Differential equations with Mathematica:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Amsterdam ; Boston ; Heidelberg ; London ; New York ; Oxford ; Paris ; San Diego ; San Francisco ; Singapore ; Sydney ; Tokyo
Elsevier Academic Press
[2016]
|
| Ausgabe: | Fourth edition |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029713713&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Includes index |
| Umfang: | xiv, 865 Seiten Illustrationen, Diagramme |
| ISBN: | 9780128047767 |
Internformat
MARC
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| 250 | |a Fourth edition | ||
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Datensatz im Suchindex
| _version_ | 1819250291978010624 |
|---|---|
| adam_text | Differential
Equations with
Mathematica
Fourth Edition
Martha L Abell
Georgia Southern University, Statesboro, USA
James P Braselton
Georgia Southern University, Statesboro, USA
ELSEVIER
AMSTERDAM • BOSTON • HEIDELBERG • LONDON
NEW YORK ■ OXFORD • PARIS • SAN DIEGO
SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO
Aud«mk Pirn it u Imprint c( Elievicr
Contents
E”
Preface xiii
1 Introduction to Differential Equations I
1 1 Definitions and Concepts 2
1 2 Solutions of Differential Equations 7
1 3 Initial and Boundary-Value Problems 19
1 4 Direction Fields 28
141 Creating Interactive Applications 41
2 First-Order Ordinary Differential Equations 45
2 1 Theory of First-Order Equations: A Brief Discussion 45
2 2 Separation of Variables 52
Application: Kidney Dialysis 62
2 3 Homogeneous Equations 66
Application: Models of Pursuit 72
2 4 Exact Equations 76
2 5 Linear Equations 82
251 Integrating Factor Approach 83
252 Variation of Parameters and the Method of Undetermined Coefficients 96
Application: Antibiotic Production 100
v
Contents
2 6 Numerical Approximations of Solutions to First-Order Equations 103
262 Built-In Methods 103
Application: Modeling the Spread of a Disease 108
262 Other Numerical Methods 114
Euler s Method 115
Improved Euler s Method 120
The Runge-Kutta Method 124
3 Applications of First-Order Equations 133
3 1 Orthogonal Trajectories 133
Application: Oblique Trajectories 142
3 2 Population Growth and Decay 145
321 The Malthus Model 145
322 The Logistic Equation 152
Application: Harvesting 163
Application: The Logistic Difference Equation 166
3 3 Newton s Law of Cooling 171
3 4 Free-Falling Bodies 177
4 Higher-Order Differential Equations 187
4 1 Preliminary Definitions and Notation 187
422 Introduction 187
422 The nth-Order Ordinary Linear Differential Equation 193
423 Fundamental Set of Solutions 200
424 Existence of a Fundamental Set of Solutions 205
425 Reduction of Order 207
4 2 Solving Homogeneous Equations With Constant Coefficients 210
422 Second-Order Equations 211
422 Higher-Order Equations 215
4 3 Introduction to Solving Nonhomogeneous Equations 223
4 4 Nonhomogeneous Equations With Constant Coefficients:
The Method of Undetermined Coefficients 229
442 Second-Order Equations 231
442 Higher-Order Equations 248
4 5 Nonhomogeneous Equations With Constant Coefficients:
Variation of Parameters 255
452 Second-Order Equations 255
452 Higher-Order Nonhomogeneous Equations 259
Contents
4 6 Cauchy-Euler Equations 262
461 Second-Order Cauchy-Euler Equations 263
462 Higher-Order Cauchy-Euler Equations 267
463 Variation of Parameters 272
4 7 Series Solutions 275
471 Power Series Solutions About Ordinary Points 275
472 Series Solutions About Regular Singular Points 287
473 Method o/Frobenius 289
Application: Zeros of the Bessel Functions of the First Kind 302
Application: The Wave Equation on a Circular Plate 304
4 8 Nonlinear Equations 308
5 Applications of Higher^Order Differential Equations 329
