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Full Description
Tips, tricks and lots of practice to help students get a handle on these complex calculus problems
Pre-calculus classes prepare students for studies in calculus and other advanced Differential equations are essential in physics, economics, engineering, and many other scientific and technical disciplines. This new Dummies Workbook is a hands-on companion for students grappling with differential equations in classes such as calculus, AP calculus, physics, and engineering. It features numerous practice exercises and clear, concise examples to help students improve their problem-solving skills and score better in science, math, and standardized tests. This practice-oriented workbook covers such challenging topics as first-order and second-order differential equations, constant coefficients, undetermined coefficients, variation of parameters, initial-value problems, the Laplace transform, and more.
Contents
Introduction 1
Part I: Tackling First Order Differential Equations 5
Chapter 1: Looking Closely at Linear First Order Differential Equations 7
Chapter 2: Surveying Separable First Order Differential Equations 29
Chapter 3: Examining Exact First Order Differential Equations 59
Part II: Finding Solutions to Second and Higher Order Differential Equations 79
Chapter 4: Working with Linear Second Order Differential Equations 81
Chapter 5: Tackling Nonhomogeneous Linear Second Order Differential Equations 105
Chapter 6: Handling Homogeneous Linear Higher Order Differential Equations 129
Chapter 7: Taking On Nonhomogeneous Linear Higher Order Differential Equations 153
Part III: The Power Stuff: Advanced Techniques 175
Chapter 8: Using Power Series to Solve Ordinary Differential Equations 177
Chapter 9: Solving Differential Equations with Series Solutions Near Singular Points 199
Chapter 10: Using Laplace Transforms to Solve Differential Equations 225
Chapter 11: Solving Systems of Linear First Order Differential Equations 249
Part IV: The Part of Tens 273
Chapter 12: Ten Common Ways of Solving Differential Equations 275
Chapter 13: Ten Real-World Applications of Differential Equations 279
Index 283
