# Differential Equations and Linear Algebra

## Gilbert Strang

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Differential equations and linear algebra are the two crucial courses in undergraduate mathematics. This new textbook develops those subjects separately and together. The complete book is a year's course, including Fourier and Laplace transforms, plus the Fast Fourier Transform and Singular Value Decomposition.

Undergraduate students in courses covering differential equations and linear algebra, either separately or together, will find this material essential to their understanding.

Contents:Preface; 1: First Order Equations; 1.1: Four Examples: Linear versus Nonlinear; 1.2: The Calculus you Need; 1.3: The Exponentials; 1.4: Four Particular Solutions; 1.5: Real and Complex Sinusoids; 1.6: Models of Growth and Decay; 1.7: The Logistic Equation; 1.8: Separable Equations and Exact Equations; 2: Second Order Equations; 2.1: Second Derivatives in Science and Engineering; 2.2: Key Facts About Complex Numbers; 2.3: Constant Coefficients A, B, C; 2.4: Forced Oscillations and Exponential Response; 2.5: Electrical Networks and Mechanical Systems; 2.6: Solutions to Second Order Equations; 2.7: Laplace Transforms Y(s) and F(s); 3: Graphical and Numerical Methods; 3.1: Nonlinear Equations; 3.2: Sources, Sinks, Saddles, and Spirals; 3.3: Linearization and Stability in 2D and 3D; 3.4: The Basic Euler Methods; 3.5: Higher Accuracy with Runge-Kutta; 4: Linear Equations and Inverse Matrices; 4.1: Two Pictures of Linear Equations; 4.2: Solving Linear Equations by Elimination; 4.3: Matrix Multiplication; 4.4: Inverse Matrices; 4.5: Symmetric Matrices and Orthogonal Matrices; 5: Vector Spaces and Subspaces; 5.1: The Column Space of a Matrix; 5.2: The Nullspace of A: Solving Av=0; 5.3: The Complete Solution to Av=b; 5.4: Independence, Basis and Dimension; 5.5: The Four Fundamental Subspaces; 5.6: Graphs and Networks; 6: Eigenvalues and Eigenvectors; 6.1: Introduction to Eigenvalues; 6.2: Diagonalizing a Matrix; 6.3: Linear Systems y =Ay; 6.4: The Exponential of a Matrix; 6.5: Second Order Systems and Symmetric Matrices; 7: Applied Mathematics and ATA; 7.1: Least Squares and Projections; 7.2: Positive Definite Matrices and the SVD; 7.3: Boundary Conditions Replace Initial Conditions; 7.4: Laplace's Equation; 7.5: Networks and the Graph Laplacian; 8: Fourier and Laplace Transforms; 8.1: Fourier Series; 8.2: The Fast Fourier Transform; 8.3: The Heat Equation; 8.4: The Wave Equation; 8.5: The Laplace Transform; 8.6: Convolution (Fourier and Laplace); Matrix Factorizations; Properties of Determinants; Index; Linear Algebra in a Nutshell.

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Book Description:

An innovative textbook that allows differential equations to be taught alone, or in parallel with linear algebra, affording extra flexibility to instructors. It covers the fundamental undergraduate topics in differential equations and linear algebra, revealing connections between these two essential subjects, and applications to the physical sciences, engineering and economics.

Gilbert Strang is a Professor of Mathematics at Massachusetts Institute of Technology and an Honorary Fellow of Balliol College, Oxford University. He is also a prolific author, with a dozen highly regarded textbooks and monographs to his credit. Strang served as president of the Society for Industrial and Applied Mathematics (SIAM) from 1999-2000 and chaired the U.S. National Committee on Mathematics from 2003-4. He won the Henrici and Su Buchin prizes at ICIAM 2007 and the Von Neumann Medal of the U.S. Association of Computational Mechanics. He is a SIAM Fellow and a member of the National Academy of Sciences.

