MATH 2401: WEEK 7

Topics for this week are:

• Unconstrained optimization, critical points and the second derivative test
• Constrained optimization, the method of Lagrange multipliers

Text coverage:     Sections 15.5 - 15.6 of Salas, Hille, and Etgen

Reference:   These topics are also discussed in Chapter 8, f:Rⁿ->R, of the Cain-Herod textbook.

Online resources:

• Maple Worksheets
  • Second Derivative Test: A linear algebra approach to classifying critical points.
  • Lagrange Multipliers: Maximization/Minimization under constrains. Analytic and geometric approaches.
• Solved Problems
  • Chapter 8, Section 2
  • Chapter 8, Section 3
  • Chapter 8, Section 4
  • Chapter 8, Section 5
  • Chapter 8, Section 6
  • Chapter 8, Section 7
• Additional Notes (by Prof. Carlen)
  • Critical points and optimization.
  • Lagrange multipliers.
  • Types of critical points.
• Projects
  • Lagrange Multipliers
• Java applets
  • Applet on the Lagrange multipliers method for solving constrained optimization problems.

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Last Modified: . School of Mathematics, Georgia Institute of Technology.