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