# Multivariable functions

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 $z=f(x, y)$
• 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 $z = f(x, y)$ and $f(x, y) = a + mx + ny$  we have $\Delta z = m \Delta x + n \Delta y$
• 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

Real world examples