Differential equations with \texttt{MATLAB} (Q2914099)

This textbook gives a basic introduction into ordinary differential equations with a particular focus on the application of the mathematical software system \texttt{MATLAB} to study differential equations using symbolic, numerical, graphical and qualitative methods. The book is suitable for an elementary course for students in mathematics, engineering and physics. It contains, though without proofs, most of fundamental results from the theory of ODEs, in particular, the existence and uniqueness theorem, comparison inequalities following from Gronwall's lemma, the general formula for the solution of a linear system of differential equations, some elements of the Sturm-Liouville theory, the Euler and Runge-Kutta methods, etc. The chapters of the book can be divided into three classes: general discussion of \texttt{MATLAB}, supplementary material on ODEs; and exercises to be solved with \texttt{MATLAB}, called problem sets. Complete solutions to selected exercises are presented at the end of the book. The detailed content is as follows.NEWLINENEWLINEChapter 1: Introduction; Chapters 2,3,4 and 9: Running \texttt{MATLAB} on a computer, basic and advanced \(\mathtt{MATLAB}\) commands; Chapter 5: Finding exact symbolic solutions, existence and uniqueness, stability; Chapter 6: Advanced aspects of the output from \texttt{MATLAB}'s symbolic calculations, software package \texttt{MuPAD}; Chapter 7: Qualitative approach for first-order linear and non-linear equations, based on direction field analysis; Chapter 8: Numerical methods of the \(\mathtt{MATLAB}\) solvers; Chapter 10: Graphical tool for solving initial value problems (the \texttt{MATLAB} companion program Simulink); Chapter 11: Sturm comparison theorem and geometric methods for second order linear equations; Chapter 12: Series solutions of ODEs; Chapter 13: Laplace transforms; Chapter 14: Systems of first order equations, phase portraits; Chapter 15: Qualitative theory for systems of differential equations.NEWLINENEWLINEThe book is equipped with a mathematical glossary containing references to \texttt{MATLAB} commands.