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