Fundamentals of Differential Equations, Global Edition (häftad)
Format
Häftad (Paperback)
Språk
Engelska
Antal sidor
720
Utgivningsdatum
2018-09-06
Upplaga
9
Förlag
Pearson
Medarbetare
Saff, Edward B. / Snider, Arthur David
Dimensioner
255 x 205 x 20 mm
Vikt
1200 g
Antal komponenter
1
ISBN
9781292240992
Fundamentals of Differential Equations, Global Edition (häftad)

Fundamentals of Differential Equations, Global Edition

Häftad Engelska, 2018-09-06
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For one-semester sophomore- or junior-level courses in Differential Equations.

 

An introduction to the basic theory and applications of differential equations      

Fundamentals of Differential Equations presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. This flexible text allows instructors to adapt to various course emphases (theory, methodology, applications, and numerical methods) and to use commercially available computer software. For the first time, MyLab Math is available for this text, providing online homework with immediate feedback, the complete eText, and more.

 

Note that a longer version of this text, entitled Fundamentals of Differential Equations and Boundary Value Problems, 7th Edition, contains enough material for a two-semester course. This longer text consists of the main text plus three additional chapters (Eigenvalue Problems and SturmLiouville Equations; Stability of Autonomous Systems; and Existence and Uniqueness Theory).

 

 

MyLab Math is not included. Students, if MyLab Math is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN. MyLab Math should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

 

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Innehållsförteckning

1.   Introduction

1.1 Background

1.2 Solutions and Initial Value Problems

1.3 Direction Fields

1.4 The Approximation Method of Euler

 

2.   First-Order Differential Equations

2.1 Introduction: Motion of a Falling Body

2.2 Separable Equations

2.3 Linear Equations

2.4 Exact Equations

2.5 Special Integrating Factors

2.6 Substitutions and Transformations

 

3.   Mathematical Models and Numerical Methods Involving First Order Equations

3.1 Mathematical Modeling

3.2 Compartmental Analysis

3.3 Heating and Cooling of Buildings

3.4 Newtonian Mechanics

3.5 Electrical Circuits

3.6 Improved Euler's Method

3.7 Higher-Order Numerical Methods: Taylor and Runge-Kutta

 

4.   Linear Second-Order Equations

4.1 Introduction: The Mass-Spring Oscillator

4.2 Homogeneous Linear Equations: The General Solution

4.3 Auxiliary Equations with Complex Roots

4.4 Nonhomogeneous Equations: The Method of Undetermined Coefficients

4.5 The Superposition Principle and Undetermined Coefficients Revisited

4.6 Variation of Parameters

4.7 Variable-Coefficient Equations

4.8 Qualitative Considerations for Variable-Coefficient and Nonlinear Equations

4.9 A Closer Look at Free Mechanical Vibrations

4.10 A Closer Look at Forced Mechanical Vibrations

 

5.   Introduction to Systems and Phase Plane Analysis

5.1 Interconnected Fluid Tanks

5.2 Elimination Method for Systems with Constant Coefficients

5.3 Solving Systems and Higher-Order Equations Numerically

5.4 Introduction to the Phase Plane

5.5 Applications to Biomathematics: Epidemic and Tumor Growth Models

5.6 Coupled Mass-Spring Systems

5.7 Electrical Systems

5.8 Dynamical Systems, Poincar Maps, and Chaos

 

6.   Theory of Higher-Order Linear Differential Equations

6.1 Basic Theory of Linear Differential Equations

6.2 Homogeneous Linear Equations with Constant Coefficients

6.3 Undetermined Coefficients and the Annihilator Method

6.4 Method of Variation of Parameters

 

7.   Laplace Transforms

7.1 Introduction: A Mixing Problem

7.2 Definition of the Laplace Transform

7.3 Properties of the Laplace Transform

7.4 Inverse Laplace Transform

7.5 Solving Initial Value Problems

7.6 Transforms of Discontinuous Functions

7.7 Transforms of Periodic and Power Functions

7.8 Convolution

7.9 Impulses and the Dirac Delta Function

7.10 Solving Linear Systems with Laplace Transforms

 

8.   Series Solutions of Differential Equations

8.1 Introduction: The Taylor Polynomial Approximation

8.2 Power Series and An...