Differential Equations (Cliffs Quick Review)

CliffsQuickReview course guides cover the essentials of your toughest subjects. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions.Whether you need a course supplement, help preparing for an exam, or a concise reference for the subject, CliffsQuickReview Differential Equations can help. This guide covers first-order and second-order equations, power series, and more. In no time, you'll be tackling topics such asLinear and homogeneous equationsIntegrating factorsThe Laplace transform operatorSimple harmonic motionOrthogonal trajectoriesCliffsQuickReview Differential Equations acts as a supplement to your other learning materials. Use this reference in any way that fits your personal style for study and review — you decide what works best with your needs. You can flip through the book until you find what you're looking for — it's organized to gradually build on key concepts. You can also get a feel for the scope of the book by checking out theContents pages that give you a chapter-by-chapter list of topics.Tabs at the top of each page that tell you what topic is being covered.Heading and subheading structure that breaks sections into clearly identifiable bites of information.Keywords in boldface type throughout the text.Wealth of formulas and figures designed to provide visual references.With titles available for all the most popular high school and college courses, CliffsQuickReview guides are comprehensive resources that can help you get the best possible grades. Cliffs Quick Review Differential Equations......Page 3 Contents......Page 5 Differentiation......Page 7 Partial Differentiation......Page 14 Integration......Page 16 Techniques of Indefinite Integration......Page 18 Partial Integration......Page 22 Introduction to Differential Equations......Page 24 Exact Equations......Page 35 Integrating Factors......Page 40 Seperable Equations......Page 47 Homogeneous Equations......Page 53 Linear Equations......Page 58 Bernoulli's Equation......Page 66 Linear Combinations & Linear Independence......Page 69 Linear Equations......Page 72 Homogeneous Equations......Page 73 Homogeneous Linear Equations with Constant Coefficients......Page 77 The Method of Undeteremined Coefficients......Page 83 Variation of Parameters......Page 96 Cauchy-Euler Equidimensional Equation......Page 103 Reduction of Order......Page 106 Introduction to Power Series......Page 119 Taylor Series......Page 123 Power Series Solutions of Differential Equations......Page 129 Linear Transformations......Page 141 The Laplace Transform Operator......Page 143 Using the Laplace Transform to Solve Differential Equations......Page 154 Applications of First-Order Equations......Page 163 Applications of Second-order Equations......Page 177 Cliffs Quick Review Differential Equations 3 Contents 5 Review & Introduction 7 Differentiation 7 Partial Differentiation 14 Integration 16 Techniques of Indefinite Integration 18 Partial Integration 22 Introduction to Differential Equations 24 First-Order Equations 35 Exact Equations 35 Integrating Factors 40 Seperable Equations 47 Homogeneous Equations 53 Linear Equations 58 Bernoulli's Equation 66 Second-Order Equations 69 Linear Combinations & Linear Independence 69 Linear Equations 72 Homogeneous Equations 73 Homogeneous Linear Equations with Constant Coefficients 77 The Method of Undeteremined Coefficients 83 Variation of Parameters 96 Cauchy-Euler Equidimensional Equation 103 Reduction of Order 106 Power Series 119 Introduction to Power Series 119 Taylor Series 123 Power Series Solutions of Differential Equations 129 The Laplace Transform 141 Linear Transformations 141 The Laplace Transform Operator 143 Using the Laplace Transform to Solve Differential Equations 154 A Few Applications 163 Applications of First-Order Equations 163 Applications of Second-order Equations 177 CliffsQuickReview course guides cover the essentials of your toughest subjects. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions. Whether you need a course supplement, help preparing for an exam, or a concise reference for the subject, CliffsQuickReview Differential Equations can help. This guide covers first-order and second-order equations, power series, and more. In no time, you'll be tackling topics such as Linear and homogeneous equations Integrating factors The Laplace transform operator Simple harmonic motion Orthogonal trajectories CliffsQuickReview Differential Equations acts as a supplement to your other learning materials. Use this reference in any way that fits your personal style for study and review -- you decide what works best with your needs. You can flip through the book unt... A comprehensive review guide to help you refresh your study. This guide is particularly useful for midterms and final exams, condensing a semester's worth of information into one concise volume This logically presented, easy-to-grasp review gives you the reference you want to effectively organize your introductory-level course work.