Practical stuff

Remember to do: "First Day Survey: Prior Knowledge #FinAid"

2.3 Differentiation

Defining the derivative

(Quick question about the chain rule)

5.1-5.3 Double Integration

Defining the double integral and some intuition.

Fubini's Theorem

Double integrals over elementary regions

5.4 Changing the Order of Integration

Mean Value Inequality/Equality

(Volume of a 3-dimensional ball)

6.1 The Geometry of Maps from R^2 to R^2

One-to-one and Onto Maps

6.2 The Change of Variables Theorem

Cylindrical and spherical coordinates

(6.3 Applications)

4.3 Vector Fields

7.1 The Path Integral

7.2 The Line Integral

7.2 The Line Integral

Reparametrizations and (simple/closed) curves

7.3 Parametrized Surfaces (introduction)

7.3 Parametrized Surfaces

7.4 Area of a Surface

7.5 Integrals of Scalar Functions Over Surfaces

7.6 Surface Integrals of Vector Fields

Independence of parametrizations, Oriented surfaces

4.4 Divergence and Curl

8.1 Green's Theorem

8.1 Green's Theorem (last part)

8.2 Stokes' Theorem (for graphs)

8.2 Stokes' Theorem

Circulation and curl

8.4 Gauss' Theorem

Gauss' Law

Since I received a positive Covid test, we are doing the last few lectures through Zoom. You can find them here or in Canvas.

Preparation for the final exam

You can also find this video in Canvas.