Guide for Week 8
Math 408 Section A
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Reading Assignment:
Chapter 5 (sections 1,2,3), all of Chapter 6, and begin Chapter 8 (intro before Section 1, page 91, and top of page 92)
Homework Assignment:
Vocabulary Words
- Elements of Multivariable Calculus
- norms for vectors and matrices and the closed unit ball
- continuity
- open, closed, bounded, and compact sets
- cluster points
- directional derivatives and partial derivatives
- derivatives and their representations as matrices of partial derivatives
- the little-o notation
- the gradient and the Hessian matrix
- first-order expansion and the first-order Taylor approximation
- second-order expansion and the second-order Taylor approximation
- the delta method for commputing derivatives
- Optimality Conditions for Unconstrained Problems
- Weierstrass extreme value theorem
- coercive functions
- The coercivity and compactness theorem
- The coercivity and existence theorem
- The basic first-order optimality result
- The first-order necessary conditions for optimality
- the second-order necessary and sufficient conditions for optimality
- convex functions and sets
- the epi-graph and of a function
- the convexity and optimality theorem
- first- and second-order conditions for convexity checking
- gradients and Hessians of linear least squares functions and general
quadratic functions
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Key Concepts:
- Elements of Multivariable Calculus
- first- and second-order expansions and approximations
- the delta method for computing derivatives
- Optimality Conditions for Unconstrained Problems
- Coercivity and existence
- first- and second-order optimality conditions
- convexity and optimality
- Coercivity and existence
- first- and second-order optimality conditions
- convexity and optimality
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Skills to Master:
- computing derivatives and Taylor approximations
- locating and classifying critical points
- checking coercivity
- checking convexity
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Quiz:
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The quiz will consist of 2 questions as usual.