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Introduction to Differential Equations Using Sage [Hardback]

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(U.S. Naval Academy), (University of Minnesota Duluth)
  • Formāts: Hardback, 280 pages, height x width x depth: 254x178x27 mm, weight: 703 g, 3 Halftones, black and white; 80 Line drawings, black and white
  • Izdošanas datums: 27-Oct-2012
  • Izdevniecība: Johns Hopkins University Press
  • ISBN-10: 1421406373
  • ISBN-13: 9781421406374
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Introduction to Differential Equations Using SagePalielināt
  • Formāts: Hardback, 280 pages, height x width x depth: 254x178x27 mm, weight: 703 g, 3 Halftones, black and white; 80 Line drawings, black and white
  • Izdošanas datums: 27-Oct-2012
  • Izdevniecība: Johns Hopkins University Press
  • ISBN-10: 1421406373
  • ISBN-13: 9781421406374
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781421406374.html

David Joyner and Marshall Hampton’s lucid textbook explains differential equations using the free and open-source mathematical software Sage.

Since its release in 2005, Sage has acquired a substantial following among mathematicians, but its first user was Joyner, who is credited with helping famed mathematician William Stein turn the program into a usable and popular choice.

Introduction to Differential Equations Using Sage extends Stein's work by creating a classroom tool that allows both differential equations and Sage to be taught concurrently. It’s a creative and forward-thinking approach to math instruction.

Topics include:

• First-Order Differential Equations • Incorporation of Newtonian Mechanics• Second-Order Differential Equations• The Annihilator Method• Using Linear Algebra with Differential Equations• Nonlinear Systems• Partial Differential Equations• Romeo and Juliet

Recenzijas

This book, with its many practice examples, would be ideal for those in the first year of a mathematics degree course and for those studying for working in physics or any area requiring a good knowledge of differential equations. -- Adrian Hamilton Institute of Mathematics and its Applications ... [ Introduction to Differential Equations Using Sage] provides a nice mix of theory and symbolic computation. The pedagogy is excellent and the exercises are models of their kind. Gazette of the Australian Mathematical Society

Papildus informācija

Differential equations can be taught using Sage as an inventive new approach.
Preface xi
Acknowledgments xiii
1 First-order differential equations
1(64)
1.1 Introduction to DEs
1(9)
1.2 Initial value problems
10(5)
1.3 Existence of solutions to ODEs
15(7)
1.3.1 First-order ODEs
15(4)
1.3.2 Second-order homogeneous ODEs
19(3)
1.4 First-order ODEs: Separable and linear cases
22(11)
1.4.1 Separable DEs
22(4)
1.4.2 Autonomous ODEs
26(3)
1.4.3 Substitution methods
29(1)
1.4.4 Linear first-order ODEs
29(4)
1.5 Isoclines and direction fields
33(5)
1.6 Numerical solutions: Euler's and improved Euler's method
38(9)
1.6.1 Euler's method
38(3)
1.6.2 Improved Euler's method
41(3)
1.6.3 Euler's method for systems and higher-order DEs
44(3)
1.7 Numerical solutions II: Runge-Kutta and other methods
47(4)
1.7.1 Fourth-order Runge-Kutta method
47(2)
1.7.2 Multistep methods: Adams-Bashforth
49(1)
1.7.3 Adaptive step size
49(2)
1.8 Newtonian mechanics
51(5)
1.9 Application to mixing problems
56(4)
1.10 Application to cooling problems
60(5)
2 Second-order differential equations
65(76)
2.1 Linear differential equations
65(4)
2.1.1 Solving homogeneous constant-coefficient ODEs
65(4)
2.2 Linear differential equations, revisited
69(5)
2.3 Linear differential equations, continued
74(5)
2.4 Undetermined coefficients method
79(8)
2.4.1 Simple case
80(2)
2.4.2 Nonsimple case
82(5)
2.5 Annihilator method
87(2)
2.6 Variation of parameters
89(3)
2.6.1 The Leibniz rule
89(1)
2.6.2 The method
90(2)
2.7 Applications of DEs: Spring problems
92(13)
2.7.1 Introduction: Simple harmonic case
92(2)
2.7.2 Simple harmonic case
94(3)
2.7.3 Free damped motion
97(4)
2.7.4 Spring-mass systems with an external force
101(4)
2.8 Applications to simple LRC circuits
105(5)
2.9 The power series method
110(11)
2.9.1 Part 1
110(8)
2.9.2 Part 2
118(3)
2.10 The Laplace transform method
121(20)
2.10.1 Part 1
121(8)
2.10.2 Part 2
129(9)
2.10.3 Part 3
138(3)
3 Matrix theory and systems of DEs
141(78)
3.1 Quick survey of linear algebra
141(4)
3.1.1 Matrix arithmetic
141(4)
3.2 Row reduction and solving systems of equations
145(21)
3.2.1 The Gauss elimination game
145(4)
3.2.2 Solving systems using inverses
149(1)
3.2.3 Computing inverses using row reduction
149(6)
3.2.4 Solving higher-dimensional linear systems
155(1)
3.2.5 Determinants
156(3)
3.2.6 Elementary matrices and computation of determinants
159(2)
3.2.7 Vector spaces
161(2)
3.2.8 Bases, dimension, linear independence, and span
163(3)
3.3 Application: Solving systems of DEs
166(22)
3.3.1 Modeling battles using Lanchester's equations
170(8)
3.3.2 Romeo and Juliet
178(5)
3.3.3 Electrical networks using Laplace transforms
183(5)
3.4 Eigenvalue method for systems of DEs
188(13)
3.4.1 Motivation
188(3)
3.4.2 Computing eigenvalues
191(4)
3.4.3 The eigenvalue method
195(1)
3.4.4 Examples of the eigenvalue method
196(5)
3.5 Introduction to variation of parameters for systems
201(6)
3.5.1 Motivation
201(2)
3.5.2 The method
203(4)
3.6 Nonlinear systems
207(12)
3.6.1 Linearizing near equilibria
208(1)
3.6.2 The nonlinear pendulum
209(2)
3.6.3 The Lorenz equations
211(1)
3.6.4 Zombies attack
212(7)
4 Introduction to partial differential equations
219(36)
4.1 Introduction to separation of variables
219(6)
4.1.1 The transport or advection equation
220(3)
4.1.2 The heat equation
223(2)
4.2 The method of superposition
225(3)
4.3 Fourier, sine, and cosine series
228(9)
4.3.1 Brief history
228(1)
4.3.2 Motivation
228(1)
4.3.3 Definitions
229(8)
4.4 The heat equation
237(9)
4.4.1 Method for zero ends
238(2)
4.4.2 Method for insulated ends
240(3)
4.4.3 Explanation via separation of variables
243(3)
4.5 The wave equation in one dimension
246(4)
4.5.1 Method
247(3)
4.6 The Schrodinger equation
250(5)
4.6.1 Method
251(4)
Bibliography 255(6)
Index 261
David Joyner is a professor in the Mathematics Department at the U.S. Naval Academy. He is the author of Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys, also published by Johns Hopkins. Marshall Hampton is a professor in the Department of Mathematics and Statistics at the University of Minnesota, Duluth.