Hardback (ISBN-13: 9780980232707)
This second edition has two parts. The first part is the complete classic by Gilbert Strang and George Fix, first published in 1973. The original book demonstrates the solid mathematical foundation of the finite element idea, and the reasons for its success. The second part is a new textbook by Strang. It provides examples, codes, and exercises to connect the theory of the Finite Element Method directly to the applications. The reader will learn how to assemble the stiffness matrix K and solve the finite element equations KU=F. Discontinuous Galerkin methods with a numerical flux function are now included. Strang's approach is direct and focuses on learning finite elements by using them.
* Updated second edition of a popular and successful graduate text on the Finite Element Method * Suitable for postgraduate teaching as well as a reference for professionals * Includes problem sets for teaching and MATLAB codes
Introduction to the second edition; Foreword to the 1997 edition; Preface; Part I: 1. An introduction to the theory; A summary of the theory; 3. Approximation; 4. Variational crimes, 5. Stability; 6. Eigenvalue problems; 7. Initial-value problems; 8. Singularities; Bibliography; Index of notations; Index; Part II: 9. Finite elements in one dimension; 10. The finite element method in 2D and 3D; 11. Errors in projections and eigenvalues; 12. Mixed finite elements: velocity and pressure; Appendix A. Discontinuous Galerkin methods; Appendix B. Fast Poisson solvers; Index for chapters 9-12 and appendices A and B.
Hardback (ISBN-13: 9780961408824)
Gilbert Strang's Calculus textbook is ideal both as a course companion and for self study. The author has a direct style. His book presents detailed and intensive explanations. Many diagrams and key examples are used to aid understanding, as well as the application of calculus to physics and engineering and economics. The text is well organized, and it covers single variable and multivariable calculus in depth. An instructor's manual and student guide are available online at http://ocw.mit.edu/ans7870/resources/Strang/strangtext.htm.
* Useful as both a reference and a self-study manual * Contains ample diagrams and examples assisting the reader’s grasp of the material * A classic which has been used by generations of students since it was published in 1991
1. Introduction to calculus; 2. Derivatives; 3. Applications of the derivative; 4. The chain rule; 5. Integrals; 6. Exponentials and logarithms; 7. Techniques of integration; 8. Applications of the integral; 9. Polar coordinates and complex numbers; 10. Infinite series; 11. Vectors and matrices; 12. Motion along a curve; 13. Partial derivatives; 14. Multiple integrals; 15. Vector calculus; 16. Mathematics after calculus.
Hardback (ISBN-13: 9780961408817)
Encompasses the full range of computational science and engineering from modelling to solution, both analytical and numerical. It develops a framework for the equations and numerical methods of applied mathematics. Gilbert Strang has taught this material to thousands of engineers and scientists (and many more on MIT's OpenCourseWare 18.085-6). His experience is seen in his clear explanations, wide range of examples, and teaching method. The book is solution-based and not formula-based: it integrates analysis and algorithms and MATLAB codes to explain each topic as effectively as possible. The topics include applied linear algebra and fast solvers, differential equations with finite differences and finite elements, Fourier analysis and optimization. This book also serves as a reference for the whole community of computational scientists and engineers. Supporting resources, including MATLAB codes, problem solutions and video lectures from Gilbert Strang's 18.085 courses at MIT, are provided at math.mit.edu/cse.
* Written by one of the world’s leading applied mathematicians * A staple reference book for any computational scientist’s or engineer’s bookshelf * MATLAB codes, solutions to problems and video lectures are available through the author’s website
1. Applied Linear Algebra: 1.1 Four special matrices; 1.2 Differences,
derivatives, and boundary conditions; 1.3 Elimination leads to K = LDL^T;
1.4 Inverses and delta functions; 1.5 Eigenvalues and eigenvectors; 1.6
Positive definite matrices; 1.7 Numerical linear algebra: LU, QR, SVD;
1.8 Best basis from the SVD; 2. A Framework for Applied Mathematics: 2.1
Equilibrium and the stiffness matrix; 2.2 Oscillation by Newton's law;
2.3 Least squares for rectangular matrices; 2.4 Graph models and Kirchhoff's
laws; 2.5 Networks and transfer functions; 2.6 Nonlinear problems; 2.7
Structures in equilibrium; 2.8 Covariances and recursive least squares;
2.9 Graph cuts and gene clustering; 3. Boundary Value Problems: 3.1 Differential
equations of equilibrium; 3.2 Cubic splines and fourth order equations;
3.3 Gradient and divergence; 3.4 Laplace's equation; 3.5 Finite differences
and fast Poisson solvers; 3.6 The finite element method; 3.7 Elasticity
and solid mechanics; 4. Fourier Series and Integrals: 4.1 Fourier series
for periodic functions; 4.2 Chebyshev, Legendre, and Bessel; 4.3 The discrete
Fourier transform and the FFT; 4.4 Convolution and signal processing; 4.5
Fourier integrals; 4.6 Deconvolution and integral equations; 4.7 Wavelets
and signal processing; 5. Analytic Functions: 5.1 Taylor series and complex
integration; 5.2 Famous functions and great theorems; 5.3 The Laplace transform
and z-transform; 5.4 Spectral methods of exponential accuracy; 6. Initial
Value Problems: 6.1 Introduction; 6.2 Finite difference methods for ODEs;
6.3 Accuracy and stability for u_t = c u_x; 6.4 The wave equation and staggered
leapfrog; 6.5 Diffusion, convection, and finance; 6.6 Nonlinear flow and
conservation laws; 6.7 Fluid mechanics and Navier-Stokes; 6.8 Level sets
and fast marching; 7. Solving Large Systems: 7.1 Elimination with reordering;
7.2 Iterative methods; 7.3 Multigrid methods; 7.4 Conjugate gradients and
Krylov subspaces; 8. Optimization and Minimum Principles: 8.1 Two fundamental
examples; 8.2 Regularized least squares; 8.3 Calculus of variations; 8.4
Errors in projections and eigenvalues; 8.5 The Saddle Point Stokes problem;
