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

Projected  
Thur, Apr 24: [M] §25 Integration of functions on manifolds
Tue, Apr 22: Review for Midterm Exam 2
   
Covered  
Thur, Apr 17: [M] §23, 24 Manifolds with boundaries
Tue, Apr 15: [M] §23 Manifolds in $\mathbb{R}^n$ (without boundary), §24 Transition maps
Thur, Apr 10: [M] §16 Partitions of Unity (finish) §23 $C^r$ functions on subsets of $\mathbb{R}^n$
Tue, Apr 8: [M] §15 Improper Integrals, §16 Bump functions, Partitions of Unity
Thur, Apr 3: [M] §21 Volume of the Parallelopiped (finish) §22 Integration on a Parametrized Manifold, §15 Exhaustion by Compacts
Tue, Apr 1: [M] §21 Volume of the Parallelopiped
Thur, Mar 27: [B] §45 Change of Variables (cont), Change of Variables (strong form)
Tue, Mar 25: [B] §45 Transformation by Nonlinear Maps, Jacobian Theorem, Change of Variables
Thur, Mar 20: Spring Break
Tue, Mar 18: Spring Break
Thur, Mar 13: [B] §45 Transformations of Sets with Content, Transformation by Linear Maps
Tue, Mar 11: Review for Midterm Exam 1
Thur, Mar 6: [B] §44 Characterization of Content Function (finish) , Integral as Iterated Integral, Fubini’s Theorem
Tue, Mar 4: [B] §44 Mean Value Theorem, Characterization of Content Function
Thur, Feb 27: [B] §43 Properties of Integral §44 Further Properties of Integral, §44 Sets with Content
Tue, Feb 25: [B] §43 Darboux’s upper and lower integrals (cont.), Riemann’s Criterion for Integrability, Existence of Integral
Thur, Feb 20: [B] §43 Content zero, Definition of Integral, Darboux’s upper and lower integrals (Project 43.$\alpha$) (start)
Tue, Feb 18: [B] §42 Lagrange’s Theorem, Inequality Constraints, Examples
Thur, Feb 13: [B] §42 Extremum Problems with Constraints, Lagrange’s Theorem
Tue, Feb 11: [B] §42 Local (Relative) Extrema, First Derivative Test, Second Derivative Test
Thur, Feb 6: [B] §41 Implicit Function Theorem
Tue, Feb 4: [B] §41 Surjective Mapping Theorem (finish), Open Mapping Theorem, Inversion Theorem
Thur, Jan 30: [B] §41 Injective and Surjective Linear Mappings, Injective Mapping Theorem, Surjective Mapping Theorem
Tue, Jan 28: [B] §40 Multi-index notation, Taylor’s Theorem §41 Class $C^1$, Approximation Lemma
Thur, Jan 23: [B] §40 Interchange of the Order of Differentiation, Higher Derivatives
Tue, Jan 21: [B] §40 Algebraic properties of derivatives, Chain rule, Mean Value Theorems
Thur, Jan 16: [B] §39 Directional and partial derivatives, Jacobian, existence of the derivative
Tue, Jan 14: [B] §21 Linear functions, §39 The derivative, directional and partial derivatives