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Differential Equations and Linear Algebra, by 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.
- Sales Rank: #111170 in Books
- Published on: 2014-06-04
- Original language: English
- Number of items: 1
- Dimensions: 9.09" h x 1.10" w x 7.24" l, 2.82 pounds
- Binding: Hardcover
- 512 pages
Review
"As with Strang's linear algebra books, now in their fourth edition, this text is destined to have a big impact on differential equations courses and applied math education. Its conversational presentation, breadth, and provocative problems will even appeal to students, who typically read little of the book assigned. Those who teach differential equations should definitely give Strang's approach serious consideration. Once again, he's making us think!" Robert E. O'Malley, Jr. SIAM Review vol. 56, ISSUE 4
About the Author
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.
Most helpful customer reviews
21 of 21 people found the following review helpful.
Text aims to impart real understanding
By David Bruce
I am a surgeon by profession and have been using this text in my "hobby", a serious self-study of mathematics and modern physics, in conjunction with MIT's Open Courseware and edx.org. I started off with just high school calculus from decades ago, and have made it to the mid-undergraduate maths covered in this volume. Although I'm giving it five stars, I have to add the caveat that at first it was hard to get started with this book. Professor Strang fills the text with all sorts of glimpses of more advanced topics that will be unfamiliar to new students. For example, some of the very first examples involve step and Dirac delta input, with a heavy emphasis on impulse response concepts to explain the time evolution of solutions. This really confused me at first. However, once I started to feel more familiar with ODEs, this presentation was very helpful to get me to "get it" at a deeper level than the mere methodology of finding and writing out solutions.
Also, the book does not follow the OCW differential equations course (18.03) very closely, at least the version currently online, even though it supposedly grew out of a rewrite of the 18.03 syllabus. Hopefully MIT will put up an updated version of 18.03 at some point (though I do love Prof. Mattuck's lectures in the current one).
I still have a decent chunk of the material ahead of me (matrix methods for ODE systems, eigenvalues, etc.) but I now find the book very easy to follow.
6 of 6 people found the following review helpful.
Yes
By Marc J. Vandenplas
There are a few strangers that have benefited me in my life. Elizabeth Taylor, Richard Burton, obviously some others, and Dr. Strang. Combine this textbook (and his others) with his lectures available online, and you're hooked up with everything that an independent learner needs.
40 of 42 people found the following review helpful.
One good idea is to combine that course with one on ...
By Candace
Differential Equations and Linear Algebra
Gilbert Strang
There’s no doubt that Gilbert Strang is a master teacher and an enthusiastic evangelist
for his perceptive vision of where applied math should be headed. After a half century and ten
editions of Boyce and DiPrima, there’s a pile of reasons (and ways) to change the typical first
course in differential equations. One good idea is to combine that course with one on linear
algebra, which occurred quite some time ago to Kreider, Kuller, Ostberg, and Perkins and to
Hirsch and Smale, among others. Now, however, we have MATLAB and Maple, the
Singular Value Decomposition, and the fast Fourier transform! Some experimentation with technology
and computing uncovers the practical importance of differential equations. Students tend to
learn the method of Frobenius and about specific special functions later, perhaps encountering
them in a course in engineering, biology, or finance. They ultimately also learn that nonlinearity
must be faced. This is hinted at by the book’s attractive cover illustration (by two artistic SIAM
staff members), which relates pictures of the Lorenz attractor from a Portuguese grad student.
As you’d expect, the emphasis here is linear differential equations with constant
coefficients. Honestly, there aren’t many variable coefficient ODEs that we can handle
analytically, though it is certainly fun to solve one. Numerical methods for initial value problems
are, admittedly, very successful and the resulting portraits provide immediate understanding of
solution behavior. Moreover, the powerful underlying A^TA philosophy employed carries over to
using eigenvalues and eigenvectors to solve boundary value problems for Laplace’s equation
and other partial differential equations, analytically and via finite differences. Most sophomores
would not have realized this without Strang’s insistence. Using Fourier series and Fourier and
Laplace transforms brings the focus successfully back to the classical syllabus. Meanwhile,
however, one has figured out many matrix decompositions, how to use delta and transfer
functions, and has understood critical ideas like stability and stiffness. The exercises, which
include challenge problems, look interesting, and extensive backup resources from MIT
websites are available.
As with Strang’s linear algebra books, now in their fourth edition, this text is destined to
have a big impact on differential equations courses and applied math education. Its
conversational presentation, breadth, and provocative problems will even appeal to students,
who typically read little of the book assigned. Those who teach differential equations should
definitely give Strang’s approach serious consideration. Once again, he’s making us think!
ROBERT E. O’MALLEY, JR.
University of Washington
SIAM REVIEW VOL. 56, ISSUE 4 (DECEMBER 2014) PP. 721-22
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