Engineering Mathematics with Examples and Applications - 1st Edition - ISBN: 9780128097304, 9780128099025

Engineering Mathematics with Examples and Applications

1st Edition

Authors: Xin-She Yang
eBook ISBN: 9780128099025
Paperback ISBN: 9780128097304
Imprint: Academic Press
Published Date: 4th January 2017
Page Count: 400
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Description

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 addition, this practical approach provides over 100 worked examples so that students can see how each step of mathematical problems can be derived without any gap or jump in steps. Thus, readers can build their understanding and mathematical confidence gradually and in a step-by-step manner.

Key Features

  • Covers fundamental engineering topics that are presented at the right level, without worry of rigorous proofs
  • Includes step-by-step worked examples (of which 100+ feature in the work)
  • Provides an emphasis on numerical methods, such as root-finding algorithms, numerical integration, and numerical methods of differential equations
  • Balances theory and practice to aid in practical problem-solving in various contexts and applications

Readership

Undergraduates and graduates in all engineering disciplines (mechanical engineering, electrical engineering, civil engineering, geotechnical, water and transport engineering), but also related applied sciences, computer science and management sciences researchers who require an understanding of key mathematical modeling techniques but are not themselves mathematicians

Table of Contents

  • About the Author
  • Preface
  • Acknowledgment
  • Part I: Fundamentals
    • Chapter 1: Equations and Functions
      • Abstract
      • 1.1. Numbers and Real Numbers
      • 1.2. Equations
      • 1.3. Functions
      • 1.4. Quadratic Equations
      • 1.5. Simultaneous Equations
      • Exercises
    • Chapter 2: Polynomials and Roots
      • 2.1. Index Notation
      • 2.2. Floating Point Numbers
      • 2.3. Polynomials
      • 2.4. Roots
      • Exercises
    • Chapter 3: Binomial Theorem and Expansions
      • Abstract
      • 3.1. Binomial Expansions
      • 3.2. Factorials
      • 3.3. Binomial Theorem and Pascal's Triangle
      • Exercises
    • Chapter 4: Sequences
      • Abstract
      • 4.1. Simple Sequences
      • 4.2. Fibonacci Sequence
      • 4.3. Sum of a Series
      • 4.4. Infinite Series
      • Exercises
    • Chapter 5: Exponentials and Logarithms
      • Abstract
      • 5.1. Exponential Function
      • 5.2. Logarithm
      • 5.3. Change of Base for Logarithm
      • Exercises
    • Chapter 6: Trigonometry
      • Abstract
      • 6.1. Angle
      • 6.2. Trigonometrical Functions
      • 6.3. Sine Rule
      • 6.4. Cosine Rule
      • Exercises
  • Part II: Complex Numbers
    • Chapter 7: Complex Numbers
      • Abstract
      • 7.1. Why Do Need Complex Numbers?
      • 7.2. Complex Numbers
      • 7.3. Complex Algebra
      • 7.4. Euler's Formula
      • 7.5. Hyperbolic Functions
      • Exercises
  • Part III: Vectors and Matrices
    • Chapter 8: Vectors and Vector Algebra
      • Abstract
      • 8.1. Vectors
      • 8.2. Vector Algebra
      • 8.3. Vector Products
      • 8.4. Triple Product of Vectors
      • Exercises
    • Chapter 9: Matrices
      • Abstract
      • 9.1. Matrices
      • 9.2. Matrix Addition and Multiplication
      • 9.3. Transformation and Inverse
      • 9.4. System of Linear Equations
      • 9.5. Eigenvalues and Eigenvectors
      • Exercises
  • Part IV: Calculus
    • Chapter 10: Differentiation
      • 10.1. Gradient and Derivative
      • 10.2. Differentiation Rules
      • 10.3. Series Expansions and Taylor Series
      • Exercises
    • Chapter 11: Integration
      • Abstract
      • 11.1. Integration
      • 11.2. Integration by Parts
      • 11.3. Integration by Substitution
      • Exercises
    • Chapter 12: Ordinary Differential Equations
      • Abstract
      • 12.1. Differential Equations
      • 12.2. First-Order Equations
      • 12.3. Second-Order Equations
      • 12.4. Higher-Order ODEs
      • 12.5. System of Linear ODEs
      • Exercises
    • Chapter 13: Partial Differentiation
      • Abstract
      • 13.1. Partial Differentiation
      • 13.2. Differentiation of Vectors
      • 13.3. Polar Coordinates
      • 13.4. Three Basic Operators
      • Exercises
    • Chapter 14: Multiple Integrals and Special Integrals
      • Abstract
      • 14.1. Line Integral
      • 14.2. Multiple Integrals
      • 14.3. Jacobian
      • 14.4. Special Integrals
      • Exercises
    • Chapter 15: Complex Integrals
      • Abstract
      • 15.1. Analytic Functions
      • 15.2. Complex Integrals
      • Exercises
  • Part V: Fourier and Laplace Transforms
    • Chapter 16: Fourier Series and Transform
      • Abstract
      • 16.1. Fourier Series
      • 16.2. Fourier Transforms
      • 16.3. Solving Differential Equations Using Fourier Transforms
      • 16.4. Discrete and Fast Fourier Transforms
