QuickStudy Differential Equations

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Will edit with respect to usefulness when I've completed the class but wanted to outline the topics contained in this Quick Study for Differential Equations (DEQ going forward) because it was hard for me to get the full picture with just pieces of the picture. Looking through the cheat sheet there appears to be a well-balanced review of materials learned in the calculus series and a more rigorous treatment of that material as well as new materials specific to DEQs. There are examples of each topic as well as definitions of the terminology. Hope this helps! Page 1. Review of the Indefinite Integral Review of Integration (in bold: "To perform integration by parts" and "To perform integration by substitution" Basic Definitions (in bold: "Solutions of a DEQ" and "Verifying a Solution of a DEQ") Classifying DEQs (in bold: "Classification by Type", "Classification by Order" and "Classification by Linearity") Page 2. Initial-Value Problems (in bold: "Existence and Uniqueness of a Solution for IVPs") Separable DEQs (in bold: "Solve a First-Order ODE by Separation of Variables" and "Solve a First-Order IVP by Separation of Variables") Exact Equations (in bold: "Differential Form", "Exact Differentials and Exact Equations") Solving a First-Order Linear Equation (in bold: "Integrating Factors" and "To solve a first-order linear DEQ") Page 3. First-Order Homogenous Equations (in bold: "Solution by Substitution", "To solve a homogeneous DEQ") Bernoulli Equations (in bold "To solve a Bernoulli DEQ") Applications of First-Order DEQs (in bold: "Growth & Decay" and "Heating & Cooling") Page 4. Higher Order Linear DEQs (in bold: "Homogeneous Equations", "Boundary-Value Problems" and "Superposition Principle for Linear Homogeneous Equations") Reduction of Order Second-Order Homogeneous Linear Equations with Constant Coefficients (in bold: "Characteristic Equations" [CE going forward], "Roots of the CE" and 3 cases) Higher-Order Homogeneous Linear Equations with Constant Coefficients (in bold: "CE" and "General Solution") Page 5. Second-Order Nonhomogeneous Linear Differential Equations (in bold: "Complementary, Particular and General Solutions") The Method of Undetermined Coefficients (in bold: "Rules for Applying the Method of Undetermined Coefficient" and 3 rules) Variation of Parameters (in bold: "The Wronskian" and "Applying the Method of Variation of Parameters") Series Solutions of Linear Equations (in bold: "Power Series" and "To solve a 2nd-Order Homogeneous LEs using the power series method) Page 6 Series Solutions of Linear Equations continued from page 5 Laplace Transform (LT going forward) (in bold: "Inverse LT", "Transform of a Derivative", "Using LTs to solve DEQs" and "To solve a DEQ with the LT") Numerical Methods for Solving DEQs (in bold: "Direction Fields", "Euler's Method", "To use Euler's Method to solve 1st-order IVPs" and "Runge-Kutta Method") Partial DEQs

Very interesting and concise information. I like it very much.

Bien pour un se remémorer ou apprendre en plus du cours les méthodes de résolutions des équa diff du 1er et 2nc degré, avec ou sans second membre. Il n'y a que 6 pages mais il y a un exemple détaillé pas à pas pour chaque type d'équa diff. Pour le prix dérisoire, à moins d'être allergique à l'anglais, c'est à avoir avec soi quand on est étudiant en licence scientifique.

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