8.6 Linear programming and duality; 8.7 Adjoint methods in design.
Hardback (ISBN-13: 9780961408800)
Renowned applied mathematician Gilbert Strang teaches applied mathematics with the clear explanations, examples and insights of an experienced teacher. This book progresses steadily through a range of topics from symmetric linear systems to differential equations to least squares and Kalman filtering and optimization. It clearly demonstrates the power of matrix algebra in engineering problem solving. This is an ideal book (beloved by many readers) for a first course on applied mathematics and a reference for more advanced applied mathematicians. The only prerequisite is a basic course in linear algebra.
* Published in 1986, this text remains up-to-date and a classic * Aids understanding through illuminating practical examples * The text is supplemented by exercises and solutions, assisting the reader’s grasp of the material
1. Symmetric Linear Systems: 1.1 Introduction; 1.2 Gaussian elimination;
1.3 Positive definite matrices; 1.4 Minimum principles; 1.5 Eigenvalues
and dynamical systems; 1.6 A review of matrix theory; 2. Equilibrium Equations:
2.1 A framework for the applications; 2.2 Constraints and Lagrange multipliers;
2.3 Electrical networks; 2.4 Structures in equilibrium; 2.5 Least squares
estimation and the Kalman filter; 3. Equilibrium in the Continuous Case:
3.1 One-dimensional problems; 3.2 Differential equations of equilibrium;
3.3 Laplace's equation and potential flow; 3.4 Vector calculus in three
dimensions; 3.5 Equilibrium of fluids and solids; 3.6 Calculus of variations;
4. Analytical Methods: 4.1 Fourier series and orthogonal expansions; 4.2
Discrete Fourier series and convolution; 4.3 Fourier integrals; 4.4 Complex
variables and conformal mapping; 4.5 Complex integration; 5. Numerical
Methods: 5.1 Linear and nonlinear equations; 5.2 Orthogonalization and
eigenvalue problems; 5.3 Semi-direct and iterative methods; 5.4 The finite
element method; 5.5 The fast Fourier transform; 6. Initial-Value Problems:
6.1 Ordinary differential equations; 6.2 Stability and the phase plane
and chaos; 6.3 The Laplace transform and the z-transform; 6.4 The heat
equation vs. the wave equation; 6.5 Difference methods for initial-value
problems; 6.6 Nonlinear conservation laws; 7. Network Flows and Combinatorics:
7.1 Spanning trees and shortest paths; 7.2 The marriage problem; 7.3 Matching
algorithms; 7.4 Maximal flow in a network; 8. Optimization: 8.1 Introduction
to linear programming; 8.2 The simplex method and Karmarkar's method; 8.3
Duality in linear programming; 8.4 Saddle points (minimax) and game theory;
8.5 Nonlinear optimization; Software for scientific computing; References
and acknowledgements; Solutions to selected exercises; Index.
Hardback (ISBN-13: 9780980232714)
This leading textbook for first courses in linear algebra comes from the hugely experienced MIT lecturer and author Gilbert Strang. The book’s tried and tested approach is direct, offering practical explanations and examples, while showing the beauty and variety of the subject. Unlike most other linear algebra textbooks, the approach is not a repetitive drill. Instead it inspires an understanding of real mathematics. The book moves gradually and naturally from numbers to vectors to the four fundamental subspaces. This new edition includes challenge problems at the end of each section. Preview five complete sections at math.mit.edu/linearalgebra. Readers can also view freely available online videos of Gilbert Strang’s 18.06 linear algebra course at MIT, via OpenCourseWare (ocw.mit.edu), that have been watched by over a million viewers. Also on the web (http://web.mit.edu/18.06/www/), readers will find years of MIT exam questions, MATLAB help files and problem sets to practise what they have learned.
