Differential Equations Workbook For Dummies®

Table of contents

1. Copyright
2. About the Author
3. Dedication
4. Author's Acknowledgments
5. Publisher's Acknowledgments
6. Introduction
7. Tackling First Order Differential Equations
   1. Looking Closely at Linear First Order Differential Equations
      1. Identifying Linear First Order Differential Equations
      2. Solving Linear First Order Differential Equations That Don't Involve Terms in y
      3. Solving Linear First Order Differential Equations That Involve Terms in y
      4. Integrating Factors: A Trick of the Trade
      5. Answers to Linear First Order Differential Equation Problems
   2. Surveying Separable First Order Differential Equations
      1. The Ins and Outs of Working with Separable Differential Equations
      2. Finding Implicit Solutions
      3. Getting Tricky: Separating the Seemingly Inseparable
      4. Practicing Your Separation Skills
      5. An Initial Peek at Separable Equations with Initial Conditions
      6. Answers to Separable First Order Differential Equation Problems
   3. Examining Exact First Order Differential Equations
      1. Exactly, Dear Watson: Determining whether a Differential Equation Is Exact
      2. Getting Answers from Exact Differential Equations
      3. Answers to Exact First Order Differential Equation Problems
8. Finding Solutions to Second and Higher Order Differential Equations
   1. Working with Linear Second Order Differential Equations
      1. Getting the Goods on Linear Second Order Differential Equations
      2. Finding the Solution When Constant Coefficients Come into Play
      3. Answers to Linear Second Order Differential Equation Problems
   2. Tackling Nonhomogeneous Linear Second Order Differential Equations
      1. Finding the General Solution for Differential Equations with a Nonhomogeneous erx Term
      2. Getting the General Solution When g(x) Is a Polynomial
      3. Solving Equations with a Nonhomogeneous Term That Involves Sines and Cosines
      4. Answers to Nonhomogeneous Linear Second Order Differential Equation Problems
   3. Handling Homogeneous Linear Higher Order Differential Equations
      1. Distinctly Different: Working with Real and Distinct Roots
      2. A Cause for Complexity: Handling Complex Roots
      3. Identity Issues: Solving Equations When Identical Roots Are Involved
      4. Answers to Homogeneous Linear Higher Order Differential Equation Problems
   4. Taking On Nonhomogeneous Linear Higher Order Differential Equations
      1. Seeking Out Solutions of the Form Aerx
      2. Trying for a Solution in Polynomial Form
      3. Working with Solutions Made Up of Sines and Cosines
      4. Answers to Nonhomogeneous Linear Higher Order Differential Equation Problems
9. The Power Stuff: Advanced Techniques
   1. Using Power Series to Solve Ordinary Differential Equations
      1. Checking On a Series with the Ratio Test
      2. Shifting the Series Index
      3. Exploiting the Power of Power Series to Find Series Solutions
      4. Answers to Solving Ordinary Differential Equations with Power Series
   2. Solving Differential Equations with Series Solutions Near Singular Points
      1. Finding Singular Points
      2. Classifying Singular Points as Regular or Irregular
      3. Working with Euler's Equation
      4. Solving General Differential Equations with Regular Singular Points
      5. Answers to Solving Differential Equations with Series Solutions Near Singular Points
   3. Using Laplace Transforms to Solve Differential Equations
      1. Finding Laplace Transforms
      2. Calculating the Laplace Transforms of Derivatives
      3. Using Laplace Transforms to Solve Differential Equations
      4. Answers to Laplace Transform Problems
   4. Solving Systems of Linear First Order Differential Equations
      1. Back to the Basics: Adding (And Subtracting) Matrices
      2. An Exercise in Muddying Your Mind: Multiplying Matrices
      3. Determining the Determinant
      4. More Than Just Tongue Twisters: Eigenvalues and Eigenvectors
      5. Solving Differential Equation Systems
      6. Answers to Systems of Linear First Order Differential Equation Problems
10. The Part of Tens
    1. Ten Common Ways of Solving Differential Equations
       1. Looking at Linear Equations
       2. Scoping Out Separable Equations
       3. Applying the Method of Undetermined Coefficients
       4. Honing in on Homogeneous Equations
       5. Examining Exact Equations
       6. Finding Solutions with the Help of Integrating Factors
       7. Getting Serious Answers with Series Solutions
       8. Turning to Laplace Transforms for Solutions
       9. Determining whether a Solution Exists
       10. Solving Equations with Computer-Based Numerical Methods
    2. Ten Real-World Applications of Differential Equations
       1. Calculating Population Growth
       2. Determining Fluid Flow
       3. Mixing Fluids
       4. Finding Out Facts about Falling Objects
       5. Calculating Trajectories
       6. Analyzing the Motion of Pendulums
       7. Applying Newton's Law of Cooling
       8. Determining Radioactive Decay
       9. Studying Inductor-Resistor Circuits
       10. Calculating the Motion of a Mass on a Spring
11. Index