Matrix Methods and Differential Equations: A Practical Introduction © 2012 Wynand S Verwoerd & bookboon.com
ISBN 978-87-403-0251-6
Trang 4Contents
Introduction Mathematical Modelling 1.1 What is a mathematical model?
1.2 Using mathematical models 9
1.3 Types of models 11
1.4 How is this book useful for modelling? 12
2 Simultaneous Linear Equations 15
2.1 Introduction 15
2.2 Matrices 18
2.3 Applying matrices to simultaneous equations 23 2.4 Determinants 26
2.5 Inverting a Matrix by Elementary Row Operations 30
2.6 Solving Equations by Elementary Row Operations 52
Zed Homogeneous and Non-homogeneous equations 39
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Trang 5Matrix Methods And Differential Equations 3.1 3.2 3.3 3.4 3.5 3.6 4.1 4.2 4.3 4.4 4.5 4.6 4.7 Matrices in Geometry Reflection Shear Plane Rotation
Orthogonal and orthonormal vectors
Geometric addition of vectors
Matrices and vectors as objects Eigenvalues and Diagonalization
Linear superpositions of vectors
Calculating Eigenvalues and Eigenvectors Similar matrices and diagonalisation How eigenvalues relate to determinants
Using diagonalisation to decouple linear equations Orthonormal eigenvectors Summary: eigenvalues, eigenvectors and diagonalisation Discover the truth at www.deloitte.ca/careers se Download free eBooks at bookboon.com Contents 48 48 49 50 54 56 56 58 58 62 68 71 72 73 80 \\ | | ` e Deloitte
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