**Ch 6 - Differential Equations**

**Chapter 6 PDF Resource**

calculus_chapter_6.pdf |

**Lecture Notes & Videos**

Lecture Notes on Slope Fields

Internet Video: *** Matching Slope Fields ***

This video shows good examples of how to do match a slope field to its differential equation and also how to match a slope field with the equation it could represent.

Internet Video: Slope Fields and Differential Equations

This video shows you how to draw a slope field, and then how to solve the differential equation analytically to verify your slope field.

Internet Video: Differential Equation & Slope Field

This is a nice video that shows you how to create a slope field for a Differential Equation and then solve the Differential Equation with both a General Solution and a Unique Solution.

Euler's Method Lecture Notes

-----VIDEO: Euler's Method

Section 6-2

Growth and Decay Models

-----VIDEO: Exponential Growth & Decay

Section 6-2 (Day 2) and Section 6-3

More on Differential Equations

-----VIDEO: More on Differential Equations - Part 1 of 3

-----VIDEO: More on Differential Equations - Part 2 of 3

-----VIDEO: More on Differential Equations - Part 3 of 3

Internet Video: *** Matching Slope Fields ***

This video shows good examples of how to do match a slope field to its differential equation and also how to match a slope field with the equation it could represent.

Internet Video: Slope Fields and Differential Equations

This video shows you how to draw a slope field, and then how to solve the differential equation analytically to verify your slope field.

Internet Video: Differential Equation & Slope Field

This is a nice video that shows you how to create a slope field for a Differential Equation and then solve the Differential Equation with both a General Solution and a Unique Solution.

Euler's Method Lecture Notes

-----VIDEO: Euler's Method

Section 6-2

Growth and Decay Models

-----VIDEO: Exponential Growth & Decay

Section 6-2 (Day 2) and Section 6-3

More on Differential Equations

-----VIDEO: More on Differential Equations - Part 1 of 3

-----VIDEO: More on Differential Equations - Part 2 of 3

-----VIDEO: More on Differential Equations - Part 3 of 3

**Worksheets**

**Study Guides**

**Interactive Animations**

Calculus is the study of change. The ability to change a parameter and immediately see the result can demonstrate that change and how things are related during that change. Many of these concepts are much easier to explain if that change, the motion, can be visually demonstrated in class. Therefore, this is a perfect place for the use of computer animations.

All animations were created using the GeoGebra dynamic mathematics software application located on GeoGebra's website.

All animations were created using the GeoGebra dynamic mathematics software application located on GeoGebra's website.

**Please be patient! It takes awhile for these to load.**

Widen the browser, if necessary, to see the entire animation.

Widen the browser, if necessary, to see the entire animation.

**Slope Field Generator**

**Euler's Method**

**Exponential Growth & Decay**

__Teaching Demonstration__

The effects of different values of k on the exponential function f(t)=e^(kt).

- If k is positive, the exponential equation models growth.

- If k is negative, the exponential equation models decay.

As k gets bigger, what is the effect on the graph?

As k gets smaller, what is the effect on the graph?

As k approaches 0, what is the effect on the graph?