A course in mathematical methods for physicists. (2013)

• Record Type: Book
• Further Information: Note: By Russell L. Herman.
• Authors: Herman, Russell L
• Contents: Introduction and Review; What Do I Need To Know From Calculus?; What I Need From My Intro Physics Class?; Technology and Tables; Appendix: Dimensional Analysis; Problems; ; Free Fall and Harmonic Oscillators; Free Fall; First Order Differential Equations; The Simple Harmonic Oscillator; Second Order Linear Differential Equations; LRC Circuits; Damped Oscillations; Forced Systems; Cauchy-Euler Equations; Numerical Solutions of ODEs; Numerical Applications; Linear Systems; Problems; ; Linear Algebra; Finite Dimensional Vector Spaces; Linear Transformations; Eigenvalue Problems; Matrix Formulation of Planar Systems; Applications; Appendix: Diagonalization and Linear Systems; Problems; ; Nonlinear Dynamics; Introduction; The Logistic Equation; Autonomous First Order Equations; Bifurcations for First Order Equations; Nonlinear Pendulum; The Stability of Fixed Points in Nonlinear Systems; Nonlinear Population Models; Limit Cycles; Nonautonomous Nonlinear Systems; Exact Solutions Using Elliptic Functions; Problems; ; The Harmonics of Vibrating Strings; Harmonics and Vibrations; Boundary Value Problems; Partial Differential Equations; The 1D Heat Equation; The 1D Wave Equation; Introduction to Fourier Series; Fourier Trigonometric Series; Fourier Series Over Other Intervals; Sine and Cosine Series; Solution of the Heat Equation; Finite Length Strings; The Gibbs Phenomenon; Green’s Functions for 1D Partial Differential Equations; Derivation of Generic 1D Equations; Problems; ; Non-sinusoidal Harmonics and Special Functions; Function Spaces; Classical Orthogonal Polynomials; Fourier-Legendre Series; Gamma Function; Fourier-Bessel Series; Sturm-Liouville Eigenvalue Problems; Nonhomogeneous Boundary Value Problems - Green’s Functions; Appendix: The Least Squares Approximation; Appendix: The Fredholm Alternative Theorem; Problems; ; Complex Representations of Functions; Complex Representations of Waves; Complex Numbers; Complex Valued Functions; Complex Differentiation; Complex Integration; Problems; ; Transform Techniques in Physics; Introduction; Complex Exponential Fourier Series; Exponential Fourier Transform; The Dirac Delta Function; Properties of the Fourier Transform; The Convolution Operation; The Laplace Transform; Applications of Laplace Transforms; The Convolution Theorem; The Inverse Laplace Transform; Transforms and Partial Differential Equations; Problems; ; Vector Analysis and EM Waves; Vector Analysis; Electromagnetic Waves; Curvilinear Coordinates; Tensors; Problems; ; Extrema and Variational Calculus; Stationary and Extreme Values of Functions; The Calculus of Variations; Hamilton’s Principle; Geodesics; Problems; ; Problems in Higher Dimensions; Vibrations of Rectangular Membranes; Vibrations of a Kettle Drum; Laplace’s Equation in 2D; Three Dimensional Cake Baking; Laplace’s Equation and Spherical Symmetry; Schrödinger Equation in Spherical Coordinates; Solution of the 3D Poisson Equation; Green’s Functions for Partial Differential Equations; Problems; ; Review of Sequences and Infinite Series; Sequences of Real Numbers; Convergence of Sequences; Limit Theorems; Infinite Series; Convergence Tests; Sequences of Functions; Infinite Series of Functions; Special Series Expansions; The Order of Sequences and Functions; Problems
• Publisher Details: Place of publication not identified : CRC Press
• Publication Date: 2013
• Extent: 1 online resource (774 pages), (420 illustrations)
• Subjects: 530.15; Mathematical physics
• Languages: English
• ISBNs: 9781466584686; 1466584688
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.