* Strang’s online lectures and learning resources freely available via http://web.mit.edu/18.06/www/ * Gives MATLAB code to implement the key algorithms * Teaches by inspiration not repetition
1. Introduction to Vectors: 1.1 Vectors and linear combinations; 1.2 Lengths and dot products; 1.3 Matrices; 2. Solving Linear Equations: 2.1 Vectors and linear equations; 2.2 The idea of elimination; 2.3 Elimination using matrices; 2.4 Rules for matrix operations; 2.5 Inverse matrices; 2.6 Elimination = factorization: A = LU; 2.7 Transposes and permutations; 3. Vector Spaces and Subspaces: 3.1 Spaces of vectors; 3.2 The nullspace of A: solving Ax = 0; 3.3 The rank and the row reduced form; 3.4 The complete solution to Ax = b; 3.5 Independence, basis and dimension; 3.6 Dimensions of the four subspaces; 4. Orthogonality: 4.1 Orthogonality of the four subspaces; 4.2 Projections; 4.3 Least squares approximations; 4.4 Orthogonal bases and Gram-Schmidt; 5. Determinants: 5.1 The properties of determinants; 5.2 Permutations and cofactors; 5.3 Cramer's rule, inverses, and volumes; 6. Eigenvalues and Eigenvectors: 6.1 Introduction to eigenvalues; 6.2 Diagonalizing a matrix; 6.3 Applications to differential equations; 6.4 Symmetric matrices; 6.5 Positive definite matrices; 6.6 Similar matrices; 6.7 Singular value decomposition (SVD); 7. Linear Transformations: 7.1 The idea of a linear transformation; 7.2 The matrix of a linear transformation; 7.3 Diagonalization and the pseudoinverse; 8. Applications: 8.1 Matrices in engineering; 8.2 Graphs and networks; 8.3 Markov matrices, population, and economics; 8.4 Linear programming; 8.5 Fourier series: linear algebra for functions; 8.6 Linear algebra for statistics and probability; 8.7 Computer graphics; 9. Numerical Linear Algebra: 9.1 Gaussian elimination in practice; 9.2 Norms and condition numbers; 9.3 Iterative methods for linear algebra; 10. Complex Vectors and Matrices: 10.1 Complex numbers; 10.2 Hermitian and unitary matrices; 10.3 The fast Fourier transform; Solutions to selected exercises; Matrix factorizations; Conceptual questions for review; Glossary: a dictionary for linear algebra; Index; Teaching codes.
Hardback (ISBN-13: 9780961408879)
This book explains wavelets to both engineers and mathematicians. It approaches the subject with a major emphasis on the filter structures attached to wavelets. Those filters are the key to algorithmic efficiency and they are well developed throughout signal processing. Now they make possible major achievements in data analysis and compression. The explanations of difficult topics are direct, rigorous and very approachable. Many practical applications are discussed. The book is ideal as an introduction to the principles of wavelets and as a reference for the analysis and applications. Also included in Wavelets and Filter Banks are many examples to make effective use of the MATLAB Wavelet Toolbox.
* Suitable for advanced undergraduates, graduates and practitioners * Established favourite with both mathematicians and engineers because it strikes a balance between the language of mathematics and the language of engineering * Contains many exercises to allow students to test their understanding of the topics discussed
1. Introduction; 2. Filters; 3. Downsampling and upsampling; 4. Filter banks; 5. Orthogonal filter banks; 6. Multiresolution; 7. Wavelet theory; 8. Finite length signals; 9. M-channel filter banks; 10. Design methods; 11. Applications; The discrete cosine transform; The lifting scheme; Block transforms in image coding.
Series: Encyclopedia of Mathematics and its Applications (No. 12
Hardback (ISBN-13: 9780521802307)
The use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature. Other books cover portions of the material here, but there are no other books with such a wide scope. This book contains fifteen expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory and the topology of surfaces. Each chapter concludes with an extensive list of references.
* Good and timely coverage of the rapidly expanding area of topological graph theory written by world leaders in the field * Covers the main parts of the subject: topology of surfaces and graph theory * Extensive introductory chapter introduces background material
Preface; Foreword Jonathan L. Gross and Thomas W. Tucker; Introduction Lowell W. Beineke and Robin J. Wilson; 1. Embedding graphs on surfaces Jonathan L. Gross and Thomas W. Tucker; 2. Maximum genus Jianer Chen and Yuanqiu Huang; 3. Distributions of embeddings Jonathan L. Gross; 4. Algorithms and obstructions for embeddings Bojan Mohar; 5. Graph minors: generalizing Kuratowski's theorem R. Bruce Richter; 6. Colouring graphs on surfaces Joan P. Hutchinson; 7. Crossing numbers R. Bruce Richter and G. Salazar; 8. Representing graphs and maps Toma* Pisanski and Arjana *itnik; 9. Enumerating coverings Jin Ho Kwak and Jaeun Lee; 10. Symmetric maps Jozef *ira* and Thomas W. Tucker; 11. The genus of a group Thomas W. Tucker; 12. Embeddings and geometries Arthur T. White; 13. Embeddings and designs M. J. Grannell and T. S. Griggs; 14. Infinite graphs and planar maps Mark E. Watkins; 15. Open problems Dan Archdeacon; Notes on contributors; Index of definitions.