96: 13.1. Partial Differentiation
Chapter 97: 13.2. Differentiation of Vectors
Chapter 98: 13.3. Polar Coordinates
Chapter 99: 13.4. Three Basic Operators
Chapter 100: Exercises
Chapter 101: Chapter 14: Multiple Integrals and Special Integrals
Chapter 102: Abstract
Chapter 103: 14.1. Line Integral
Chapter 104: 14.2. Multiple Integrals
Chapter 105: 14.3. Jacobian
Chapter 106: 14.4. Special Integrals
Chapter 107: Exercises
Chapter 108: Chapter 15: Complex Integrals
Chapter 109: Abstract
Chapter 110: 15.1. Analytic Functions
Chapter 111: 15.2. Complex Integrals
Chapter 112: Exercises
Chapter 113: Part V: Fourier and Laplace Transforms
Chapter 114: Chapter 16: Fourier Series and Transform
Chapter 115: Abstract
Chapter 116: 16.1. Fourier Series
Chapter 117: 16.2. Fourier Transforms
Chapter 118: 16.3. Solving Differential Equations Using Fourier Transforms
Chapter 119: 16.4. Discrete and Fast Fourier Transforms
Chapter 120: Exercises
Chapter 121: Chapter 17: Laplace Transforms
Chapter 122: Abstract
Chapter 123: 17.1. Laplace Transform
Chapter 124: 17.2. Transfer Function
Chapter 125: 17.3. Solving ODE via Laplace Transform
Chapter 126: 17.4. Z-Transform
Chapter 127: 17.5. Relationships between Fourier, Laplace and Z-transforms
Chapter 128: Exercises
Chapter 129: Part VI: Statistics and Curve Fitting
Chapter 130: Chapter 18: Probability and Statistics
Chapter 131: Abstract
Chapter 132: 18.1. Random Variables
Chapter 133: 18.2. Mean and Variance
Chapter 134: 18.3. Binomial and Poisson Distributions
Chapter 135: 18.4. Gaussian Distribution
Chapter 136: 18.5. Other Distributions
Chapter 137: 18.6. The Central Limit Theorem
Chapter 138: 18.7. Weibull Distribution
Chapter 139: Exercises
Chapter 140: Chapter 19: Regression and Curve Fitting
Chapter 141: Abstract
Chapter 142: 19.1. Sample Mean and Variance
Chapter 143: 19.2. Method of Least Squares
Chapter 144: 19.3. Correlation Coefficient
Chapter 145: 19.4. Linearization
Chapter 146: 19.5. Generalized Linear Regression
Chapter 147: 19.6. Hypothesis Testing
Chapter 148: Exercises
Chapter 149: Part VII: Numerical Methods
Chapter 150: Chapter 20: Numerical Methods
Chapter 151: Abstract
Chapter 152: 20.1. Finding Roots
Chapter 153: 20.2. Bisection Method
Chapter 154: 20.3. Newton-Raphson Method
Chapter 155: 20.4. Numerical Integration
Chapter 156: 20.5. Numerical Solutions of ODEs
Chapter 157: Exercises
Chapter 158: Chapter 21: Computational Linear Algebra
Chapter 159: Abstract
Chapter 160: 21.1. System of Linear Equations
Chapter 161: 21.2. Gauss Elimination
Chapter 162: 21.3. LU Factorization
Chapter 163: 21.4. Iteration Methods
Chapter 164: 21.5. Newton-Raphson Method
Chapter 165: 21.6. Conjugate Gradient Method
Chapter 166: Exercises
Chapter 167: Part VIII: Optimization
Chapter 168: Chapter 22: Linear Programming
Chapter 169: Abstract
Chapter 170: 22.1. Linear Programming
Chapter 171: 22.2. Simplex Method
Chapter 172: 22.3. A Worked Example
Chapter 173: Exercises
