Matrix Methods and Differential Equations A Practical Introduction
Publisher: Bookboon
Published: 2013
ISBN-13: 9788740302516
Table of contents: title: Introduction Mathematical Modelling; title: What is a mathematical model?; title: Using mathematical models; title: Types of models; title: How is this book useful for modelling?; title: Simultaneous Linear Equations; title: Introduction; title: Matrices; title: Applying matrices to simultaneous equations; title: Determinants; title: Inverting a Matrix by Elementary Row Operations; title: Solving Equations by Elementary Row Operations; title: Homogeneous and Non-homogeneous equations; title: Matrices in Geometry; title: Reflection; title: Shear; title: Plane Rotation; title: Orthogonal and orthonormal vectors; title: Geometric addition of vectors; title: Matrices and vectors as objects; title: Eigenvalues and Diagonalization; title: Linear superpositions of vectors; title: Calculating Eigenvalues and Eigenvectors; title: Similar matrices and diagonalisation; title: How eigenvalues relate to determinants; title: Using diagonalisation to decouple linear equations; title: Orthonormal eigenvectors; title: Summary: eigenvalues, eigenvectors and diagonalisation.; title: Revision: Calculus Results; title: Differentiation formulas; title: Rules of Differentiation; title: Integration Formulas; title: Integration Methods; title: First Order Differential Equations; title: Introduction; title: Initial value problems; title: Classifying First Order Differential Equations; title: Separation of variables; title: General Method for solving LFODE’s.; title: Applications to modelling real world problems; title: Characterising Solutions Using a Phase Line; title: Variation of Parameters method; title: The Main Points Again – A stepwise strategy for solving FODE’s.; title: General Properties of Solutions to Differential Equations; title: Introduction; title: Homogenous Linear Equations; title: Systems of Linear Differential Equations; title: Introduction; title: Homogenous Systems; title: The Fundamental Matrix; title: Repeated Eigenvalues; title: Non-homogenous systems; title: Appendix: Complex Numbers; title: Representing complex numbers; title: Algebraic operations; title: Euler’s formula; title: Log, Exponential and Hyperbolic functions; title: Differentiation Formulae