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A Course in Mathematical Methods for Physicists

A Course in Mathematical Methods for Physicists

By: Russell L. Herman (author)Paperback

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Based on the author's junior-level undergraduate course, this introductory textbook is designed for a course in mathematical physics. Focusing on the physics of oscillations and waves, A Course in Mathematical Methods for Physicists helps students understand the mathematical techniques needed for their future studies in physics. It takes a bottom-up approach that emphasizes physical applications of the mathematics. The book offers: * A quick review of mathematical prerequisites, proceeding to applications of differential equations and linear algebra * Classroom-tested explanations of complex and Fourier analysis for trigonometric and special functions * Coverage of vector analysis and curvilinear coordinates for solving higher dimensional problems * Sections on nonlinear dynamics, variational calculus, numerical solutions of differential equations, and Green's functions


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 Schrodinger 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

Product Details

  • ISBN13: 9781466584679
  • Format: Paperback
  • Number Of Pages: 774
  • ID: 9781466584679
  • weight: 1950
  • ISBN10: 146658467X

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