5 1 Harmonic Motion 329
511 Simple Harmonic Motion 329
512 Damped Motion 339
513 Forced Motion 352
514 Soft Springs 369
535 Hard Springs 372
526 Aging Springs 374
Application: Hearing Beats and Resonance 376
5 2 The Pendulum Problem 377
5 3 Other Applications 390
532 L-R-C Circuits 390
532 Deflection of a Beam 394
533 Bode Plots 397
534 The Catenary 402
6 Systems of Ordinary Differential Equations 415
6 1 Review of Matrix Algebra and Calculus 415
612 Defining Nested Lists, Matrices, and Vectors 415
622 Extracting Elements of Matrices 421
623 Basic Compulations With Matrices 423
624 Systems of Linear Equations 426
625 Eigenvalues and Eigenvectors 429
616 Matrix Calculus 434
viii Contents
6 2 Systems of Equations: Preliminary Definitions and Theory 435
621 Preliminary Theory 439
622 Linear Systems 451
6 3 Homogeneous Linear Systems With Constant Coefficients 461
631 Distinct Real Eigenvalues 462
632 Complex Conjugate Eigenvalues 468
633 Alternate Method for Solving Initial-Value Problems 477
634 Repeated Eigenvalues 480
6 4 Nonhomogeneous First-Order Systems: Undetermined
Coefficients, Variation of Parameters, and the Matrix Exponential 488
641 Undetermined Coefficients 489
642 Variation of Parameters 493
643 The Matrix Exponential 499
6 5 Numerical Methods 507
651 Built-In Methods 507
Application: Controlling the Spread of a Disease 514
652 Euler s Method 525
653 Runge-Kutta Method 531
6 6 Nonlinear Systems, Linearization, and Classification
of Equilibrium Points 535
661 Real Distinct Eigenvalues 535
662 Repeated Eigenvalues 542
663 Complex Conjugate Eigenvalues 546
664 Nonlinear Systems 550
Classification of Equilibrium Points 551
7 Applications of Systems of Ordinary Differential Equations 565
7 1 Mechanical and Electrical Problems With First-Order
Linear Systems 565
711 L-R-C Circuits With Loops 565
712 L-R-C Circuit With One Loop 566
713 L-R-C Circuit With Two Loops 569
714 Spring-Mass Systems 572
7 2 Diffusion and Population Problems With First-Order
Linear Systems 574
721 Diffusion Through a Membrane 574
722 Diffusion Through a Double-Walled Membrane 577
723 Population Problems 581
Contents
7 3 Applications That Lead to Nonlinear Systems 585
731 Biological Systems: Predator-Prey Interactions, The Lotka-Volterra
System, and Food Chains in the Chemostat 586
732 Physical Systems: Variable Damping 603
733 Differential Geometry: Curvature 609
8 Laplace Transform Methods 613
8 1 The Laplace Transform 613
811 Definition of the Laplace Transform 613
812 Exponential Order, Jump Discontinuities and
Piecewise-Continuous Functions 617
813 Properties of the Laplace Transform 620
8 2 The Inverse Laplace Transform 626
821 Definition of the Inverse Laplace Transform 626
822 Laplace Transform of an Integral 633
8 3 Solving Initial-Value Problems With the Laplace Transform 635
8 4 Laplace Transforms of Step and Periodic Functions 643
841 Piecewise-Defined Functions: The Unit Step Function 643
842 Solving Initial-Value Problems With Piecewise-Continuous
Forcing Functions 648
843 Periodic Functions 652
844 Impulse Functions: The Delta Function 662
8 5 The Convolution Theorem 668
851 The Convolution Theorem 668
852 Integral and Integrodifferential Equations 670
8 6 Applications of Laplace Transforms, Part I 673
861 Spring-Mass Systems Revisited 673
862 L-R-C Circuits Revisited 678
863 Population Problems Revisited 685
Application: The Tautochrone 686
8 7 Laplace Transform Methods for Systems 690
8 8 Applications of Laplace Transforms, Part II 704
881 Coupled Spring-Mass Systems 704
882 The Double Pendulum 709
Application: Free Vibration of a Three-Story Building 715
x Contents
9 Eigenvalue Problems and Fourier Series 721
9 1 Boundary-Value Problems, Eigenvalue Problems,
