Advanced Engineering Mathematics 1st Edition by Alan Jeffrey ISBN 012382592X 9780123825926

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ISBN 10: 012382592X 
ISBN 13: 9780123825926
Author: Alan Jeffrey

Advanced Engineering Mathematics provides comprehensive and contemporary coverage of key mathematical ideas, techniques, and their widespread applications, for students majoring in engineering, computer science, mathematics and physics. Using a wide range of examples throughout the book, Jeffrey illustrates how to construct simple mathematical models, how to apply mathematical reasoning to select a particular solution from a range of possible alternatives, and how to determine which solution has physical significance. Jeffrey includes material that is not found in works of a similar nature, such as the use of the matrix exponential when solving systems of ordinary differential equations. The text provides many detailed, worked examples following the introduction of each new idea, and large problem sets provide both routine practice, and, in many cases, greater challenge and insight for students. Most chapters end with a set of computer projects that require the use of any CAS (such as Maple or Mathematica) that reinforce ideas and provide insight into more advanced problems. A Student Solutions Manual is also available.

* Comprehensive coverage of frequently used integrals, functions and fundamental mathematical results
* Contents selected and organized to suit the needs of students, scientists, and engineers
* Contains tables of Laplace and Fourier transform pairs
* New section on numerical approximation
* New section on the z-transform
* Easy reference system

 Advanced Engineering Mathematics 1st Table of contents:

• Chapter 1: Review of Basic Mathematics

  • Algebra and Trigonometry Refresher
  • Functions and Graphs
  • Complex Numbers and Polar Coordinates
  • Logarithms and Exponents
  • Elementary Differentiation and Integration

• Chapter 2: Ordinary Differential Equations (ODEs)

  • Introduction to Ordinary Differential Equations
  • First-Order Differential Equations: Linear, Separable, and Exact
  • Second-Order Linear Differential Equations
  • Higher-Order Linear Differential Equations
  • Solutions to Linear Differential Equations: Homogeneous and Non-Homogeneous
  • Laplace Transforms and Their Applications to ODEs
  • Systems of Ordinary Differential Equations

• Chapter 3: Partial Differential Equations (PDEs)

  • Introduction to Partial Differential Equations
  • First-Order Linear PDEs
  • Second-Order Linear PDEs
  • Separation of Variables Method
  • The Heat Equation, Wave Equation, and Laplace’s Equation
  • Boundary and Initial Conditions
  • Fourier Series Solutions to PDEs

• Chapter 4: Linear Algebra

  • Matrices and Matrix Operations
  • Determinants and Inverse Matrices
  • Systems of Linear Equations: Gaussian Elimination and Matrix Inversion
  • Eigenvalues and Eigenvectors
  • Diagonalization of Matrices
  • Inner Product Spaces and Orthogonality
  • Applications of Linear Algebra in Engineering

• Chapter 5: Vector Calculus

  • Scalar and Vector Fields
  • Gradient, Divergence, and Curl
  • Line, Surface, and Volume Integrals
  • The Fundamental Theorems of Vector Calculus: Green’s, Gauss’s, and Stokes’ Theorems
  • Applications in Fluid Mechanics and Electromagnetism

• Chapter 6: Complex Analysis

  • Complex Numbers and Functions
  • Analytic Functions and Cauchy-Riemann Equations
  • Contour Integration and Cauchy’s Integral Theorem
  • Residue Theorem and Applications
  • Laurent Series and Singularities
  • Mapping and Conformal Transformation

• Chapter 7: Fourier Series and Fourier Transforms

  • Introduction to Fourier Series
  • Convergence of Fourier Series
  • Applications of Fourier Series in Engineering
  • Fourier Transforms and Their Properties
  • Applications of Fourier Transforms: Signal Processing and Heat Conduction

• Chapter 8: Laplace Transforms

  • Introduction to Laplace Transforms
  • Properties and Theorems of Laplace Transforms
  • Inverse Laplace Transform
  • Applications of Laplace Transforms to ODEs and PDEs
  • Transfer Functions and System Analysis in Engineering

• Chapter 9: Numerical Methods

  • Introduction to Numerical Methods
  • Numerical Solutions of Algebraic Equations: Bisection, Newton-Raphson, and Secant Methods
  • Numerical Differentiation and Integration
  • Numerical Solutions to Ordinary Differential Equations
  • Finite Difference Methods for Partial Differential Equations
  • Interpolation and Curve Fitting Techniques

• Chapter 10: Probability and Statistics

  • Introduction to Probability Theory
  • Probability Distributions: Binomial, Poisson, Normal Distribution
  • Descriptive Statistics: Mean, Variance, and Standard Deviation
  • Hypothesis Testing and Confidence Intervals
  • Regression and Correlation Analysis
  • Applications in Engineering Data Analysis

• Chapter 11: Transform Methods

  • Fourier Series and Fourier Transforms Revisited
  • Laplace Transforms and Their Applications
  • Z-Transforms and Their Applications to Discrete Systems
  • Applications of Transform Methods in Engineering Systems

• Chapter 12: Special Functions and Their Applications

  • Bessel Functions and Legendre Polynomials
  • Hermite and Laguerre Polynomials
  • Gamma and Beta Functions
  • Applications of Special Functions in Engineering Problems

• Chapter 13: Advanced Topics in Engineering Mathematics

  • Nonlinear Differential Equations and Chaos Theory
  • Computational Fluid Dynamics (CFD) and Simulation
  • Advanced Matrix Methods and Optimization Techniques
  • Stability Analysis of Engineering Systems
  • Mathematical Modelling of Complex Systems in Engineering

• Chapter 14: Applications of Engineering Mathematics

  • Mathematical Modelling in Mechanical, Civil, and Electrical Engineering
  • Structural Analysis and Vibration Theory
  • Control Systems and System Dynamics
  • Electromagnetic Wave Propagation
  • Heat Transfer and Fluid Flow in Engineering Systems

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