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

Fri, Apr 29: Discussion for Final Exam
Wed, Apr 27: [M] §25 Integration of functions on manifolds (finish)
Mon, Apr 25: Overview of Midterm Exam 2, Manifolds through Implicit Function Theorem
Fri, Apr 22: Discussion
Wed, Apr 20: Review for Midterm Exam 2
Mon, Apr 18: [M] §24 The Boundary of a Manifold
Fri, Apr 15: [M] §23 Manifolds in $\mathbb{R}^n$ (cont.)
Wed, Apr 13: [M] §16 Partitions of Unity (finish), §23 Manifolds in $\mathbb{R}^n$
Mon, Apr 11: [M] §16 Partitions of Unity
Fri, Apr 8: [M] §22 Volume of a Parametrized Manifold, Integration on a Parametrized Manifold
Wed, Apr 6: [M] §21 Volume of the Parallelopiped
Mon, Apr 4: [B] §45 Change of Variables (Strong Form)
Fri, Apr 1: [B] §45 Change of Variables
Wed, Mar 30: [B] §45 Transformation by Nonlinear Maps, Jacobian Theorem
Mon, Mar 28: [B] §45 Transformation by Linear Maps, Transformation by Nonlinear Maps (start)
Fri, Mar 25: [B] §45 Transformations of Sets with Content
Wed, Mar 23: [B] §44 Integral as Iterated Integral, §45 Transformations of Sets with Content (start)
Mon, Mar 21: Overview of Midterm Exam 1, [B] §44 Mean Value Theorem
Fri, Mar 11: No class (cancelled because of the exam)
Wed, Mar 9: Review for Midterm Exam 1
Mon, Mar 7: [B] §44 Characterization of Content Function (finish), Further Properties of Integral
Fri, Mar 4: [B] §44 Characterization of Content Function
Wed, Mar 2: [B] §44 Sets with Content
Mon, Feb 29: [B] §43 Properties of Integral (cont.), Existence of Integral
Fri, Feb 26: [B] §43 Riemann’s Criterion for Integrability, Properties of Integral
Wed, Feb 24: [B] §43 Definition of Integral, Darboux’s upper and lower integrals (Project 43.$\alpha$)
Mon, Feb 22: [B] §43 Content zero
Fri, Feb 19: [B] §42 Examples on extremum problems with constraints
Wed, Feb 17: [B] §42 Inequality Constraints
Mon, Feb 15: [B] §42 Lagrange’s Theorem (finish)
Fri, Feb 12: [B] §42 Second Derivate Test (finish), Extremum Problems with Constraints, Lagrange’s Theorem (start)
Wed, Feb 10: [B] §42 Second Derivate Test
Mon, Feb 8: [B] §41 Implicit Function Theorem (finish), §42 Local (Relative) Extrema, First Derivative Test
Fri, Feb 5: [B] §41 Implicit Function Theorem
Wed, Feb 3: [B] §41 Inversion Theorem, Implicit Function Theorem (start)
Mon, Feb 1: [B] §41 Surjective Mapping Theorem (finish), Open Mapping Theorem
Fri, Jan 29: [B] §41 Injective Mapping Theorem, Surjective Mapping Theorem (start)
Wed, Jan 27: [B] §40 Taylor’s Theorem (finish), §41 Class $C^1$, Approximation Lemma
Mon, Jan 25: [B] §40 Interchange of the Order of Differentiation (cont.), Taylor’s Theorem
Fri, Jan 22: [B] §40 Mean Value Theorems, Interchange of the Order of Differentiation
Wed, Jan 20: [B] §40 Algebraic properties of derivatives, Chain rule
Mon, Jan 18: No class: MLK day
Fri, Jan 15: [B] §39 Jacobian, existence of the derivative
Wed, Jan 13: [B] §39 Directional and partial derivatives, the derivative
Mon, Jan 11: [B] §21 Linear functions