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Mathematical Methods in Physics-6 Pages 910-1011
This document provides an overview of mathematical methods in physics, including partial differential equations and differential equations. It discusses important second-order partial differential equations like the wave equation, diffusion equation, and Poisson's equation. It also covers general solutions to first and second order differential equations, separation of variables, integral transform methods, and Green's functions. Examples are provided of solving separable, homogeneous, and exact first order differential equations, as well as Bernoulli, Riccati, and other nonlinear equations.
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Mathematical Methods in Physics-6 Pages 910-1011
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- 41. 950 Mathematical Methods inPhysics 210 Partial Differential Equations: Introduction to important PDEs in Physics (wave equation, diffusion equation, Poisson’s equation, Schrodinger’s equation), general form of solution, general and particular solutions (first order, inhomogeneous, second order), characteristics and existence of solutions, uniqueness of solutions, separation of variables in Cartesian coordinates, superposition of separated solutions, separation of variables in curvilinear coordinates, integral transform methods, Green’s
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- 43. 952 Here c isa positive constant, t is time, x, y, z are Cartesian coordinates, and dimension is the number of these coordinates in the equation.
- 44. 953 Example Separable first orderequations The differential equation
- 45. 954 Homogeneous differential equations Thefirst order ODE in differential form Exact equations The first order ODE
- 46. 955 Test for exactness Thedifferential equation
- 47. 956 The Bernoulli equationis a nonlinear first order differential equation with the standard form Reduces to the linear first order ODE The Riccati equation is an important nonlinear equation with the standard form
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