MATH-GA1002 Multivariable Analysis Spring 2024 Calendar
Week Date Topics Links
1 Monday
1/22/2024
  • Linear and Multilinear Algebra
  • \(1\)-Tensors, \(2\)-Tensors
 Slides
2 Monday
1/29/2024
  • Topology of \(\mathbb{R}^n\)
  • Differentiable Functions
  • Differential of a Function
  • Directional Derivatives
 Slides
3 Monday
2/5/2024
  • Differential of a Function
  • Smooth Functions
  • Directional Derivatives
  • Derivations
 Slides
4 Monday
2/12/2024
  • Differentiable Maps
  • Directional Derivative of Map
  • Differential of Map
  • Immersions, Embeddings, Submersions, Diffeomorphisms
 Slides
5 Monday
2/19/2024		 No class  
6 Monday
2/26/2024
  • Inverse Function Theorem
 Slides
7 Monday
3/4/2024
  • Implicit Function Theorem
  • Normal Form for Submersion
  • Normal Form for Immersion
  • Linear Atlas of Vector Space
  • Atlas of Open Subset of \(\mathbb{R}^n\)
  • Atlas of Manifold
 Slides
8 Monday
3/11/2024
  • Integration over Rectangles
  • Sets of Measure Zero or Content Zero
  • Fubini's Theorem
 Slides
9 Monday
3/18/2024		 No class  
10 Monday
3/25/2024
  • Oriented Volume of Parallelopiped
  • Permutations
  • Exterior \(m\)-Tensors
  • Oriented Basis
  • Orientation of Vector Space
 Slides
11 Monday
4/1/2024
  • Change of Variables Formula for Integral
  • Tangent Bundle
  • Pushforward of Tangent Vector
  • Cotangent Bundle
  • Differential \(1\)-Forms
  • Pullback of Differential \(1\)-Form
 Slides
12 Monday
4/8/2024
  • Alternating Tensors
  • Differential Forms
  • Wedge Product
  • Pullback of Wedge Product
  • Differential Forms in Coordinates
 Slides
13 Monday
4/15/2024		 Class Canceled
14 Monday
4/22/2024
  • Integral of \(n\)-Form on Oriented Rectangle
  • Integral of \(1\)-Form on Oriented Line Segment
  • Integral of \(1\)-Form on Oriented Curve
  • Outer Orientation of Boundary of Rectangle
  • Fundamental Theorem of Calculus on Rectangle
  • Exterior Derivative of \(1\)-Form
 Slides
15 Monday
4/29/2024
  • Geometry of Surface in Euclidean Space
 Slides
16 Monday
5/6/2024
  • Gauss-Bonnet Theorem
17 Monday
5/13/2024
4-5:50pm		 Final Exam Warren Weaver Hall 1302