Fundamentals of Differential Equations, Global Edition + MyLab Mathematics with Pearson eText (Package)
9th Edition
Published on 13. September 2018
Book
Mixed media product
978-1-292-24149-4 (ISBN)
More details
Edition
9th edition
Language
English
Place of publication
Harlow
United Kingdom
Target group
College/higher education
Dimensions
Height: 255 mm
Width: 205 mm
Thickness: 20 mm
Weight
1220 gr
ISBN-13
978-1-292-24149-4 (9781292241494)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Content
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, Poincare 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 Analytic Functions
8.3 Power Series Solutions to Linear Differential Equations
8.4 Equations with Analytic Coefficients
8.5 Cauchy-Euler (Equidimensional) Equations
8.6 Method of Frobenius
8.7 Finding a Second Linearly Independent Solution
8.8 Special Functions
9. Matrix Methods for Linear Systems
9.1 Introduction
9.2 Review 1: Linear Algebraic Equations
9.3 Review 2: Matrices and Vectors
9.4 Linear Systems in Normal Form
9.5 Homogeneous Linear Systems with Constant Coefficients
9.6 Complex Eigenvalues
9.7 Nonhomogeneous Linear Systems
9.8 The Matrix Exponential Function
10. Partial Differential Equations
10.1 Introduction: A Model for Heat Flow
10.2 Method of Separation of Variables
10.3 Fourier Series
10.4 Fourier Cosine and Sine Series
10.5 The Heat Equation
10.6 The Wave Equation
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, Poincare 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 Analytic Functions
8.3 Power Series Solutions to Linear Differential Equations
8.4 Equations with Analytic Coefficients
8.5 Cauchy-Euler (Equidimensional) Equations
8.6 Method of Frobenius
8.7 Finding a Second Linearly Independent Solution
8.8 Special Functions
9. Matrix Methods for Linear Systems
9.1 Introduction
9.2 Review 1: Linear Algebraic Equations
9.3 Review 2: Matrices and Vectors
9.4 Linear Systems in Normal Form
9.5 Homogeneous Linear Systems with Constant Coefficients
9.6 Complex Eigenvalues
9.7 Nonhomogeneous Linear Systems
9.8 The Matrix Exponential Function
10. Partial Differential Equations
10.1 Introduction: A Model for Heat Flow
10.2 Method of Separation of Variables
10.3 Fourier Series
10.4 Fourier Cosine and Sine Series
10.5 The Heat Equation
10.6 The Wave Equation