Applied Mathematics
Published on 17. September 2012
Book
Paperback/Softback
XI, 368 pages
978-1-4613-5493-2 (ISBN)
Description
This volume is a textbook for a year-long graduate level course in All research universities have applied mathematics for scientists and engineers. such a course, which could be taught in different departments, such as mathematics, physics, or engineering. I volunteered to teach this course when I realized that my own research students did not learn much in this course at my university. Then I learned that the available textbooks were too introduc tory. While teaching this course without an assigned text, I wrote up my lecture notes and gave them to the students. This textbook is a result of that endeavor. When I took this course many, many, years ago, the primary references were the two volumes of P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953). The present text returns the contents to a similar level, although the syllabus is quite different than given in this venerable pair of books.
Reviews / Votes
` ...the treatment is user-friendly. [...] The printing is excellent and the publishers are to be thanked for producing a hard back volume for what is, these days, a reasonable price. I have no hesitation giving a warm recommendation for this book. 'Mathematical Reviews, 2003
More details
Edition
Softcover reprint of the original 1st ed. 2002
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Research
Illustrations
XI, 368 p.
Dimensions
Height: 254 mm
Width: 178 mm
Thickness: 21 mm
Weight
721 gr
ISBN-13
978-1-4613-5493-2 (9781461354932)
DOI
10.1007/978-1-4615-1315-5
Schweitzer Classification
Other editions
Additional editions
Gerald D. Mahan
Applied Mathematics
Book
12/2001
Kluwer Academic/Plenum Publishers
€106.99
Shipment within 10-15 days
Content
1. Determinants.- 1.1. Cramer's Rule.- 1.2. Gaussian Elimination.- 1.3. Special Determinants.- 2. Matrices.- 2.1. Several Theorems.- 2.2. Linear Equations.- 2.3. Inverse of a Matrix.- 2.4. Eigenvalues and Eigenvectors.- 2.5. Unitary Transformations.- 2.6. Hon-Hermitian Matrices.- 2.7. A Special Matrix.- 2.8. Gram-Schmidt.- 2.9. Chains.- 3. Group Theory.- 3.1. Basic Properties of Groups.- 3.2. Group Representations.- 3.3. Characters.- 3.4. Direct Product Groups.- 3.5. Basis Functions.- 3.6. Angular Momentum.- 3.7. Products of Representations.- 3.8. Quantum Mechanics.- 3.9. Double Groups.- 4. Complex Variables.- 4.1. Introduction.- 4.2. Analytic Functions.- 4.3. Multivalued Functions.- 4.4. Contour Integrals.- 4.5. Meromorphic Functions.- 4.6. Higher Poles.- 4.7. Integrals Involving Branch Cuts.- 4.8. Approximate Evaluation of Integrals.- 5. Series.- 5.1. Taylor Series.- 5.2. Convergence.- 5.3. Laurent Series.- 5.4. Meromorphic Functions.- 5.5. Asymptotic Series.- 5.6. Summing Series.- 5.7. Padé Approximants.- 6. Conformal Mapping.- 6.1. Laplace's Equation.- 6.2. Mapping.- 6.3. Examples.- 6.4. Schwartz-Christoffel Transformations.- 6.5. van der Pauw.- 7. Markov Averaging.- 7.1. Random Walk.- 7.2. Speckle.- 7.3. Inhomogeneous Broadening.- 8. Fourier Transforms.- 8.1. Fourier Transforms.- 8.2. Laplace Transforms.- 8.3. Wavelets.- 9. Equations of Physics.- 9.1. Boundary and Initial Conditions.- 9.2. Boltzmann Equation.- 9.3. Solving Differential Equations.- 9.4. Elliptic Integrals.- 10. One Dimension.- 10.1. Introduction.- 10.2. Diffusion Equation.- 10.3. Wave Equation.- 11. Two Dimensions.- 11.1. Rectangular Coordinates.- 11.2. Polar Coordinates.- 12. Three Dimensions.- 12.1. Cartesian Coordinates.- 12.2. Cylindrical Coordinates.- 12.3. Spherical Coordinates.- 12.4.Problems Inside a Sphere.- 12.5. Vector Wave Equation.- 13. Odds and Ends.- 13.1. Hypergeometric Functions.- 13.2. Orthogonal Polynomials.- 13.3. Sturm-Liouville.- 13.4. Green's Functions.- 13.5. Singular Integral Equations.