{"product_id":"differential-equations-with-matlab-isbn-9781118376805","title":"Differential Equations with Matlab","description":"\u003cp\u003e\u003cb\u003eA supplemental text that can enrich and enhance any first course in ordinary differential equations\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThis 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, \u003ci\u003eDifferential Equations with MATLAB\u003c\/i\u003e can perfectly complement and enhance other texts from Wiley.\u003c\/p\u003e \u003cp\u003eSince the third edition of \u003ci\u003eDifferential Equations with MATLAB\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003ePreface v\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Guiding Philosophy 1\u003c\/p\u003e \u003cp\u003e1.2 Student’s Guide 3\u003c\/p\u003e \u003cp\u003e1.3 Instructor’s Guide 5\u003c\/p\u003e \u003cp\u003e1.3.1 MATLAB and Simulink 5\u003c\/p\u003e \u003cp\u003e1.3.2 ODE Chapters 5\u003c\/p\u003e \u003cp\u003e1.3.3 Computer Problem Sets 6\u003c\/p\u003e \u003cp\u003e1.4 A Word about Software Versions 7\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Getting Started with MATLAB 9\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Platforms and Versions 9\u003c\/p\u003e \u003cp\u003e2.2 Installation 10\u003c\/p\u003e \u003cp\u003e2.3 Starting MATLAB 10\u003c\/p\u003e \u003cp\u003e2.4 Typing in the Command Window 11\u003c\/p\u003e \u003cp\u003e2.5 Online Help 11\u003c\/p\u003e \u003cp\u003e2.6 MATLAB Windows 13\u003c\/p\u003e \u003cp\u003e2.7 Ending a Session 14\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Doing Mathematics with MATLAB 15\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Arithmetic 15\u003c\/p\u003e \u003cp\u003e3.2 Symbolic Computation 16\u003c\/p\u003e \u003cp\u003e3.2.1 Substituting in Symbolic Expressions 17\u003c\/p\u003e \u003cp\u003e3.2.2 Symbolic Expressions and Variable Precision Arithmetic 17\u003c\/p\u003e \u003cp\u003e3.3 Vectors 18\u003c\/p\u003e \u003cp\u003e3.3.1 Suppressing Output 19\u003c\/p\u003e \u003cp\u003e3.4 Recovering from Problems 19\u003c\/p\u003e \u003cp\u003e3.4.1 Errors in Input 20\u003c\/p\u003e \u003cp\u003e3.4.2 Aborting Calculations 20\u003c\/p\u003e \u003cp\u003e3.5 Functions 20\u003c\/p\u003e \u003cp\u003e3.5.1 Built-in Functions 20\u003c\/p\u003e \u003cp\u003e3.5.2 User-defined Functions 21\u003c\/p\u003e \u003cp\u003e3.6 Managing Variables 21\u003c\/p\u003e \u003cp\u003e3.7 Solving Equations 23\u003c\/p\u003e \u003cp\u003e3.8 Graphics 25\u003c\/p\u003e \u003cp\u003e3.8.1 Graphing with \u003cb\u003efplot\u003c\/b\u003e 25\u003c\/p\u003e \u003cp\u003e3.8.2 Modifying Graphs 26\u003c\/p\u003e \u003cp\u003e3.8.3 Graphing with \u003cb\u003eplot\u003c\/b\u003e 26\u003c\/p\u003e \u003cp\u003e3.8.4 Plotting Multiple Curves 28\u003c\/p\u003e \u003cp\u003e3.8.5 Parametric Plots 28\u003c\/p\u003e \u003cp\u003e3.8.6 Implicit Plots and Contour Plots 29\u003c\/p\u003e \u003cp\u003e3.9 Calculus 31\u003c\/p\u003e \u003cp\u003e3.10 Some Tips and Reminders 32\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Using the Desktop and Scripts 33\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 The MATLAB Desktop 33\u003c\/p\u003e \u003cp\u003e4.1.1 The Workspace 33\u003c\/p\u003e \u003cp\u003e4.1.2 The Current Folder and Search Path 34\u003c\/p\u003e \u003cp\u003e4.1.3 The Command History 35\u003c\/p\u003e \u003cp\u003e4.2 Scripts and Functions 36\u003c\/p\u003e \u003cp\u003e4.2.1 Plain Code Scripts 36\u003c\/p\u003e \u003cp\u003e4.2.2 Live Scripts 38\u003c\/p\u003e \u003cp\u003e4.2.3 Functions 39\u003c\/p\u003e \u003cp\u003e4.3 Loops 40\u003c\/p\u003e \u003cp\u003e4.4 Presenting Your Results 41\u003c\/p\u003e \u003cp\u003e4.4.1 Presenting Graphics 42\u003c\/p\u003e \u003cp\u003e4.4.2 Pretty Printing 44\u003c\/p\u003e \u003cp\u003e4.4.3 “Publishing” a script 44\u003c\/p\u003e \u003cp\u003e4.4.4 Preparing Homework Solutions 45\u003c\/p\u003e \u003cp\u003e4.4.5 Exporting a Live Script 46\u003c\/p\u003e \u003cp\u003e4.5 Debugging Your Scripts 48\u003c\/p\u003e \u003cp\u003eProblem Set A: Practice with MATLAB 51\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Solutions of Differential Equations 55\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Finding Symbolic Solutions 55\u003c\/p\u003e \u003cp\u003e5.2 Existence and Uniqueness 58\u003c\/p\u003e \u003cp\u003e5.3 Stability of Differential Equations 60\u003c\/p\u003e \u003cp\u003e5.4 Different Types of Symbolic Solutions 63\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Finer Points of the Symbolic Math Toolbox 69\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 A Qualitative Approach to Differential Equations 75\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Direction Field for a First Order Linear Equation 75\u003c\/p\u003e \u003cp\u003e7.2 Direction Field for a Non-Linear Equation 77\u003c\/p\u003e \u003cp\u003e7.3 Autonomous Equations 79\u003c\/p\u003e \u003cp\u003e7.3.1 Examples of Autonomous Equations 81\u003c\/p\u003e \u003cp\u003eProblem Set B: First Order Equations 85\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Numerical Methods 97\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Numerical Solutions Using MATLAB 98\u003c\/p\u003e \u003cp\u003e8.2 Some Numerical Methods 101\u003c\/p\u003e \u003cp\u003e8.2.1 The Euler Method 102\u003c\/p\u003e \u003cp\u003e8.2.2 The Improved Euler Method 105\u003c\/p\u003e \u003cp\u003e8.2.3 The Runge-Kutta Method 106\u003c\/p\u003e \u003cp\u003e8.2.4 Inside \u003cb\u003eode45\u003c\/b\u003e 107\u003c\/p\u003e \u003cp\u003e8.2.5 Round-off Error 108\u003c\/p\u003e \u003cp\u003e8.3 Controlling the Error in \u003cb\u003eode45\u003c\/b\u003e 108\u003c\/p\u003e \u003cp\u003e8.4 Reliability of Numerical Methods 109\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Features of MATLAB 113\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Data Classes 113\u003c\/p\u003e \u003cp\u003e9.1.1 Symbolic and Floating Point Numbers 114\u003c\/p\u003e \u003cp\u003e9.1.2 Structures 115\u003c\/p\u003e \u003cp\u003e9.1.3 String Manipulation 116\u003c\/p\u003e \u003cp\u003e9.2 Functions and Expressions 116\u003c\/p\u003e \u003cp\u003e9.3 More about Scripts and Functions 118\u003c\/p\u003e \u003cp\u003e9.3.1 Variables and Input\/Output in Scripts 118\u003c\/p\u003e \u003cp\u003e9.3.2 Variables in Functions 118\u003c\/p\u003e \u003cp\u003e9.3.3 Structure of Functions 119\u003c\/p\u003e \u003cp\u003e9.4 Matrices 120\u003c\/p\u003e \u003cp\u003e9.4.1 Solving Linear Systems 121\u003c\/p\u003e \u003cp\u003e9.4.2 Calculating Eigenvalues and Eigenvectors 121\u003c\/p\u003e \u003cp\u003e9.5 Graphics 121\u003c\/p\u003e \u003cp\u003e9.5.1 Figure Windows and Live Script Graphics 122\u003c\/p\u003e \u003cp\u003e9.5.2 Editing Figures 123\u003c\/p\u003e \u003cp\u003e9.6 Features of MATLAB’s Numerical ODE Solvers 125\u003c\/p\u003e \u003cp\u003e9.6.1 Evaluation of Numerical Solutions with \u003cb\u003edeval\u003c\/b\u003e 125\u003c\/p\u003e \u003cp\u003e9.6.2 Plotting Families of Numerical Solutions of ODEs 126\u003c\/p\u003e \u003cp\u003e9.6.3 Event Detection 127\u003c\/p\u003e \u003cp\u003e9.7 Troubleshooting 129\u003c\/p\u003e \u003cp\u003e9.7.1 The Most Common Mistakes 129\u003c\/p\u003e \u003cp\u003e9.7.2 Error and Warning Messages 130\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Using Simulink 