AUMELBAS281

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

...show all # Advanced Mathematics for Engineering and Applied Sciences (Pearson Original), 4th Edition

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Overview
Author
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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