Differential Equations with Maple: An Interactive Approach - Rilegato

Davis, Jon

Rilegato

ISBN 10: 0817641815 ISBN 13: 9780817641818

Casa editrice: Birkhauser Boston Inc, 2000

Riassunto

An introduction to differential equations using an interactive approach. It integrates the basics of ODEs and the symbolic computation package MAPLE. This book offers: coverage of topics essential to differential equations; rigorous mathematics with examples from many different fields of application; a discussion of standard solution methods; an introduction to MAPLE fundamentals; and problems to solve.

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Recensione

"A very novel approach to the teaching/learning of all basic aspects of differential equations. ... The book, therefore, provides an introduction to MAPLE as well as standard material on differential equations written in a friendly style." ―Aslib Book Guide

"The course in differential equations starts with fairly well-explained examples from different fields of application. The theory is presented in a student-friendly, understandable form.... The problems presented at the end of each chapter contain material for using the theory or the tools presented in the frame of MAPLE. ... The textbook is recommended for those who start solving differential equation problems by MAPLE and also for those who need an introduction in (mainly ordinary) differential equations." ―Applications of Mathematics

 

Contenuti

I Maple Use and Programming.- 1 Introduction to Maple.- 1.1 Calculator or What?.- 1.1.1 First Contact.- 1.2 Programming in Maple.- 1.3 Maple Variables.- 1.3.1 Variable Types.- 1.3.2 Maple Expressions.- 1.3.3 Aggregate Types.- 1.3.4 Maple Tables.- 1.4 Maple Syntax.- 1.4.1 Function Declarations.- 1.4.2 Assignments.- 1.4.3 Conditionals.- 1.4.4 Loops.- 1.4.5 Maple Evaluation.- 1.4.6 Details about Maple Procedures.- 1.4.7 Procedure Arguments.- 1.4.8 Programming Gotchas.- 1.4.9 Maple Program Development.- II Differential Equations.- 2 Introduction to Differential Equations.- 2.1 Example Problems.- 2.1.1 Simple Rate Equations.- 2.1.2 Mechanical Problems.- 2.1.3 Electrical Models.- 2.1.4 Kinetics.- 2.1.5 Beam Models.- 2.2 Order, Dimension and Type.- 2.2.1 First and Higher Order.- 2.2.2 Partial Derivative Problems.- 2.3 Problems.- 3 First Order Equations.- 3.1 Separable Problems.- 3.1.1 Separable Examples.- 3.2 Level Sets and Exact Equations.- 3.2.1 Solving Exact Problems.- 3.2.2 Exact Equation Examples.- 3.3 Linear Equations.- 3.3.1 Linear Examples.- 3.4 Tricky Substitutions.- 3.4.1 Lagrange.- 3.4.2 Riccati.- 3.4.3 Mechanics.- 3.5 Do Solutions Exist?.- 3.5.1 The Issue.- 3.5.2 Existence Theorems.- 3.6 Problems.- 4 Introduction to Numerical Methods.- 4.1 The Game and Euler’s Method.- 4.2 Solution Taylor Series.- 4.3 Runge-Kutta Methods.- 4.4 General Runge-Kutta Methods.- 4.5 Maple Numeric Routines.- 4.6 Calling all RK4’s (and relatives).- 4.7 Variable Step Size Methods.- 4.7.1 Running RK4 With RK3.- 4.7.2 Adjusting h.- 4.8 Serious Methods.- 4.9 Problems.- 5 Higher Order Differential Equations.- 5.1 Equations of Order N.- 5.1.1 Vector Equations.- 5.1.2 Equivalent Formulations.- 5.2 Linear Independence and Wronskians.- 5.2.1 Linear Independence.- 5.2.2 Wronskians.- 5.3 Fundamental Solutions.- 5.3.1 Existence of Fundamental Solutions.- 5.3.2 Constructing Fundamental Solutions.- 5.4 General and Particular Solutions.- 5.5 Constant Coefficient Problems.- 5.5.1 Homogeneous Case.