Applied mathematical methods
/ Bhaskar Dasgupta
- New Delhi : Pearson Education, 2007
- xvii, 505 p.
includes index
1. Preliminary background 2. Matrices and linear transformations 3. Operational fundamentals of linear algebra 4. Systems of linear equations 5. Gauss elimination family of methods 6. Special systems and special methods 7. Numerical aspects in linear systems 8. Eigenvalues and eigenvectors 9. Diagonalization and similarity transformations 10. Jacobi and givens rotation methods 11. Householder transformation and tridiagonal matrices 12. Qr decomposition method 13. Eigenvalue problem of general matrices 14. Singular value decomposition 15. Vector spaces: fundamental concepts 16. Topics in multivariate calculus 17. Vector analysis: curves and surfaces 18. Scalar and vector fields 19. Polynomial equations 20. Solution of non liner equations and systems 21. Optimization: introduction 22. Multivariate optimization 23. Methods of nonlinear optimization 24. Constrained optimization 25. Linear and quadratic programming problems 26. Interpolation and approximation 27. Basic methods of numerical integration 28. Advanced topics in numerical integration 29. Numerical solution of ordinary differential equations 30. Ode solutions: advanced issues 31. Existence and uniqueness theory 32. First order ordinary differential equations 33. Second order liner homogeneous ode's 34. Second order linear non-homogeneous ode's 35. Higher order linear ode's 36. Laplace transforms 37. Ode systems 38. Stability of dynamic systems 39. Series solutions and special functions 40. Sturm-liouville theory 41. Fouriers series and integrals 42. Fourier transforms 43. Minimax approximation 44. Partial differential equations 45. Analytic functions 46. Integrals in the complex plane singularities of complex functions 47. Variational calculus