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(Ebook) Differential Equations with Mathematica 4th Edition by Martha L Abell, James P Braselton ISBN 0128047763 9780128047767

  • SKU: EBN-42658900
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Authors: Martha L. Abell_ James P. Braselton
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ISBNS:9780128047767, 0128047763
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(Ebook) Differential Equations with Mathematica 4th Edition by Martha L Abell, James P Braselton ISBN 0128047763 9780128047767

(Ebook) Differential Equations with Mathematica 4th Edition by Martha L Abell, James P Braselton - Ebook PDF Instant Download/Delivery: 0128047763, 9780128047767
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ISBN 10: 0128047763 
ISBN 13: 9780128047767
Author: Martha L Abell, James P Braselton

Differential Equations with Mathematica, Fourth Edition is a supplementing reference which 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 10
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

(Ebook) Differential Equations with Mathematica 4th Table of contents:

1: Introduction to Differential Equations
Abstract
1.1 Definitions and Concepts
1.2 Solutions of Differential Equations
1.3 Initial and Boundary-Value Problems
1.4 Direction Fields
2: First-Order Ordinary Differential Equations
Abstract
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
3: Applications of First-Order Equations
Abstract
3.1 Orthogonal Trajectories
3.2 Population Growth and Decay
3.3 Newton’s Law of Cooling
3.4 Free-Falling Bodies
4: Higher-Order Differential Equations
Abstract
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
5: Applications of Higher-Order Differential Equations
Abstract
5.1 Harmonic Motion
5.2 The Pendulum Problem
5.3 Other Applications
6: Systems of Ordinary Differential Equations
Abstract
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
7: Applications of Systems of Ordinary Differential Equations
Abstract
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
8: Laplace Transform Methods
Abstract
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
9: Eigenvalue Problems and Fourier Series
Abstract
9.1 Boundary-Value Problems, Eigenvalue Problems, Sturm-Liouville Problems
9.2 Fourier Sine Series and Cosine Series
9.3 Fourier Series
9.4 Generalized Fourier Series
10: Partial Differential Equations
Abstract
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
Appendix A: Getting Started

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Tags: Martha L Abell, James P Braselton, Equations, Mathematica

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