- 5.5.2 Undetermined Coefficients.- 5.6 Problems.- 6 Laplace Transform Methods.- 6.1 Basic Definition.- 6.1.1 Examples.- 6.2 New Wine From Old.- 6.2.1 Algebra and Tables.- 6.3 Maple Facilities.- 6.4 Derivatives and Laplace.- 6.5 High Order Problems by Laplace.- 6.5.1 Fundamental Solutions.- 6.5.2 Undetermined Coefficients Redux.- 6.6 Convolutions.- 6.6.1 Inhomogeneous Problems.- 6.7 Problems.- 7 Systems of Equations.- 7.1 Linear Systems.- 7.2 Bases and Eigenvectors.- 7.3 Diagonalization.- 7.3.1 Using Maple.- 7.4 Jordan Forms.- 7.4.1 Using Maple.- 7.5 Matrix Exponentials.- 7.5.1 Laplace Transforms.- 7.5.2 Using Maple.- 7.6 Problems.- 8 Stability.- 8.1 Second Order Problems.- 8.2 Harmonic Oscillator Again.- 8.3 Nodes and Spirals.- 8.4 Higher Order Problems.- 8.4.1 The Easy Cases.- 8.4.2 Jordan Form.- 8.5 Linearization.- 8.6 Introduction to Lyapunov Theory.- 8.6.1 Linear Problems.- 8.6.2 Applications.- 8.7 Problems.- 9 Periodic Problems.- 9.1 Periodic Inputs.- 9.2 Phasors.- 9.3 Fourier Series.- 9.4 Time Domain Methods.- 9.5 Periodic Coefficients.- 9.6 Fundamental Matrices.- 9.7 Stability.- 9.8 Floquet Representation.- 9.9 Problems.- 10 Impedances and Differential Equations.- 10.1 Introduction to Impedances.- 10.2 AC Circuits.- 10.3 Transient Circuits.- 10.4 Circuit Impedance Examples.- 10.5 Loops and Nodes.- 10.6 Problems.- 11 Partial Differential Equations.- 11.1 Basic Problems.- 11.1.1 Heat Equation.- 11.1.2 Wave Equation.- 11.1.3 Laplace’s Equation.- 11.1.4 Beam Vibrations.- 11.2 Boundary Conditions.- 11.2.1 Heat and Diffusion Problems.- 11.2.2 Wave Equations.- 11.2.3 Laplace’s Equation.- 11.3 Separation of Variables.- 11.3.1 Cooling of a Slab.- 11.3.2 Standing Wave Solutions.- 11.3.3 Steady State Heat Conduction.- 11.4 Problems.- III Maple Application Topics.- 12 Introduction to Maple Applications.- 13 Plotting With Maple.- 13.1 Maple Plotting Structures.- 13.2 Remember Tables.- 13.3 Plotting Numerical Results.- 13.4 Plotting Vector Variables.- 13.5 Further Plotting.- 14 Maple and Laplace Transforms.- 14.1 Walking Maple Through Problems.- 14.2 Coding a Beam Problem Solver.- 15 Maple Linear Algebra Applications.- 15.1 Canonical Forms.- 15.1.1 Eigenvalues and Eigenvectors.- 15.1.2 Jordan Form Calculations.- 15.2 Matrix Exponentials.- 15.3 Stability Examples.- 15.4 Periodic Solutions with Maple.- 16 Runge-Kutta Designs.- 16.1 Orientation and Overview.- 16.2 Notational Issues.- 16.3 True Solution Derivatives.- 16.4 Runge-Kutta Derivatives.- 16.5 Traps and Tricky Bits.- 16.6 A Sample Run.- 16.7 Order Condition Code.- 17 Maple Packages.- 17.1 Introduction.- 17.2 Constructing Packages.- 17.3 A Control Design Package.- 17.3.1 Root Locus.- 17.3.2 Nyquist Locus.- 17.3.3 Bode Plots.- 17.3.4 Classical vs. State Space.- 17.3.5 LQR Utility Code.- 17.3.6 Least Squares Optimal Control.- 17.3.7 Control Equation Generation.- 17.3.8 LTI Realization Calculations.- 17.3.9 Initialization.- 17.4 Package Creation and Installation.- 17.5 How About Help?.- 17.5.1 Maple Libraries.- 17.5.2 Creating and Installing Help Files.- 17.6 Control Package Demo.- IV Appendices.- A Review Problems.- B Laplace Transform Table.- References.

Dettagli dell'edizione

• Editore: Birkhauser Boston Inc
• Data di pubblicazione: 2000
• Lingua: Inglese
• ISBN 10: 0817641815
• ISBN 13: 9780817641818
• Rilegatura: Copertina rigida
• Numero di pagine: 428
• Contatto del produttore: non disponibile
• Persona responsabile: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Germania