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

Projected  
Thur, Apr 27: [M] Midterm Exam 2 Discussion; Review for Final Exam
   
Covered  
Tue, Apr 25: [M] §25 Integration of functions on manifolds
Thur, Apr 20: [M] §23, 24 Manifolds with boundaries
Tue, Apr 18: Review for Midterm Exam 2
Thur, Apr 13: [M] §23 Manifolds in $\mathbb{R}^n$ (without boundary), §24 Transition maps
Tue, Apr 11: [M] §16 Partitions of Unity (finish) §23 $C^r$ functions on subsets of $\mathbb{R}^n$
Thur, Apr 6: [M] §15 Improper Integrals, §16 Bump functions, Partitions of Unity
Tue, Apr 4: [M] §21 Volume of the Parallelopiped (finish) §22 Integration on a Parametrized Manifold, §15 Exhaustion by Compacts
Thur, Mar 30: [M] §21 Volume of the Parallelopiped
Tue, Mar 28: [B] §45 Change of Variables (strong form)
Thur, Mar 23: [B] §45 Jacobian Theorem, Change of Variables
Tue, Mar 21: [B] §45 Transformation by Linear Maps, Transformation by Nonlinear Maps, Jacobian Theorem
Thur, Mar 16: Spring Break
Tue, Mar 14: Spring Break
Thur, Mar 9: Midterm Exam 1 discussion
Tue, Mar 7: Review for Midterm Exam 1
Thur, Mar 2: [B] §45 Transformations of Sets with Content
Tue, Feb 28: [B] §44 Mean Value Theorem, Integral as Iterated Integral
Thur, Feb 23: [B] §44 Sets with Content (cont.), Characterization of Content Function
Tue, Feb 21: [B] §43 Properties of Integral §44 Further Properties of Integral, §44 Sets with Content
Thur, Feb 16: [B] §43 Darboux’s upper and lower integrals (cont.), Riemann’s Criterion for Integrability, Existence of Integral
Tue, Feb 14: [B] §43 Content zero, Definition of Integral, Darboux’s upper and lower integrals (Project 43.$\alpha$)
Thur, Feb 9: [B] §42 Lagrange’s Theorem, Inequality Constraints, Examples
Tue, Feb 7: [B] §42 Extremum Problems with Constraints, Lagrange’s Theorem
Thur, Feb 2: [B] §42 First Derivative Test, Second Derivative Test
Tue, Jan 31: [B] §41 Implicit Function Theorem, §42 Local (Relative) Extrema
Thur, Jan 26: [B] §41 Surjective Mapping Theorem, Open Mapping Theorem, Inversion Theorem
Tue, Jan 24: [B] Multi-index notation, §41 Class $C^1$, Approximation Lemma, Injective Mapping Theorem
Thur, Jan 19: [B] §40 Interchange of the Order of Differentiation, Higher Derivatives, Taylor’s Theorem
Tue, Jan 17: [B] §40 Algebraic properties of derivatives, Chain rule, Mean Value Theorems
Thur, Jan 12: [B] §39 Directional and partial derivatives, Jacobian, existence of the derivative
Tue, Jan 10: [B] §21 Linear functions, §39 The derivative, directional and partial derivatives