18.02, Spring 1999 -- Brief Lecture notes,
Second part: Differentiation

• Lecture 7: Feb 18.
  1. Review
  2. Functions and derivatives
  3. Partial derivatives
  4. Tangent plane
• Lecture 8: Feb 19: In-class test
• Lecture 9: Feb 23. Max/Min
  1. Tangent plane
  2. Critical points
  3. Least squares
• Lecture 10: Feb 25. Approximation
  1. Tangent approximation
  2. Sensitivity analysis
  3. Chain rule in 2-D
• Lecture 11: Feb 26. Gradient of a function.
  1. Chain rule in 3 variables.
  2. Gradient normal to level curves.
  3. Vector form of chain rule.
• Lecture 12: Mar 2. Lagrange multipliers.
  1. Gradient in 3 variables.
  2. Constrained max/min.
  3. Lagrange's method.
• Lecture 13: Mar 4. Second derivatives.
  1. Iterated derivatives.
  2. Quadratic functions.
  3. Determination of max/min/saddle.
• Lecture 14: Mar 5. Implicit differentiation. EP 13.7, p. 848-850; SN Sect N.
  1. Max/min example.
  2. Non-independent variables.
  3. Implicit functions.
  4. Chain rule again.