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## 1.Differential Equations and Linear Algebra (Hardback)

Editorial: Wellesley-Cambridge Press,U.S., United States (2015)
ISBN 10: 0980232791 ISBN 13: 9780980232790
Librería
The Book Depository
(London, Reino Unido)
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Descripción Wellesley-Cambridge Press,U.S., United States, 2015. Hardback. Estado de conservación: New. UK ed.. Language: English . Brand New Book. Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author s distinguished career as an applied mathematician and expositor. Nº de ref. de la librería AAU9780980232790

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## 2.Differential Equations and Linear Algebra

Editorial: Wellesley-Cambridge (2014)
ISBN 10: 0980232791 ISBN 13: 9780980232790
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Descripción Wellesley-Cambridge, 2014. Estado de conservación: New. Num Pages: 510 pages. BIC Classification: PBKJ. Category: (U) Tertiary Education (US: College). Dimension: 240 x 196 x 28. Weight in Grams: 1038. . 2014. Hardcover. . . . . . Nº de ref. de la librería V9780980232790

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## 3.Differential Equations and Linear Algebra

Editorial: Wellesley-Cambridge Press 2015-02-12, Wellesley, MA (2015)
ISBN 10: 0980232791 ISBN 13: 9780980232790
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Descripción Wellesley-Cambridge Press 2015-02-12, Wellesley, MA, 2015. hardback. Estado de conservación: New. Nº de ref. de la librería 9780980232790

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## 4.Differential Equations and Linear Algebra (Hardback)

Editorial: Wellesley-Cambridge Press,U.S., United States (2015)
ISBN 10: 0980232791 ISBN 13: 9780980232790
Librería
The Book Depository US
(London, Reino Unido)
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Descripción Wellesley-Cambridge Press,U.S., United States, 2015. Hardback. Estado de conservación: New. UK ed.. Language: English . Brand New Book. Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author s distinguished career as an applied mathematician and expositor. Nº de ref. de la librería AAU9780980232790

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## 5.Differential Equations and Linear Algebra

Editorial: Wellesley-Cambridge Press (2015)
ISBN 10: 0980232791 ISBN 13: 9780980232790
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Descripción Wellesley-Cambridge Press, 2015. HRD. Estado de conservación: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Nº de ref. de la librería BB-9780980232790

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## 6.Differential Equations and Linear Algebra

Editorial: Wellesley-Cambridge Press (2015)
ISBN 10: 0980232791 ISBN 13: 9780980232790
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Descripción Wellesley-Cambridge Press, 2015. Estado de conservación: New. book. Nº de ref. de la librería ria9780980232790_rkm

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## 7.Differential Equations and Linear Algebra

Editorial: Wellesley-Cambridge
ISBN 10: 0980232791 ISBN 13: 9780980232790
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Descripción Wellesley-Cambridge. Estado de conservación: New. Num Pages: 510 pages. BIC Classification: PBKJ. Category: (U) Tertiary Education (US: College). Dimension: 240 x 196 x 28. Weight in Grams: 1038. . 2014. Hardcover. . . . . Books ship from the US and Ireland. Nº de ref. de la librería V9780980232790

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## 8.Differential Equations and Linear Algebra

Editorial: Wellesley-Cambridge Press (2015)
ISBN 10: 0980232791 ISBN 13: 9780980232790
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Descripción Wellesley-Cambridge Press, 2015. Estado de conservación: New. Nº de ref. de la librería EH9780980232790

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## 9.Differential Equations and Linear Algebra

Editorial: U.S. Wellesley-Cambridge Press Feb 2015 (2015)
ISBN 10: 0980232791 ISBN 13: 9780980232790
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Descripción U.S. Wellesley-Cambridge Press Feb 2015, 2015. Buch. Estado de conservación: Neu. Neuware - 510 pp. Englisch. Nº de ref. de la librería 9780980232790

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## 10.Differential Equations and Linear Algebra

Editorial: Wellesley-Cambridge (2015)
ISBN 10: 0980232791 ISBN 13: 9780980232790
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Descripción Wellesley-Cambridge, 2015. Hardcover. Estado de conservación: Brand New. uk ed. edition. 512 pages. 9.20x8.00x1.40 inches. In Stock. Nº de ref. de la librería __0980232791

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