Sturm-Liouville Problems 721
911 Boundary-Value Problems 721
912 Eigenvalue Problems 724
913 Sturm-Liouville Problems 729
9 2 Fourier Sine Series and Cosine Series 731
921 Fourier Sine Series 731
922 Fourier Cosine Series 739
9 3 Fourier Series 743
931 Fourier Series 743
932 Even, Odd, and Periodic Extensions 754
933 Differentiation and Integration of Fourier Series 760
934 Parseval s Equality 765
9 4 Generalized Fourier Series 767
10 Partial Differential Equations 781
10 1 Introduction to Partial Differential Equations and
Separation of Variables 781
10 1 1 Introduction 781
10 1 2 Separation of Variables 783
10 2 The One-Dimensional Heat Equation 785
10 2 1 The Heat Equation With Homogeneous Boundary Conditions 786
30 2 2 Nonhomogeneous Boundary Conditions 790
10 2 3 Insulated Boundary 794
10 3 The One-Dimensional Wave Equation 798
10 3 1 The Wave Equation 798
10 3 2 D Alembert s Solution 805
10 4 Problems in Two Dimensions: Laplace s Equation 809
10 4 1 Laplace s Equation 809
10 5 Two-Dimensional Problems in a Circular Region 816
10 5 1 Laplace s Equation in a Circular Region 817
10 5 2 The Wave Equation in a Circular Region 821
Appendix: Getting Started 835
Introduction to Mathematica 835
A Note Regarding Different Versions of Mathematica 836
Contents
xi
Getting Started With Mathematica 837
Five Basic Rules of Mathematica Syntax 843
Getting Help From Mathematica 844
Mathematica Help 849
The Mathematica Menu 853
Bibliography 855
|
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| discipline | Mathematik |
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| id | DE-604.BV044310038 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:59:31Z |
| institution | BVB |
| isbn | 9780128047767 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029713713 |
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| open_access_boolean | |
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| owner_facet | DE-20 |
| physical | xiv, 865 Seiten Illustrationen, Diagramme |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Elsevier Academic Press |
| record_format | marc |
| spellingShingle | Abell, Martha L. 1962- Braselton, James P. 1965- Differential equations with Mathematica Datenverarbeitung Datenverarbeitung (DE-588)4011152-0 gnd Differentialgleichung (DE-588)4012249-9 gnd Mathematica Programm (DE-588)4268208-3 gnd |
| subject_GND | (DE-588)4011152-0 (DE-588)4012249-9 (DE-588)4268208-3 |
| title | Differential equations with Mathematica |
| title_auth | Differential equations with Mathematica |
| title_exact_search | Differential equations with Mathematica |
| title_full | Differential equations with Mathematica Martha L. Abell (Georgia Southern University, Statesboro, USA), James P. Braselton (Georgia Southern University, Statesboro, USA) |
| title_fullStr | Differential equations with Mathematica Martha L. Abell (Georgia Southern University, Statesboro, USA), James P. Braselton (Georgia Southern University, Statesboro, USA) |
| title_full_unstemmed | Differential equations with Mathematica Martha L. Abell (Georgia Southern University, Statesboro, USA), James P. Braselton (Georgia Southern University, Statesboro, USA) |
| title_short | Differential equations with Mathematica |
| title_sort | differential equations with mathematica |
| topic | Datenverarbeitung Datenverarbeitung (DE-588)4011152-0 gnd Differentialgleichung (DE-588)4012249-9 gnd Mathematica Programm (DE-588)4268208-3 gnd |
| topic_facet | Datenverarbeitung Differentialgleichung Mathematica Programm |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029713713&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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