Supplements

Past Final Exams 

Note: Solutions will not be provided on line, but you can ask about them in class or office hours.

• Winter 2012
• Fall 2013
• Spring 2014

Study Guides

• SG 1 - Indefinite integration and applications. Solutions
• SG 2 - Definite integrals and applications. Solutions
• SG 3 - More applications of integrals and partial derivatives. Solutions
• SG 4 - Linear approximation and optimization. Solutions
• SG 5 - Optimization, constrained optimization (and integration). Solutions

Supplementary Notes

• SN 1 - Summation
• SN 2 - Taylor polynomials in two variables
• SN 3 - Unconstrained optimization in several variables 
• SN 4 - The envelope theorem
• SN 5 - Constrained optimization

11A Supplements 

Lecture slides

• Wed. Jan 6
• Mon. Jan 11
• Wed. Jan 13
• Fri. Jan 15
• Wed. Jan 20 (Definite Integrals)
• Fri. Jan 22 (FTC)
• Wed&Fri, Feb 3&5 (Differential equations)
• Mon, Feb 8 (logistic growth; partial derivatives)
• Wed, Feb 17 (Linear Taylor polynomial; higher order partial derivatives)
• Fri, Feb 19 (Quadratic Taylor polynomial)
• Mon, Feb 22 (Critical points and critical values)
• Wed, Feb 24 (Second derivative test in two variables)
• Fri&Mon, Feb 26&29 (Envelope theorem)