Ordinary and Partial Differential Equations With Special Functions, Fourier Series, and Boundary Value Problems /

• Κύριοι συγγραφείς: Agarwal, Ravi P. (Συγγραφέας), O’Regan, Donal (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York, 2009.
• Σειρά: Universitext
• Θέματα: Mathematics.; Differential equations.; Partial differential equations.; Numerical analysis.; Physics.; Applied mathematics.; Engineering mathematics.; Partial Differential Equations.; Ordinary Differential Equations.; Numerical Analysis.; Mathematical Methods in Physics.; Appl.Mathematics/Computational Methods of Engineering.

This textbook provides a genuine treatment of ordinary and partial differential equations (ODEs and PDEs) through 50 class tested lectures. Key Features: Explains mathematical concepts with clarity and rigor, using fully worked-out examples and helpful illustrations. Develops ODEs in conjuction with...

Πίνακας περιεχομένων:

• Solvable Differential Equations
• Second-Order Differential Equations
• Preliminaries to Series Solutions
• Solution at an Ordinary Point
• Solution at a Singular Point
• Solution at a Singular Point (Cont’d.)
• Legendre Polynomials and Functions
• Chebyshev, Hermite and Laguerre Polynomials
• Bessel Functions
• Hypergeometric Functions
• Piecewise Continuous and Periodic Functions
• Orthogonal Functions and Polynomials
• Orthogonal Functions and Polynomials (Cont’d.)
• Boundary Value Problems
• Boundary Value Problems (Cont’d.)
• Green’s Functions
• Regular Perturbations
• Singular Perturbations
• Sturm–Liouville Problems
• Eigenfunction Expansions
• Eigenfunction Expansions (Cont’d.)
• Convergence of the Fourier Series
• Convergence of the Fourier Series (Cont’d.)
• Fourier Series Solutions of Ordinary Differential Equations
• Partial Differential Equations
• First-Order Partial Differential Equations
• Solvable Partial Differential Equations
• The Canonical Forms
• The Method of Separation of Variables
• The One-Dimensional Heat Equation
• The One-Dimensional Heat Equation (Cont’d.)
• The One-Dimensional Wave Equation
• The One-Dimensional Wave Equation (Cont’d.)
• Laplace Equation in Two Dimensions
• Laplace Equation in Polar Coordinates
• Two-Dimensional Heat Equation
• Two-Dimensional Wave Equation
• Laplace Equation in Three Dimensions
• Laplace Equation in Three Dimensions (Cont’d.)
• Nonhomogeneous Equations
• Fourier Integral and Transforms
• Fourier Integral and Transforms (Cont’d.)
• Fourier Transform Method for Partial DEs
• Fourier Transform Method for Partial DEs (Cont’d.)
• Laplace Transforms
• Laplace Transforms (Cont’d.)
• Laplace Transform Method for Ordinary DEs
• Laplace Transform Method for Partial DEs
• Well-Posed Problems
• Verification of Solutions.