# MA442 Multivariate Analysis I (Honors)

Purdue University Spring 2006

## Thursday, April 20, 2006

### Couse Log

Planned
Apr 24-28 Review for Final Exam
What was covered
Apr 17-19: Review for Midterm 2
Apr 14: § Problems on Change of Variables
Apr 12: § Jacobian Theorem, Change of Variables
Apr 10: § 45 Linear Change of Variables, Transformations Close to Linear
Apr 7: §45 Transformation of Sets, Content and Linear Mappings
Apr 5: §44 Integral as Iterated Integral; §45 Transformations of Sets of Content Zero
Apr 3: §44 Further Properties of Integral, Mean Value Theorem
Mar 31: §44 Content and Integral
Mar 29: §43 Properties of Integral, Existence of Integral
Mar 27: §43 Definition of Integral, Riemman, Upper and Lower Sums
Mar 24: §42 Inequality Constraints, §43 Content Zero
Mar 22: §42 Extremum Problems with Constraints: Problems
Mar 20: §42 Extremum Problems with Constraints
Mar 10: Class cancelled (because of evening exam)
Mar 8: §42 Extremum Problems, Second Derivative Test
Mar 6: §41 Implicit Function Theorem, §42 Extremum Problems.
Mar 3: §41 Implicit Function Theorem
Mar 1: Overview of Midterm Exam
Feb 27: Review for Midterm Exam
Feb 24: §41 Inverse Mapping Theorem
Feb 22: §41 Surjective Mapping Theorem, Open Mapping Theorem
Feb 20: §41 Injective Mapping Theorem, Surjective Mapping Theorem (started)
Feb 17: §41 C1 functions, Injective Mapping Theorem (started)
Feb 15: §40 Mixed derivatives (finished), higher derivatives, Taylor's theorem
Feb 13: §40 Mean Value Theorem, mixed derivatives (stared)
Feb 10: §39 Tangent planes, §40 Combinations of Diff. Functions, the Chain Rule
Feb 8: §39 Examples, Existence of the derivative
Feb 6: §39 Partial derivatives, differentiability
Feb 3: §22 Global continuity theorem, preservation of compacteness, connectedness
Feb 1: §21 Linear functions, §22 Relative topology, global continuity
Jan 30: §20 Continuity at a point (different definitions)
Jan 27: §17 Sequences of functions, pointwise and uniform convergence
Jan 25: §§15-16 Bolzano-Weierstrass (revisited), Cauchy sequences
Jan 23: Finish §12; §§14-15 Convergence of sequences
Jan 20: §12 Connected sets
Jan 18: §11 Compactness, Heine-Borel, Cantor Intersection Theorem
Jan 16: MLK day, no class
Jan 13: §10 Cluster points, Bolzano-Weierstrass, Nested Cells; started §11
Jan 11: §9 Open and closed sets, interior, boundary, closure
Jan 9: §8 Cartesian spaces, inner products, norms