For courses in Differential Equations and Linear Algebra .
Concepts, methods, and core topics covering elementary differential equations and linear algebra through real-world applications
In a contemporary introduction to differential equations and linear algebra, acclaimed authors Edwards and Penney combine core topics in elementary differential equations with concepts and methods of elementary linear algebra. Renowned for its real-world applications and blend of algebraic and geometric approaches, Differential Equations and Linear Algebra introduces you to mathematical modeling of real-world phenomena and offers the best problems sets in any differential equations and linear algebra textbook. The 4th Edition includes fresh new computational and qualitative flavor evident throughout in figures, examples, problems, and applications. Additionally, an Expanded Applications website containing expanded applications and programming tools is now available.
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1. First-Order Differential Equations
1.1 Differential Equations and Mathematical Models
1.2 Integrals as General and Particular Solutions
1.3 Slope Fields and Solution Curves
1.4 Separable Equations and Applications
1.5 Linear First-Order Equations
1.6 Substitution Methods and Exact Equations
2. Mathematical Models and Numerical Methods
2.1 Population Models
2.2 Equilibrium Solutions and Stability
2.3 Acceleration–Velocity Models
2.4 Numerical Approximation: Euler's Method
2.5 A Closer Look at the Euler Method
2.6 The Runge–Kutta Method
3. Linear Systems and Matrices
3.1 Introduction to Linear Systems
3.2 Matrices and Gaussian Elimination
3.3 Reduced Row-Echelon Matrices
3.4 Matrix Operations
3.5 Inverses of Matrices
3.6 Determinants
3.7 Linear Equations and Curve Fitting
4. Vector Spaces
4.1 The Vector Space R3
4.2 The Vector Space Rn and Subspaces
4.3 Linear Combinations and Independence of Vectors
4.4 Bases and Dimension for Vector Spaces
4.5 Row and Column Spaces
4.6 Orthogonal Vectors in Rn
4.7 General Vector Spaces
5. Higher-Order Linear Differential Equations
5.1 Introduction: Second-Order Linear Equations
5.2 General Solutions of Linear Equations
5.3 Homogeneous Equations with Constant Coefficients
5.4 Mechanical Vibrations
5.5 Nonhomogeneous Equations and Undetermined Coefficients
5.6 Forced Oscillations and Resonance
6. Eigenvalues and Eigenvectors
6.1 Introduction to Eigenvalues
6.2 Diagonalization of Matrices
6.3 Applications Involving Powers of Matrices
7. Linear Systems of Differential Equations
7.1 First-Order Systems and Applications
7.2 Matrices and Linear Systems
7.3 The Eigenvalue Method for Linear Systems
7.4 A Gallery of Solution Curves of Linear Systems
7.5 Second-Order Systems and Mechanical Applications
7.6 Multiple Eigenvalue Solutions
7.7 Numerical Methods for Systems
8. Matrix Exponential Methods
8.1 Matrix Exponentials and Linear Systems
8.2 Nonhomogeneous Linear Systems
8.3 Spectral Decomposition Methods
9. Nonlinear Systems and Phenomena
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About the Book
New text and graphics have been inserted in a number of sections, to enhance student understanding of the subject matter.
Nearly 80 new figures illustrating interactive computer applications
Now includes Python, an increasingly popular computer platform that is freely available on the internet and an all-purpose scientific computing environment.
The online Expanded Applications companion website enhances the text's applications material through technology, and provides detailed coverage of Maple, Mathematica, and MATLAB techniques.
Content Updates
Chapter 7 has a new section devoted to the construction of a “gallery” of phase plane portraits illustrating all the possible geometric behaviors of solutions of the 2-dimensional linear system x' = Ax.
Chapter 9 now contains a new biological application whichincludes a substantial investigation of the nonlinear FitzHugh-Nagumo equations of neuroscience.
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Produktdetaljer
ISBN
9780134497181
Publisert
2017-05-22
Utgave
4. utgave
Utgiver
Vendor
Pearson
Vekt
1400 gr
Høyde
254 mm
Bredde
206 mm
Dybde
33 mm
Aldersnivå
U, 05
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
768