**Learning objectives**

- Explore commonly occurring functions of 2-variables: linear, quadratic, Cobb-Douglas, traveling wave
- Make and read tables of values for 2-variable functions
- Visually represent 2-variable functions
- 3D: graphs, axes x, y, and z
- 2D: contour diagrams, axes x and y
- 2D: cross sections, axes x and z OR y and z

- Use Mathematica to graph 1-variable functions
- Use Mathematica to visualize 2-variable functions
- Master linear functions of 2 or more variables, numerically, visually and algebraically
- Table of values: all rows are linear with the same slope, all columns are linear with the same slope, row slope and column slope can be different
- Graph: a plane in 3-space
- Contour plot: equally spaced parallel lines
- Master equation: for and we have

- Explore level sets of 3-variable functions

**Resources**

- Post comments, questions, or replies to piazza
- Download Mathematica here and install on your laptop for use throughout the semester, including in class
- Wolfram Alpha
- Textbook: 12.1-12.5
- Suggested problems: 12.1: 21, 23, 33; 12.2: 3, 7, 15; 12.3: 1, 7, 9, 19; 12.4: 2, 3, 7, 9, 13, 21, 23; 12.5: 1, 17, 31, 41.

**In class**

- Day 1: Activities
- Day 2: Mathematica activity
- Day 3: Problems on linear functions

**Real world examples**