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

Biographical note

C. Henry Edwards is emeritus professor of mathematics at the University of Georgia. He earned his Ph.D. at the University of Tennessee in 1960, and recently retired after 40 years of classroom teaching (including calculus or differential equations almost every term) at the universities of Tennessee, Wisconsin, and Georgia, with a brief interlude at the Institute for Advanced Study (Princeton) as an Alfred P. Sloan Research Fellow. He has received numerous teaching awards, including the University of Georgia's honoratus medal in 1983 (for sustained excellence in honors teaching), its Josiah Meigs award in 1991 (the institution's highest award for teaching), and the 1997 statewide Georgia Regents award for research university faculty teaching excellence. His scholarly career has ranged from research and dissertation direction in topology to the history of mathematics to computing and technology in the teaching and applications of mathematics. In addition to being author or co-author of calculus, advanced calculus, linear algebra, and differential equations textbooks, he is well-known to calculus instructors as author of The Historical Development of the Calculus (Springer-Verlag, 1979). During the 1990s he served as a principal investigator on three NSF-supported projects: (1) A school mathematics project including Maple for beginning algebra students, (2) A Calculus-with-Mathematica program, and (3) A MATLAB-based computer lab project for numerical analysis and differential equations students.   David E. Penney, University of Georgia, completed his Ph.D. at Tulane University in 1965 (under the direction of Prof. L. Bruce Treybig) while teaching at the University of New Orleans. Earlier he had worked in experimental biophysics at Tulane University and the Veteran's Administration Hospital in New Orleans under the direction of Robert Dixon McAfee, where Dr. McAfee's research team's primary focus was on the active transport of sodium ions by biological membranes. Penney's primary contribution here was the development of a mathematical model (using simultaneous ordinary differential equations) for the metabolic phenomena regulating such transport, with potential future applications in kidney physiology, management of hypertension, and treatment of congestive heart failure. He also designed and constructed servomechanisms for the accurate monitoring of ion transport, a phenomenon involving the measurement of potentials in microvolts at impedances of millions of megohms. Penney began teaching calculus at Tulane in 1957 and taught that course almost every term with enthusiasm and distinction until his retirement at the end of the last millennium. During his tenure at the University of Georgia he received numerous University-wide teaching awards as well as directing several doctoral dissertations and seven undergraduate research projects. He is the author of research papers in number theory and topology and is the author or co-author of textbooks on calculus, computer programming, differential equations, linear algebra, and liberal arts mathematics.