Here you will find information about the material that was already covered or will be covered in the next few lectures.

Covered
4/30 Review for Final Project
4/28 Review for Final Project
4/23 Midterm Exam 2 (in class)
4/21 Review for Midterm Exam 2
4/16 §45 Jacobian Theorem, Change of Variables
4/14 §45 Transformations by Linear and Nonlinear Mappings
4/9 §44 The Integral as Iterated Integral, §45 Transformations of Sets with Content
4/7 §44 Characterization of Content Function, Further Properties of Integral
4/2 §43 Existence of Integral, §44 Content and Integral, Sets with Content
3/31 §43 Properties of Integral, Darboux’s upper and lower integrals, Riemann’s Criterion for Integrability
3/26 §43 Content zero, Definition of Integral
3/24 §42 Extremum Problems with Constraints, Exercises, Inequality Constraints
3/17–19 Spring Break
3/12 §42 Extremum Problems with Constraints, Lagrange’s Theorem
3/10 Review for Midterm Exam 1
3/5 §42 Local Extrema, Second Derivative Test
3/3 §41 Implicit Functions (finish)
2/26 §41 Surjective Mapping Theorem (finish), Open Mapping Theorem, Inversion Theorem, Implicit Functions (start)
2/24 §41 C1 functions, Approximation Lemma, Injective Mapping Theorem, Surjective Mapping Theorem
2/19 No class (to be made up)
2/17 No class (to be made up)
2/12 §40 Mixed derivatives, higher derivatives, Taylor’s theorem
2/10 §40 Chain Rule, Mean Value Theorem, Mixed derivatives (start)
2/5 §39 Examples, Existence of the derivative, §40 Algebraic operations and derivative
2/3 §23 Uniform continuity, §21 Linear functions, §39 Partial derivatives, differentiability
1/29 §22 Relative topology, Global Continuity Theorem, preservation of connectedness, compactness, continuity of inverse function
1/27 §17 Sequences of functions, pointwise and uniform convergence, §20 Continuity at a point (different definitions)
1/22 §14 Convergence of sequences, §§15-16 Subsequences, Bolzano-Weierstrass (revisited), Cauchy sequences
1/20 §11 Cantor Intersection Thm, Corollaries, §12 Connected sets
1/15 §10 Cluster points, Bolzano-Weierstrass, Nested Cells, §11 Compactness, Heine-Borel
1/13 §8 Cartesian spaces, inner products, norms, §9 Open and closed sets, interior, boundary, exterior points