MAT 1332 Lecture Notes - Lecture 20: Row Echelon Form, Elementary Matrix, Diagonal Matrix

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1332
• Professor: Eric Hua

Document Summary

M3: systems of di erential equations, linear case 53. 6. 3 6. 5: integration review: de nite integral = limit of riemann sum: Z b a f (x)dx = lim n n. Xi=1 f (ci) x, where x0 = a, x1 = a + b a xi 1 ci xi. The relation to area is: n , x2 = a + 2(b a) n. ,, xn = a + n(b a) n = b, x = b a n , Z b a f (x)dx = area above x-axis - area below x-axis: the fundamental theorem of calculus : If f (x) = f (x), then z b. If g(x) =z x a a: the substitution rules: f (x)dx = f (b) f (a). f (t)dt, then g (x) = f (x). result, we have to replace u by g(x); For inde nite integral: z f (g(x))g (x)dx = z f (u)du,