MATH 231 Fall 2008: Topics in Equations, Series Methods, and Laplace Transform, Study notes of Differential Equations

Download MATH 231 Fall 2008: Topics in Equations, Series Methods, and Laplace Transform and more Study notes Differential Equations in PDF only on Docsity! MATH 231, FALL 2008- OUTLINE OF TOPICS (Numbers in parenthesis refer to lessons in Tenenbaum-Pollard) 1.First-order equations. Equations with separable variables (6C)/Equations with homogeneous coefficients (7)/ Exact differential equations (9)/Linear first-order equations (11ABC)/ Bernouilli equations (11D)/ Applications (14B, 15, 17) 2.Second-order linear equations (complex numbers are needed- review material in lesson 18) Homogeneous equations with constant coefficients(20)/Non-homogeneous equations (21,22)/Non-constant coefficients: reduction of order (23)/ appli- cations: harmonic motion, damped motion, mechanics, circuits (ch. 6) 3.Systems of first-order equations. 2X2 homogeneous systems: eigenvalues, phase-plane diagrams/ solution methods: linear algebra, substitution/ non-homogeneous systems/Applications in mechanics: coupled springs (33A), motion under central force (34)/ solu- tion of special second-order equations (35)/ other applications (36) 4. Series methods. Power series solutions of linear DEs (37)/Legendre DE and Legendre polynomials (41)/ The Bessel DE (42) 5. Laplace transform (27) 1