Math 267 Review Sheet: Fall2004 - Topics in Differential Equations and Laplace Transforms , Study notes of Mathematics

Download Math 267 Review Sheet: Fall2004 - Topics in Differential Equations and Laplace Transforms and more Study notes Mathematics in PDF only on Docsity! Math 267 Review Sheet Fall2004@ISU: 1. First-order Differential Equations (Chapter 1-2) —Identify the types of equations (integrable eqs, saparable eqs, linear eqs, exact eqs); — Substitution methods(homogeneous equation, Bernouli equation, y′ = f(ax + by + c)); 2. Linear Equations of Higher Order (Chapter 4) — Solution structure — Homogeneous equations with constant Coefficients — Variation of Parameters — Method of undetermined coefficients 3. Laplace Transform Methods (Chapter 5) — Definition of Laplace Transform & Inverse Transform — Transformation of Initial Value Problems — Some formulas and important properties — Solving initial value problem via Laplace Transform. 4*. Numerical methods (Chapter 6) — Euler’s method — Runge-Kutta Methods 5. Linear Systems of Differential Equation (Chapter 7-9) — Higher order equations & First-order systems; — The Method of Elimination for solving linear system; — Matrix and Linear Systems; — Solution Structure of linear systemx′ = Ax + f(t); — The Eigenvalue Method for homogeneous Systems. — Variation of parameters for inhomogeneous system. 6*. Qualitative analysis of Systems (9.3, 9.6 + Chapter 10 ) — The linearization of a nonlinear system — Type and Stability of equilibrium points; — Phase plane analysis; 1