MAT3320- Midterm Exam Guide - Comprehensive Notes for the exam ( 80 pages long!)

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 3320
• Professor: Eric Hua

Document Summary

10. 1 bessel"s equation: the solution jn(x) of the first kind. Review of methods in solving di erential equations: separable de: dy. De = ode + pde dx = f (x)g(y), dy/g(y) = f (x)dx: homogeneous second order linear eqn: ay + by + cy = 0. Then y2 = u(x)y1, where u = 1 y2. Solve the di erential equation y y = 0. Solve the di erential equation y 2y + y = 0. (1) Functions y1, y2, de ned on an interval a x b are called orthogonal on a x b with respect to a weight function p(x) > 0 if. The norm kymk is de ned by a p(x)ym(x)yn(x) dx = 0 (m 6= n). kymk =sz b a p(x)y2 m(x) dx. (2) (3) The functions are called orthonormal on a x b with respect to a weight func- tion if they are orthogonal and have norm 1.