133\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Constructing and Running a Simulink Model 133\u003c\/p\u003e \u003cp\u003e10.2 Output to the Workspace and How Simulink Works 138\u003c\/p\u003e \u003cp\u003eProblem Set C: Numerical Solutions\u003cb\u003e 143\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Solving and Analyzing Second Order Linear Equations 151\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Second Order Equations with MATLAB 153\u003c\/p\u003e \u003cp\u003e11.2 Second Order Equations with Simulink 157\u003c\/p\u003e \u003cp\u003e11.3 Comparison Methods 159\u003c\/p\u003e \u003cp\u003e11.3.1 The Interlacing of Zeros 160\u003c\/p\u003e \u003cp\u003e11.3.2 Proof of the Sturm Comparison Theorem 161\u003c\/p\u003e \u003cp\u003e11.4 A Geometric Method 162\u003c\/p\u003e \u003cp\u003e11.4.1 The Constant Coefficient Case 163\u003c\/p\u003e \u003cp\u003e11.4.2 The Variable Coefficient Case 164\u003c\/p\u003e \u003cp\u003e11.4.3 Airy’s Equation 165\u003c\/p\u003e \u003cp\u003e11.4.4 Bessel’s Equation 166\u003c\/p\u003e \u003cp\u003e11.4.5 Other Equations 167\u003c\/p\u003e \u003cp\u003eProblem Set D: Second Order Equations 169\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Series Solutions 183\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Series Solutions 184\u003c\/p\u003e \u003cp\u003e12.2 Singular Points 186\u003c\/p\u003e \u003cp\u003e12.3 Other Linear and Nonlinear Equations 187\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Laplace Transforms 189\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Differential Equations and Laplace Transforms 191\u003c\/p\u003e \u003cp\u003e13.2 Discontinuous Functions 194\u003c\/p\u003e \u003cp\u003e13.3 Differential Equations with Discontinuous Forcing 196\u003c\/p\u003e \u003cp\u003eProblem Set E: Series Solutions and Laplace Transforms 199\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Higher Order Equations and Systems of First Order Equations 213\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Higher Order Linear Equations 214\u003c\/p\u003e \u003cp\u003e14.2 Systems of First Order Equations 215\u003c\/p\u003e \u003cp\u003e14.2.1 Linear First Order Systems 215\u003c\/p\u003e \u003cp\u003e14.2.2 Using MATLAB to Find Eigenpairs 218\u003c\/p\u003e \u003cp\u003e14.3 Phase Portraits 222\u003c\/p\u003e \u003cp\u003e14.3.1 Plotting a Single Trajectory 222\u003c\/p\u003e \u003cp\u003e14.3.2 Plotting Several Trajectories 223\u003c\/p\u003e \u003cp\u003e14.3.3 Numerical Solutions of First Order Systems 225\u003c\/p\u003e \u003cp\u003e14.3.4 A Non-Linear System 227\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Qualitative Theory for Systems of Differential Equations 229\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eProblem Set F: Systems of Differential Equations 237\u003c\/p\u003e \u003cp\u003eSample Solutions 255\u003c\/p\u003e \u003cp\u003eIndex 276\u003c\/p\u003e \u003cp\u003e\u003cb\u003eBrian Hunt\u003c\/b\u003e and \u003cb\u003eRonald Lipsman\u003c\/b\u003e are Professors Emeriti of Mathematics, and \u003cb\u003eJonathan Rosenberg\u003c\/b\u003e is Ruth M. Davis Professor of Mathematics, at the University of Maryland.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eJohn E. Osborn\u003c\/b\u003e was Professor Emeritus of Mathematics at the University of Maryland until his death in 2011.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989062598885,"sku":"NP9781118376805","price":111.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118376805.jpg?v=1761782640","url":"https:\/\/k12savings.com\/products\/differential-equations-with-matlab-isbn-9781118376805","provider":"K12savings","version":"1.0","type":"link"}