Matrix Methods and Differential Equations A Practical Introduction
Publisher: Bookboon.com
Published: 2013
ISBN-13: 9788740302516
Table of contents: title: Content; title: 1. Introduction Mathematical Modelling; title: 2. What is a mathematical model?; title: 2.1. Using mathematical models; title: 2.2. Types of models; title: 2.3. How is this book useful for modelling?; title: 3. Simultaneous Linear Equations; title: 3.1. Introduction; title: 3.2. Matrices; title: 3.3. Applying matrices to simultaneous equations; title: 3.4. Determinants; title: 3.5. Inverting a Matrix by Elementary Row Operations; title: 3.6. Solving Equations by Elementary Row Operations; title: 3.7. Homogeneous and Non-homogeneous equations; title: 4. Matrices in Geometry; title: 4.1. Reflection; title: 4.2. Shear; title: 4.3. Plane Rotation; title: 4.4. Orthogonal and orthonormal vectors; title: 4.5. Geometric addition of vectors; title: 4.6. Matrices and vectors as objects; title: 5. Eigenvalues and Diagonalization; title: 5.1. Linear superpositions of vectors; title: 5.2. Calculating Eigenvalues and Eigenvectors; title: 5.3. Similar matrices and diagonalisation; title: 5.4. How eigenvalues relate to determinants; title: 5.5. Using diagonalisation to decouple linear equations; title: 5.6. Orthonormal eigenvectors; title: 5.7. Summary: eigenvalues, eigenvectors and diagonalisation.; title: 6. Revision: Calculus Results; title: 6.1. Differentiation formulas; title: 6.2. Rules of Differentiation; title: 6.3. Integration Formulas; title: 6.4. Integration Methods; title: 7. First Order Differential Equations; title: 7.1. Introduction; title: 7.2. Initial value problems; title: 7.3. Classifying First Order Differential Equations; title: 7.4. Separation of variables; title: 7.5. General Method for solving LFODE’s.; title: 7.6. Applications to modelling real world problems; title: 7.7. Characterising Solutions Using a Phase Line; title: 7.8. Variation of Parameters method; title: 7.9. The Main Points Again – A stepwise strategy for solving FODE’s.; title: 8. General Properties of Solutions to Differential Equations; title: 8.1. Introduction; title: 8.2. Homogenous Linear Equations; title: 9. Systems of Linear Differential Equations; title: 9.1. Introduction; title: 9.2. Homogenous Systems; title: 9.3. The Fundamental Matrix; title: 9.4. Repeated Eigenvalues; title: 9.5. Non-homogenous systems; title: 10. Appendix: Complex Numbers; title: 10.1. Representing complex numbers; title: 10.2. Algebraic operations; title: 10.3. Euler’s formula; title: 10.4. Log, Exponential and Hyperbolic functions; title: 10.5. Differentiation Formulae