MAT237Y1Y

Lecture 1: Parametric curves

Lecture 2: Real-valued functions

Lecture 3: Vector fields

Lecture 4: Coordinate transformations

Lecture 5: Parametric, explicit, and implicit form

Lecture 6: Interior, boundary, and closure

Lecture 7: Sequences

Lecture 8: Open sets and closed sets

Lecture 9: Compact sets

Lecture 10: Limits

Lecture 11: Continuity

Lecture 12: Path-connected sets

Lecture 13: Global extrema

Lecture 14: Derivatives of one variable

Lecture 15: Partial derivatives

Lecture 16: Directional derivatives

Lecture 17: Gradients

Lecture 18: Differentials and Jacobians

Lecture 19: Differentiability

Lecture 20: Chain rule + Mean Value Theorem

Lecture 21: Local extrema and critical points

Lecture 22: Optimization

Lecture 23: Tangent spaces

Lecture 24: Smooth manifolds

Lecture 25: Diffeomorphisms

Lecture 26: Inverse function theorem

Lecture 27: Nonlinear systems

Lecture 28: Implicit function theorem

Lecture 29: Smooth manifolds and implicit form

Lecture 30: Lagrange multipliers

Lecture 31: Optimization with constraints

Lecture 32: Second order derivatives and the Hessian

Lecture 33: Higher order derivatives

Lecture 34: Taylor polynomials

Lecture 35: Classification of critical points

Lecture 36: Partitions

Lecture 37: Upper sums and lower sums

Lecture 38: Integration over rectangles

Lecture 39: Uniform continuity and integration

Lecture 40: Jordan measurable sets and volume

Lecture 41: Sets with zero volume

Lecture 42: Integration over non-rectangles

Lecture 43: Volume under a graph

Lecture 44: Average value

Lecture 45: Mass

Lecture 46: Probability

Lecture 47: Fubini’s theorem in 2D

Lecture 48: Double integrals

Lecture 49: Double integrals in polar coordinates 

Lecture 50: Fubini’s theorem in 3D and higher 

Lecture 51: Triple integrals 

Lecture 52: Triple integrals in cylindrical coordinates 

Lecture 53: Triple integrals in spherical coordinates 

Lecture 54: Change of variables

Lecture 55: Vector Calculus: Curves

Lecture 56: Arc Length

Lecture 57: Line integrals

Lecture 58: Fundamental theorem of line integrals

Lecture 59: Conservative vector fields

Lecture 60: Circulation, curl, flux and divergence in 2D

Lecture 61: Green’s theorem and curl

Lecture 62: Green’s theorem and divergence

Lecture 63: Surfaces

Lecture 64: Surface Area

Lecture 65: Orientation and Relative Boundary 

Lecture 66: Surface integrals

Lecture 67: Flux and Divergence in 3D

Lecture 68: Divergence theorem

Lecture 69: Circulation and curl in 3D

Lecture 70: Stokes' theorem

Lecture 71: Div, grad, and curl

Lecture 72: Review.