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Advanced Mathematics for Engineering and Applied Sciences (Pearson Original), 4th Edition

William W. Guo
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Advanced Mathematics for Engineering and Applied Sciences (Pearson Original), 4th Edition

By William W. Guo, Yucang Wang
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Overview
Author
William W. Guo
...show all
Edition
4th
ISBN
9780655700579
Published Date
02/09/2019
Pages
348
This Pearson Original is published for Central Queensland University.
Table of contents
  • Chapter 1 Ordinary Differential Equations 
  • 1.1 ESSENTIALS OF ORDINARY DIFFERENTIAL EQUATIONS 
  • 1.1.1  Concepts of ordinary differential equations (Odes) 
  • 1.1.2  Classification of Odes 
  • 1.2 DIRECT INTEGRATION & SEPARATION OF VARIABLES 
  • 1.2.1  Direct integration 
  • 1.2.2  Separation of variables 
  • 1.2.3  Solving y´=g(y/x) by substitution
  • 1.3 FIRST-ORDER LINEAR ODES
  • 1.3.1  Solving first-order linear Odes by integrating factors 
  • 1.3.2  The structure of general solutions of linear Odes 
  • 1.3.3  Bernoulli equations
  • 1.4 SECOND-ORDER LINEAR ODES
  • 1.4.1  The structure of general solutions to second-order linear Odes 
  • 1.4.2  Second-order constant-coefficient homogeneous linear Odes 
  • 1.4.3 Second-order constant-coefficient inhomogeneous linear Odes 
  • 1.5 EULER EQUATIONS AND SYSTEMS OF ODES 
  • 1.5.1  Euler equations 
  • 1.5.2  Systems of Odes
  • 1.6 APPLICATIONS OF ODES 
  • 1.6.1 Procedure of modelling and simulation 
  • 1.6.2 Applications of ODEs
  • Chapter 2 Linear Algebra and Applications
  • 2.1 REVIEW OF LINEAR ALGEBRA 
  • 2.1.1 Fundamentals of matrices and vectors 
  • 2.1.2  Basic operations of matrices and vectors 
  • 2.1.3  Determinants and basic operations 
  • 2.1.4  The inverse of a matrix 
  • 2.2 SOLVING LINEAR SYSTEMS OF EQUATIONS 
  • 2.2.1  Linear systems, coefficient matrices, and augmented matrices 
  • 2.2.2  General properties of linear systems of equations 
  • 2.2.3  Solving linear systems by Cramer’s rule 
  • 2.2.4  Solving linear systems by Gauss elimination 
  • 2.2.5 Solving linear systems using the inverse of a matrix 
  • 2.2.6 Solving linear systems by Gauss-Jordan elimination 
  • 2.3 EIGENVALUES AND EIGENVECTORS 
  • 2.3.1 Eigenvalues
  • 2.3.2 Eigenvectors 
  • 2.4 APPLICATIONS OF LINEAR ALGEBRA 
  • 2.4.1  Applications of matrix operations 
  • 2.4.2 Solving ODEs by eigenvalues and eigenvectors 
  • Chapter 3 Laplace Transforms
  • 3.1 FUNDAMENTALS OF LAPLACE TRANSFORMS  
  • 3.1.1 The concept of Laplace transforms 
  • 3.1.2 Laplace transforms of common functions 
  • 3.1.3 Properties of Laplace transforms 
  • 3.2 INVERSE LAPLACE TRANSFORMS 
  • 3.2.1 The concept of inverse Laplace transforms 
  • 3.2.2 Solving inverse Laplace transforms using partial fractions 
  • 3.3 THE CONVOLUTION THEOREM
  • 3.3.1 The concept of convolution 
  • 3.3.2  The convolution theorem 
  • 3.4 APPLICATIONS OF LAPLACE TRANSFORMS 
  • 3.4.1 Solving ODEs by Laplace transforms 
  • 3.4.2 Solving systems of ODEs by Laplace transforms
  • 3.4.3  Transfer functions of linear systems 
  • Chapter 4 Numeric Methods 
  • 4.1 INTRODUCTION TO NUMERIC METHODS 
  • 4.1.1 The general procedure of numeric computation  
  • 4.1.2  Errors in numeric computation 
  • 4.1.3  Concepts of some numeric methods 
  • 4.2 CURVE FITTING BY THE LEAST SQUARES METHOD 
  • 4.2.1  Concepts of curve fitting and the least squares method 
  • 4.2.2  Linear regression 
  • 4.2.3  Quadratic fitting 
  • 4.3 INTERPOLATION 
  • 4.3.1  Lagrange interpolations 
  • 4.3.2  Newton’s divided difference interpolations 
  • 4.3.3  Cubic spline interpolations 
  • 4.4 NUMERIC METHODS FOR SOLVING ODES 
  • 4.4.1  Euler methods 
  • 4.4.2  Runge-Kutta methods 
  • 4.4.3  Numeric methods for systems of ODEs and higher-order ODEs 
  • Chapter 5 Fourier Series 
  • 5.1 THE CONCEPT OF FOURIER SERIES 
  • 5.2 FOURIER SINE AND COSINE SERIES 
  • 5.2.1  Fourier series of even and odd functions 
  • 5.2.2  Half-range expansion 
  • 5.3 FOURIER SERIES OF FUNCTIONS WITH ANY PERIOD 
  • 5.3.1  Fourier series of functions with period p = 2L 
  • 5.3.2  Parseval’s theorem 
  • 5.3.3  Complex notation of Fourier series 
  • 5.4 APPLICATIONS OF FOURIER SERIES 
  • 5.4.1  Component analysis of periodic functions with Parseval’s theorem 
  • 5.4.2  Solving ODEs using Fourier series 
  • 5.4.3 Principles of time-domain signal filtering by Fourier series
  • Chapter 6 Partial Differential Equations 
  • 6.1 ESSENTIALS OF PARTIAL DIFFERENTIAL EQUATIONS 
  • 6.1.1 Basic concepts of partial differential equations (PDEs) 
  • 6.1.2 Solutions of PDEs 
  • 6.2 SOLVING SIMPLE PDES 
  • General References 
  • Appendix A: Common Formulas 
  • Appendix B: Differentiation 
  • Appendix C: Integration 
  • Index