Differential Equations: a QuickStudy Laminated Reference Guide

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 helpful - teen loves them

I'm a Electrical Engineering Student. I made a folder of lots of these quick reference guides. No one's memory is perfect. All these concepts build on top of one another and there is so much to remember. When I'm working on a project or homework there are times I'm not 100% sure of a concept I learned in the past. It saves me so much time to just pull out my quick study guide, look up the concept real quick and review. Then I can quickly get back to the problem I'm working on with greater confidence.

If you are reading this you are in one of two boats...Boat A, you are a new student taking diff eq, if this is you this will help but chances are the nomenclature between you class and this sheet is different and may be a pain. Boat B, you use diff eq at your job or once in a while and need a quick reference. If this is the case it will work great, not allot of info on PDEs or more complex forms of expansion but it will get you by. It is not as helpful as a Table of integrals or derivatives but still useful.

I am a math major and I love this sheet. It has a lot of the really important things summarized in this sheet and would recommend it for anything taking this class or needing review for PDE or anything above. I have a whole stack of these cheat sheets and this one is my favorite and the most useful. PLEASE please come out with PDE, Differential Geometry, Vector Calculus, and more on biochemistry. I would buy those!!!!! ❤️❤️❤️❤️❤️

Does not cover everything we do in class but helps a lot on the homework. It is nice to have a great summary for review later.

It's been a lot of years since I studied this in college. This is a great review of the subject. Brings it back without using a big book on the subject.

As an instructor, I think this is a great study tool for students!