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Differential equations with boundary value problems

Author: John C Polking; Albert Boggess; David Arnold
Publisher: Upper Saddle River, N.J. : Pearson Education, ©2002.
Edition/Format:   Print book : EnglishView all editions and formats
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Designed for introductory courses, this text aims to strike a balance between the traditional and the modern. It combines traditional material with a modern systems emphasis, offering flexibility of  Read more...

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Additional Physical Format: Online version:
Polking, John C.
Differential equations with boundary value problems.
Upper Saddle River, N.J. : Pearson Education, ©2002
(OCoLC)682181305
Document Type: Book
All Authors / Contributors: John C Polking; Albert Boggess; David Arnold
ISBN: 0130911062 9780130911063
OCLC Number: 50115723
Notes: Includes index.
Description: xiii, 827 pages : illustrations (some color) ; 25 cm
Contents: 1.1 Differential Equation Models 2 --
1.2 The Derivative 7 --
1.3 Integration 10 --
2 First-Order Equations 18 --
2.1 Differential Equations and Solutions 18 --
2.2 Solutions to Separable Equations 31 --
2.3 Models of Motion 44 --
2.4 Linear Equations 54 --
2.5 Mixing Problems 64 --
2.6 Exact Differential Equations 73 --
2.7 Existence and Uniqueness of Solutions 90 --
2.8 Dependence of Solutions on Initial Conditions 102 --
2.9 Autonomous Equations and Stability 107 --
Project 2.10 The Daredevil Skydiver 120 --
3 Modeling and Applications 123 --
3.1 Modeling Population Growth 124 --
3.2 Models and the Real World 138 --
3.3 Personal Finance 143 --
3.4 Electrical Circuits 152 --
Project 3.5 The Spruce Budworm 158 --
Project 3.6 Social Security, Now or Later 161 --
4 Second-Order Equations 163 --
4.2 Second-Order Equations and Systems 174 --
4.3 Linear, Homogeneous Equations with Constant Coefficients 179 --
4.4 Harmonic Motion 190 --
4.5 Inhomogeneous Equations; the Method of Undetermined Coefficients 199 --
4.6 Variation of Parameters 209 --
4.7 Forced Harmonic Motion 215 --
Project 4.8 Nonlinear Oscillators 228 --
5 The Laplace Transform 231 --
5.1 The Definition of the Laplace Transform 232 --
5.2 Basic Properties of the Laplace Transform 241 --
5.3 The Inverse Laplace Transform 248 --
5.4 Using the Laplace Transform to Solve Differential Equations 256 --
5.5 Discontinuous Forcing Terms 266 --
5.6 The Delta Function 280 --
5.7 Convolutions 287 --
Project 5.9 Forced Harmonic Oscillators 299 --
6 Numerical Methods 301 --
6.1 Euler's Method 302 --
6.2 Runge-Kutta Methods 314 --
6.3 Numerical Error Comparisons 322 --
6.4 Practical Use of Solvers 327 --
6.5 A Cautionary Tale 332 --
Project 6.6 Numerical Error Comparison 334 --
7 Matrix Algebra 335 --
7.1 Vectors and Matrices 335 --
7.2 The Geometry of Systems of Linear Equations 348 --
7.3 Solving Systems of Equations 353 --
7.4 Properties of Solution Sets 362 --
7.5 Subspaces 371 --
7.6 Determinants 384 --
8 An Introduction to Systems 396 --
8.2 Geometric Interpretation of Solutions 405 --
8.3 Qualitative Analysis 417 --
8.4 Linear Systems 425 --
Project 8.5 Long-Term Behavior of Solutions 441 --
9 Linear Systems with Constant Coefficients 444 --
9.1 Overview of the Technique 444 --
9.2 Planar Systems 452 --
9.3 Phase Plane Portraits 466 --
9.4 Higher Dimensional Systems 484 --
9.5 The Exponential of a Matrix 492 --
9.6 Qualitative Analysis of Linear Systems 510 --
9.7 Higher-Order Linear Equations 515 --
9.8 Inhomogeneous Linear Systems 528 --
Project 9.9 Phase Plane Portraits 538 --
Project 9.10 Oscillations of Linear Molecules 539 --
10 Nonlinear Systems 545 --
10.1 The Linearization of a Nonlinear System 545 --
10.2 Long-Term Behavior of Solutions 559 --
10.3 Invariant Sets and the Use of Nullclines 566 --
10.4 Long-Term Behavior of Solutions to Planar Systems 574 --
10.5 Conserved Quantities 586 --
10.6 Nonlinear Mechanics 592 --
10.7 The Method of Lyapunov 609 --
10.8 Predator-Prey Systems 619 --
Project 10.9 Human Immune Response to Infectious Disease 631 --
Project 10.10 Analysis of Competing Species 634 --
11 Series Solutions to Differential Equations 637 --
11.1 Review of Power Series 638 --
11.2 Series Solutions Near Ordinary Points 650 --
11.3 Legendre's Equation 662 --
11.4 Types of Singular Points --
Euler's Equation 668 --
11.5 Series Solutions Near Regular Singular Points 677 --
11.6 Solutions in the Exceptional Cases 690 --
11.7 Bessel's Equation and Bessel Functions 701 --
12 Fourier Series 712 --
12.1 Computation of Fourier Series 713 --
12.2 Convergence of Fourier Series 724 --
12.3 Fourier Cosine and Sine Series 733 --
12.4 The Complex Form of a Fourier Series 738 --
12.5 The Discrete Fourier Transform and the FFT 741 --
13 Partial Differential Equations 750 --
13.1 Derivation of the Heat Equation 750 --
13.2 Separation of Variables for the Heat Equation 756 --
13.3 The Wave Equation 768 --
13.4 Laplace's Equation 778 --
13.5 Laplace's Equation on a Disk 785 --
13.6 Sturm Liouville Problems 791 --
13.7 Orthogonality and Generalized Fourier Series 801 --
13.8 Temperature in a Ball --
Legendre Polynomials 810 --
13.9 Time Dependent PDEs in Higher Dimension 814 --
13.10 Domains with Circular Symmetry --
Bessel Functions 821.
Responsibility: John Polking, Albert Boggess, David Arnold.

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