Course Log
Here you will find information about the material that was already covered or will be covered in the next few lectures.
Covered | |
---|---|
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 |