Read more
Informationen zum Autor Brian Hunt and Ronald Lipsman are Professors Emeriti of Mathematics, and Jonathan Rosenberg is Ruth M. Davis Professor of Mathematics, at the University of Maryland. John E. Osborn was Professor Emeritus of Mathematics at the University of Maryland until his death in 2011. Klappentext A supplemental text that can enrich and enhance any first course in ordinary differential equations This supplement helps instructors move towards an earlier use of numerical and geometric methods, place a greater emphasis on systems (including nonlinear ones), and increase discussions of both the benefits and possible pitfalls in numerical solution of ODEs. By providing an introduction to the software that is integrated with the relevant mathematics, Differential Equations with MATLAB can perfectly complement and enhance other texts from Wiley. Since the third edition of Differential Equations with MATLAB first appeared in 2012, there have been many changes and enhancements to MATLAB and Simulink. These include addition of live scripts, new plotting commands, and major changes to the Symbolic Math Toolbox. This revised version brings the text completely up to date with the 2019a release of MATLAB. Inhaltsverzeichnis Preface v 1 Introduction 1 1.1 Guiding Philosophy 1 1.2 Student's Guide 3 1.3 Instructor's Guide 5 1.3.1 MATLAB and Simulink 5 1.3.2 ODE Chapters 5 1.3.3 Computer Problem Sets 6 1.4 A Word about Software Versions 7 2 Getting Started with MATLAB 9 2.1 Platforms and Versions 9 2.2 Installation 10 2.3 Starting MATLAB 10 2.4 Typing in the Command Window 11 2.5 Online Help 11 2.6 MATLAB Windows 13 2.7 Ending a Session 14 3 Doing Mathematics with MATLAB 15 3.1 Arithmetic 15 3.2 Symbolic Computation 16 3.2.1 Substituting in Symbolic Expressions 17 3.2.2 Symbolic Expressions and Variable Precision Arithmetic 17 3.3 Vectors 18 3.3.1 Suppressing Output 19 3.4 Recovering from Problems 19 3.4.1 Errors in Input 20 3.4.2 Aborting Calculations 20 3.5 Functions 20 3.5.1 Built-in Functions 20 3.5.2 User-defined Functions 21 3.6 Managing Variables 21 3.7 Solving Equations 23 3.8 Graphics 25 3.8.1 Graphing with fplot 25 3.8.2 Modifying Graphs 26 3.8.3 Graphing with plot 26 3.8.4 Plotting Multiple Curves 28 3.8.5 Parametric Plots 28 3.8.6 Implicit Plots and Contour Plots 29 3.9 Calculus 31 3.10 Some Tips and Reminders 32 4 Using the Desktop and Scripts 33 4.1 The MATLAB Desktop 33 4.1.1 The Workspace 33 4.1.2 The Current Folder and Search Path 34 4.1.3 The Command History 35 4.2 Scripts and Functions 36 4.2.1 Plain Code Scripts 36 4.2.2 Live Scripts 38 4.2.3 Functions 39 4.3 Loops 40 4.4 Presenting Your Results 41 4.4.1 Presenting Graphics 42 4.4.2 Pretty Printing 44 4.4.3 "Publishing" a script 44 4.4.4 Preparing Homework Solutions 45 4.4.5 Exporting a Live Script 46 4.5 Debugging Your Scripts 48 Problem Set A: Practice with MATLAB 51 5 Solutions of Differential Equations 55 5.1 Finding Symbolic Solutions 55 5.2 Existence and Uniqueness 58 5.3 Stability of Differential Equations 60 5.4 Different Types of Symbolic Solutions 63 6 Finer Points of the Symbolic Math Toolbox 69 7 A Qualitative Approach to Differential Equations 75 7.1 Direction Field for a First Order Linear Equation 75 7.2 Direction Field for a Non-Linear Equation 77 7.3 Autonomous Equations 79 7.3.1 Example...