Chapter 174: Chapter 23: Optimization
Chapter 175: Abstract
Chapter 176: 23.1. Optimization
Chapter 177: 23.2. Optimality Criteria
Chapter 178: 23.3. Unconstrained Optimization
Chapter 179: 23.4. Gradient-Based Methods
Chapter 180: 23.5. Nonlinear Optimization
Chapter 181: 23.6. Karush-Kuhn-Tucker Conditions
Chapter 182: 23.7. Sequential Quadratic Programming
Chapter 183: Exercises
Chapter 184: Part IX: Advanced Topics
Chapter 185: Chapter 24: Partial Differential Equations
Chapter 186: Abstract
Chapter 187: 24.1. Introduction
Chapter 188: 24.2. First-Order PDEs
Chapter 189: 24.3. Classification of Second-Order PDEs
Chapter 190: 24.4. Classic Mathematical Models: Some Examples
Chapter 191: 24.5. Solution Techniques
Chapter 192: Exercises
Chapter 193: Chapter 25: Tensors
Chapter 194: Abstract
Chapter 195: 25.1. Summation Notations
Chapter 196: 25.2. Tensors
Chapter 197: 25.3. Hooke's Law and Elasticity
Chapter 198: Exercises
Chapter 199: Chapter 26: Calculus of Variations
Chapter 200: Abstract
Chapter 201: 26.1. Euler-Lagrange Equation
Chapter 202: 26.2. Variations with Constraints
Chapter 203: 26.3. Variations for Multiple Variables
Chapter 204: Exercises
Chapter 205: Chapter 27: Integral Equations
Chapter 206: Abstract
Chapter 207: 27.1. Integral Equations
Chapter 208: 27.2. Solution of Integral Equations
Chapter 209: Exercises
Chapter 210: Chapter 28: Mathematical Modeling
Chapter 211: Abstract
Chapter 212: 28.1. Mathematical Modeling
Chapter 213: 28.2. Model Formulation
Chapter 214: 28.3. Different Levels of Approximations
Chapter 215: 28.4. Parameter Estimation
Chapter 216: 28.5. Types of Mathematical Models
Chapter 217: 28.6. Brownian Motion and Diffusion: A Worked Example
Chapter 218: Exercises
Chapter 219: Appendix A: Mathematical Formulas
Chapter 220: A.1. Differentiation and Integration
Chapter 221: A.2. Complex Numbers
Chapter 222: A.3. Vectors and Matrices
Chapter 223: A.4. Fourier Series and Transform
Chapter 224: A.5. Asymptotics
Chapter 225: A.6. Special Integrals
Chapter 226: Appendix B: Mathematical Software Packages
Chapter 227: B.1. Matlab
Chapter 228: B.2. Software Packages Similar to Matlab
Chapter 229: B.3. Symbolic Computation Packages
Chapter 230: B.4. R and Python
Chapter 231: Appendix C: Answers to Exercises
Chapter 232: Chapter 1
Chapter 233: Chapter 2
Chapter 234: Chapter 3
Chapter 235: Chapter 4
Chapter 236: Chapter 5
Chapter 237: Chapter 6
Chapter 238: Chapter 7
Chapter 239: Chapter 8
Chapter 240: Chapter 9
Chapter 241: Chapter 10
Chapter 242: Chapter 11
Chapter 243: Chapter 12
Chapter 244: Chapter 13
Chapter 245: Chapter 14
Chapter 246: Chapter 15
Chapter 247: Chapter 16
Chapter 248: Chapter 17
Chapter 249: Chapter 18
Chapter 250: Chapter 19
Chapter 251: Chapter 20
Chapter 252: Chapter 21
Chapter 253: Chapter 22
Chapter 254: Chapter 23
Chapter 255: Chapter 24
Chapter 256: Chapter 25
Chapter 257: Chapter 26
Chapter 258: Chapter 27
Chapter 259: Chapter 28
Chapter 260: Bibliography
Chapter 261: Index