Courses
- Differential And Integral Calculus2 (90902) תקציר הקורס:
- Partial Differential Equations (90915) תקציר הקורס:
Abstract:
Infinite series. Convergence tests. Series of f?unctions; convergence and uniform convergence. Power series; representation of functions by power series. Taylor series. F?unctionsof several variables- limits and continuity, partial and directional derivatives, Linear approximation, Gradient. The chain rule. Higher order partial derivatives and second degree Taylor polynomial. Relative/absolute maximum and minimum values. Lagrange multipliers. Multiple integrals. Fubini's theorem. Change of variables. Polar, cylindrical and spherical coordinates. Line integrals of scalar f?unctions. Line integrals of vector fields. Independence of path and Green theorem. Surface integrals of scalar f?unctions. Oriented surfaces and surface integrals of vector fields. The divergence theorem (Gauss-Ostrogradsky). Stokes' theorem. Applications.Abstract:
Derivation of the wave equation.
D’Alembert solution for an infinite string, wave bouncing from a clamped and a free end of a string.
Well-posedness. Classification of second order linear problems.
Canonical forms. Laplace equation.
Solution of the wave equation on a bounded interval by separations of variables.
Uniqueness of the solution using the energy method. The maximum principle.
Separation of variables to Laplace equation in a rectangular and in a circle.
The heat equation. The maximum principle for the heat equation.
Solution of the inhomogeneous problem.
Solution of partial differential equations using Integral transforms.
Waves in a rounded membrane and Bessel equation.