      • Exercises
    • Chapter 17: Laplace Transforms
      • Abstract
      • 17.1. Laplace Transform
      • 17.2. Transfer Function
      • 17.3. Solving ODE via Laplace Transform
      • 17.4. Z-Transform
      • 17.5. Relationships between Fourier, Laplace and Z-transforms
      • Exercises
  • Part VI: Statistics and Curve Fitting
    • Chapter 18: Probability and Statistics
      • Abstract
      • 18.1. Random Variables
      • 18.2. Mean and Variance
      • 18.3. Binomial and Poisson Distributions
      • 18.4. Gaussian Distribution
      • 18.5. Other Distributions
      • 18.6. The Central Limit Theorem
      • 18.7. Weibull Distribution
      • Exercises
    • Chapter 19: Regression and Curve Fitting
      • Abstract
      • 19.1. Sample Mean and Variance
      • 19.2. Method of Least Squares
      • 19.3. Correlation Coefficient
      • 19.4. Linearization
      • 19.5. Generalized Linear Regression
      • 19.6. Hypothesis Testing
      • Exercises
  • Part VII: Numerical Methods
    • Chapter 20: Numerical Methods
      • Abstract
      • 20.1. Finding Roots
      • 20.2. Bisection Method
      • 20.3. Newton-Raphson Method
      • 20.4. Numerical Integration
      • 20.5. Numerical Solutions of ODEs
      • Exercises
    • Chapter 21: Computational Linear Algebra
      • Abstract
      • 21.1. System of Linear Equations
      • 21.2. Gauss Elimination
      • 21.3. LU Factorization
      • 21.4. Iteration Methods
      • 21.5. Newton-Raphson Method
      • 21.6. Conjugate Gradient Method
      • Exercises
  • Part VIII: Optimization
    • Chapter 22: Linear Programming
      • Abstract
      • 22.1. Linear Programming
      • 22.2. Simplex Method
      • 22.3. A Worked Example
      • Exercises
    • Chapter 23: Optimization
      • Abstract
      • 23.1. Optimization
      • 23.2. Optimality Criteria
      • 23.3. Unconstrained Optimization
      • 23.4. Gradient-Based Methods
      • 23.5. Nonlinear Optimization
      • 23.6. Karush-Kuhn-Tucker Conditions
      • 23.7. Sequential Quadratic Programming
      • Exercises
  • Part IX: Advanced Topics
    • Chapter 24: Partial Differential Equations
      • Abstract
      • 24.1. Introduction
      • 24.2. First-Order PDEs
      • 24.3. Classification of Second-Order PDEs
      • 24.4. Classic Mathematical Models: Some Examples
      • 24.5. Solution Techniques
      • Exercises
    • Chapter 25: Tensors
      • Abstract
      • 25.1. Summation Notations
      • 25.2. Tensors
      • 25.3. Hooke's Law and Elasticity
      • Exercises
    • Chapter 26: Calculus of Variations
      • Abstract
      • 26.1. Euler-Lagrange Equation
      • 26.2. Variations with Constraints
      • 26.3. Variations for Multiple Variables
      • Exercises
    • Chapter 27: Integral Equations
      • Abstract
      • 27.1. Integral Equations
      • 27.2. Solution of Integral Equations
      • Exercises
    • Chapter 28: Mathematical Modeling
      • Abstract
      • 28.1. Mathematical Modeling
      • 28.2. Model Formulation
      • 28.3. Different Levels of Approximations
      • 28.4. Parameter Estimation
      • 28.5. Types of Mathematical Models
      • 28.6. Brownian Motion and Diffusion: A Worked Example
      • Exercises
  • Appendix A: Mathematical Formulas
    • A.1. Differentiation and Integration
    • A.2. Complex Numbers
    • A.3. Vectors and Matrices
    • A.4. Fourier Series and Transform
    • A.5. Asymptotics
    • A.6. Special Integrals
  • Appendix B: Mathematical Software Packages
    • B.1. Matlab
    • B.2. Software Packages Similar to Matlab
    • B.3. Symbolic Computation Packages
    • B.4. R and Python
  • Appendix C: Answers to Exercises
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 8
    • Chapter 9
    • Chapter 10
    • Chapter 11
    • Chapter 12
    • Chapter 13
    • Chapter 14
    • Chapter 15
    • Chapter 16
    • Chapter 17
    • Chapter 18
    • Chapter 19
    • Chapter 20
    • Chapter 21
    • Chapter 22
    • Chapter 23
    • Chapter 24
    • Chapter 25
    • Chapter 26
    • Chapter 27
    • Chapter 28
  • Bibliography
  • Index

Details

No. of pages:
400
Language:
English
Copyright:
© Academic Press 2017
Published:
Imprint:
Academic Press
eBook ISBN:
9780128099025
Paperback ISBN:
9780128097304

About the Author

Xin-She  Yang

Xin-She Yang

Xin-She Yang obtained his DPhil in Applied Mathematics from the University of Oxford. He then worked at Cambridge University and National Physical Laboratory (UK) as a Senior Research Scientist. He is currently a Reader at Middlesex University London, Adjunct Professor at Reykjavik University (Iceland) and Guest Professor at Xi’an Polytechnic University (China). He is an elected Bye-Fellow at Downing College, Cambridge University. He is also the IEEE CIS Chair for the Task Force on Business Intelligence and Knowledge Management, and the Editor-in-Chief of International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO).

Affiliations and Expertise

School of Science and Technology, Middlesex University, UK