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MATH 310 (10)
Sj Ruuth (2)
Final

# final review note

4 Pages
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School
Department
Mathematics
Course
MATH 310
Professor
Sj Ruuth
Semester
Summer

Description
By chapter: ▯ Chapter 1: { direction ▯elds { classi▯cation of DEs: order; linear vs. nonlinear; ordinary vs. partial; system of eqns vs. a single equation ▯ Chapter 2: { methods for solving equations: ▯ x2.1 integrating factors for 1st order linear DEs ▯ x2.2 separable equations ▯ x2.2 homogeneous equations ▯ x2.6 exact equations ▯ integrating factors for exact equations { theory: ▯ x2.4: existence and uniqueness { miscellaneous techniques: ▯ x2.5 autonomous equations and the phase line ▯ x2.7 Euler’s method ▯ x2.9 ▯rst-order di▯erence equations { applications: ▯ x2.3: modeling with ▯rst order equations ▯ Chapter 3: { methods for solving equations: ▯ xx3.1, 3.3, 3.4: solving ay +by +c = 0 via ar +br+c = 0 with roots r 1nd r : 2 r1t r2t ▯ x3.1: r16= r2real numbers: y(t) = c e 1 + c 2 ▯ x3.3: r ;r = ▯ ▯ i▯: y(t) = c e ▯t cos(▯t) + c e ▯tsin(▯t) 1 2 1 2 ▯ x3.4: r1= r 2 R: y(t) = c e 1 r1t+ c 2e r1t ▯ xx3.4, 3.5, 3.6: three methods: ▯ x3.4: reduction of order ▯ x3.5: undetermined coe▯cients ▯ x3.6: variation of parameters { theory: ▯ x3.2: The Wronskian, and various theorems { applications: ▯ x3.7: application to mechanical & electrical vibrations ▯ mu + u + ku = F ▯ LQ + RQ + 0 1Q = E C 1 Methods: ▯ x2.1: integrating factor for 1st order linear equation: Given y + p(t)y = g(t); compute R p(t) dt; ▯(t) = e and solve Z ▯y = g▯ dt: ▯ x2.2: se
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