Chapter 5 - Modeling with Differential Equations
- Index
-
About this Chapter
- Section 5.1 Raindrops
- 5.1.1 Galileo's Model
- 5.1.2 Stokes' Law
- 5.1.3 The Velocity-Squared Model
- Section Summary
- Exercises
- Problems
- Section 5.2 Euler's Method
- 5.2.1 A Numerical Solution for the Velocity-Squared Model
- 5.2.2 The General Euler's Method
- Section Summary
- Exercises
- Problems
- Section 5.3 Periodic Motion
- 5.3.1 Spring Mass Systems
- 5.3.2 A Differential Equation for Spring Motion
- 5.3.3 Circular Motion: Sines and Cosines
- 5.3.4 Period and Frequency
- 5.3.5 Derivatives of Sine and Cosine 1: Examination
- 5.3.6 Derivatives of Sine and Cosine 2: Calculation
- Section Summary
- Exercises
- Problems
- Section 5.4 Modeling With Circular Functions
- 5.4.1 How Much Daylight?
- 5.4.2 Euler's Method Solutions for the Spring Equation
- 5.4.3 Symbolic Solutions of the Spring Equation
- Section Summary
- Exercises
- Problems
- Section 5.5 Trigonometric and Inverse Trigonometric Functions
- 5.5.1 How Tall is a Tree?
- 5.5.2 Derivative of the Tangent Function
- 5.5.3 Inverse Trigonometric Functions
- Section Summary
- Exercises
- Problems
- Section 5.6 Derivative Calculations
- 5.6.1 Why Hand Calculation?
- 5.6.2 Calculations with Algebraic Functions
- 5.6.3 Calculations with Transcendental Functions
- Section Summary
- Exercises
- Problems
- Chapter Summary
- Chapter Review
- Concepts and Applications
- Formulas
- Project 1. Hyperbolic and Inverse Hyperbolic Functions
- Project 2. The SIR Model of the Spread of Disease