Differential Equations with Mathematica
- 5th Edition - January 18, 2022
- Authors: Martha L. Abell, James P. Braselton
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 8 2 4 1 6 0 - 8
- eBook ISBN:9 7 8 - 0 - 3 2 3 - 9 8 4 3 6 - 2
Differential Equations with Mathematica, Fifth Edition uses the fundamental concepts of the popular platform to solve (analytically, numerically, and/or graphically) different… Read more
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Request a sales quoteDifferential Equations with Mathematica, Fifth Edition uses the fundamental concepts of the popular platform to solve (analytically, numerically, and/or graphically) differential equations of interest to students, instructors, and scientists.
Mathematica’s diversity makes it particularly well suited to performing calculations encountered when solving many ordinary and partial differential equations. In some cases, Mathematica’s built-in functions can immediately solve a differential equation by providing an explicit, implicit, or numerical solution. In other cases, Mathematica can be used to perform the calculations encountered when solving a differential equation.
Because one goal of elementary differential equations courses is to introduce students to basic methods and algorithms so that they gain proficiency in them, nearly every topic covered this book introduces basic commands, also including typical examples of their application. A study of differential equations relies on concepts from calculus and linear algebra, so this text also includes discussions of relevant commands useful in those areas. In many cases, seeing a solution graphically is most meaningful, so the book relies heavily on Mathematica’s outstanding graphics capabilities.
- Demonstrates how to take advantage of the advanced features of Mathematica
- Introduces the fundamental theory of ordinary and partial differential equations using Mathematica to solve typical problems of interest to students, instructors, scientists, and practitioners in many fields
- Showcases practical applications and case studies drawn from biology, physics, and engineering
Students at the undergraduate level taking Differential Equations courses, in Mathematics Departments, in which the instructor is using Mathematica. Researchers/Professionals
- Cover image
- Title page
- Table of Contents
- Copyright
- Preface
- Chapter 1: Introduction to differential equations
- 1.1. Definitions and concepts
- 1.2. Solutions of differential equations
- 1.3. Initial- and boundary-value problems
- 1.4. Direction fields
- Bibliography
- Chapter 2: First-order ordinary differential equations
- 2.1. Theory of first-order equations: a brief discussion
- 2.2. Separation of variables
- 2.3. Homogeneous equations
- 2.4. Exact equations
- 2.5. Linear equations
- 2.6. Numerical approximations of solutions to first-order equations
- Bibliography
- Chapter 3: Applications of first-order equations
- 3.1. Orthogonal trajectories
- 3.2. Population growth and decay
- 3.3. Newton's law of cooling
- 3.4. Free-falling bodies
- Bibliography
- Chapter 4: Higher-order linear differential equations
- 4.1. Preliminary definitions and notation
- 4.2. Solving homogeneous equations with constant coefficients
- 4.3. Introduction to solving nonhomogeneous equations
- 4.4. Nonhomogeneous equations with constant coefficients: the method of undetermined coefficients
- 4.5. Nonhomogeneous equations with constant coefficients: variation of parameters
- 4.6. Cauchy–Euler equations
- 4.7. Series solutions
- 4.8. Nonlinear equations
- Bibliography
- Chapter 5: Applications of higher-order differential equations
- 5.1. Harmonic motion
- 5.2. The pendulum problem
- 5.3. Other applications
- Chapter 6: Systems of ordinary differential equations
- 6.1. Review of matrix algebra and calculus
- 6.2. Systems of equations: preliminary definitions and theory
- 6.3. Homogeneous linear systems with constant coefficients
- 6.4. Nonhomogeneous first-order systems: undetermined coefficients, variation of parameters, and the matrix exponential
- 6.5. Numerical methods
- 6.6. Nonlinear systems, linearization, and classification of equilibrium points
- Bibliography
- Chapter 7: Applications of systems of ordinary differential equations
- 7.1. Mechanical and electrical problems with first-order linear systems
- 7.2. Diffusion and population problems with first-order linear systems
- 7.3. Applications that lead to nonlinear systems
- Bibliography
- Chapter 8: Laplace transform methods
- 8.1. The Laplace transform
- 8.2. The inverse Laplace transform
- 8.3. Solving initial-value problems with the Laplace transform
- 8.4. Laplace transforms of step and periodic functions
- 8.5. The convolution theorem
- 8.6. Applications of Laplace transforms, Part I
- 8.7. Laplace transform methods for systems
- 8.8. Applications of Laplace transforms, Part II
- Chapter 9: Eigenvalue problems and Fourier series
- 9.1. Boundary-value problems, eigenvalue problems, and Sturm–Liouville problems
- 9.2. Fourier sine series and cosine series
- 9.3. Fourier series
- 9.4. Generalized Fourier series
- Chapter 10: Partial differential equations
- 10.1. Introduction to partial differential equations and separation of variables
- 10.2. The one-dimensional heat equation
- 10.3. The one-dimensional wave equation
- 10.4. Problems in two dimensions: Laplace's equation
- 10.5. Two-dimensional problems in a circular region
- Bibliography
- Bibliography
- Index
- No. of pages: 608
- Language: English
- Edition: 5
- Published: January 18, 2022
- Imprint: Academic Press
- Paperback ISBN: 9780128241608
- eBook ISBN: 9780323984362
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Martha L. Abell
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