Table of Contents

## PH 423 (Energy and Entropy) Math Bits

On 11/14/17, Paul edited this page to reflect the Math Bits implemented in Autumn 2017; the original version of the information for the EE Math Bits is currently archived at the bottom of the page, but can be deleted once the page is finalized.

#### Differentials (50 minutes)

- Math pre-test (20 minutes)
- Differentials and Zapping (Lecture 30 minutes)
- Homework and propagate to the other units below

#### Variables and Representations (2 hours)

- Exploring the Partial Derivative Machine (Integrated PDM Lecture/Lab) – a new activity was used here and still needs to be created on the wiki. This activity included lots of small whiteboard questions and so forth that need to be expanded on above.
- PDM Dictionary (Lecture 25 minutes)

#### Energy and Integrals (50 minutes)

- Energy and Integrals (Integrated PDM Lecture/Lab) – a new activity was used here and still needs to be created on the wiki.

#### Derivatives and Chain Rules (2 hours)

- PDM Derivatives (Integrated PDM Lecture/Lab) – a new activity was used here and still needs to be created on the wiki.
- Chain Rules and Chain Rule Diagrams (Lecture minutes)
- Finding a Chain Rule (Small Group Activity) – a new activity was used here and still needs to be created on the wiki.

#### The Elevator Cycle (30 minutes)

- The Elevator Cycle (Integrated PDM Lecture/Lab) – a new activity was used here and still needs to be created on the wiki.

#### OLD MATH BITS PAGE STARTS HERE

#### Partial Derivatives (40 minutes)

- Quantifying Change (Small Group PDM Activity)
- Isowidth and Isoforce Stretchability (Small Group PDM Activity)

#### Potential Energy and the Partial Derivative Machine (1 hour 40 minutes)

- Math pre-test (Class actvity, 15 minutes)
- Easy and Hard Derivatives (Small Group PDM Activity)
- Potential Energy of a Spring (Lecture 5 minutes)
- Potential Energy of an Elastic System (Integrated PDM Lab)

#### Total Differentials and Partial Derivatives (1 hour 30 minutes)

- Total Differentials (Lecture 10 minutes)
- Evaluating Total Differentials: "Zapping with d" (Small Group Activity)
- What You Can Do with Total Differentials (Lecture 5 minutes)
- Upside Down Derivatives (Small Group PDM Activity)
- Cyclic Chain Rule (Small Group PDM Activity)
- Deriving Change of Variables (Small Group PDM Activity)

#### Maxwell Relations and Legendre Transforms

- Mixed Partials and Maxwell Relations (Lecture 30 minutes)
- Legendre Transforms (Lecture 5 minutes)