# Winter 2022: MAT B42 Techniques of the Calculus of Several Variables II

From the Course Calendar: “Fourier series. Vector fields in $\mathbb{R}^n$, Divergence and curl, curves, parametric representation of curves, path and line integrals, surfaces, parametric representations of surfaces, surface integrals. Green’s, Gauss’, and Stokes’ theorems will also be covered. An introduction to differential forms, total derivative.”

# Week-by-Week Schedule

- Week 1: Parametric Equations
- Marsden and Tromba: 2.4 Introduction to Paths and Curves
- Marsden and Tromba: 4.1 Acceleration and Newton’s Second Law
- Marsden and Tromba: 4.2 Arc Length

- Week 2: Vector Fields
- Marsden and Tromba: 4.3 Vector Fields
- Marsden and Tromba: 7.1 The Path Integral

- Week 3: Vector Fields
- Marsden and Tromba: 7.2: Line Integrals
- Marsden and Tromba: 8.1: Green’s Theorem (without the vector form)

- Week 4: Vector Valued Functions
- Marsden and Tromba: 4.4 Divergence and Curl
- Marsden and Tromba: 8.1 Green’s Theorem (without the vector form)

- Week 5: Line Integrals 1
- Marsden and Tromba: 7.3 Parametrized Surfaces
- Marsden and Tromba: 7.4 Area of a Surface

- Week 6: Line Integrals 2
- Marsden and Tromba: 7.4 Area of a Surface
- Marsden and Tromba: 7.5: Integrals of Scalar Functions over Surfaces

- Week 7: Surfaces
- Marsden and Tromba: 7.5: Integrals of Scalar Functions over Surfaces
- Marsden and Tromba: 7.6: Surface Integrals of Vector Fields

- Week 8: Surface Integrals
- Marsden and Tromba: 8.2: Stokes’ Theorem
- Marsden and Tromba: 8.4: Gauss’ Theorem

- Week 9: Introduction to Differential Forms
- Marsden and Tromba: 8.5: Differential Forms

- Week 10: Orthogonal Functions
- Orthogonal Functions

- Week 11: Fourier Series
- Fourier Series

- Week 12: Calculus and Beyond!
- Summary and wrap-up