September October November December
Mo 9 16 23 30 7 14 21 28 4 11 18 25 2 9
Tu 3 10 17 24 1 8 15 22 29 5 12 19 26 3 10
We 4 11 18 25 2 9 16 23 30 6 13 20 27 4 11
Th 5 12 19 26 3 10 17 24 31 7 14 21 TG 5 12
Fr 6 13 20 27 4 11 18 25 1 8 15 22 6 13
| 1 | Chapter 1. |
Vectors : dot product, (cross product), defining equations for lines and
planes.
This should be a quick introduction; the cross product will be needed occasionally, but the dot-product and defining equations for lines and planes do show up a lot. |
| 2 | Ch.2, §1–9. | Parametric curves: lines, circles, helix; velocity & acceleration. |
| 3 | Ch.2 §10–16. | Parametric curves: arc length, unit tangent, curvature, normal for space curves, the osculating plane. |
| 4 | Ch.3 §1–5. | Functions of several variables: level sets, linear functions, quadratic forms (completing the square to classify them), *functions in polar coordinates (the helicoid) |
| 5 | Ch.4 §1–5. | Derivatives: partials, the linear approximation, tangent plane to a graph |
| 6 | Ch.4 §6–9. | The Chain Rule and the gradient of a function |
| 7 | *Ch.4 §10. | Implicit function theorem |
| 8 | Ch.4 §11. | The Chain Rule with more variables: coordinate transformations. |
| 9 | Ch.4 §13–14. | Higher partial derivatives and “Clairaut’s theorem” (mixed partials are equal) |
| Midterm 1 | Evening exam, location to be announced | |
| 10 | Ch.5 §1–6. | Define Maxima, Minima, discuss “continuous functions on closed and bounded sets,” explain why interior maxima and minima are critical points (but not always the other way around). |
| 11 | Ch.5 §7. | Special lecture on linear regression as an example. |
| 12 | Ch.5 §9.1–9.5. | Discuss Taylor expansion of order 2, as preparation for the second derivative test. |
| 13 | Ch.5 §9.5–9.7, §11. | Second derivative test, examples; for saddle points show how you get the tangents to the two branches. |
| 14 | Ch.5 §12. | Lagrange multipliers |
| 15 | Ch.6 §1–2.4. | Integration: the general idea, double integral over a rectangle can be computed as an iterated integral. |
| 16 | Ch.6 §2.5–3. | Double integral examples, and double integral over non-rectangles. |
| 17 | Ch.6 §4–5.3. | An example of switching the order of integration. Double integral in polar coordinates. |
| 18 | Ch.6 §5.4–5.8. | Triple integrals, definition, expression in terms of iterated integrals, examples |
| 19 | Ch.6 §6 | Applications of triple (and double) integrals. Averages of functions, the concept of adensity, moment of inertia. |
| 20 | Ch.6 §1–2.4. | Triple integrals in special coordinate systems: spherical and cylindrical coordinates. Derive the “volume element” and show some examples. |
| Midterm 2 | Evening exam, location to be announced | |
| 21 | Ch7 §3 | Start vector calculus; define line integrals of functions (“scalars”) |
| 22 | Ch.7 §1, 2, §5.1 | Describe vector fields, line integral of a vector field, interpretation as “work” |
| 23 | Ch.7 §5 | Examples of line integrals around closed curves, along piecewise defined curves. |
| 24 | Ch.7 §6, 7 | Fundamental Theorem: line integral of a gradient does not depend on the path, definition of aconservative vector field |
| 25 | Ch.7 §9 | Flux integrals (for fluid flows in the plane); example, flux through a closed curve and the “production of stuff” (leads to the idea that the integral over the boundary of a region may have something to do with what happens inside the region). |
| 26 | Ch.7 §10 | Green’s theorem—both line integral and flux versions; examples (e.g. the expanding flow again) |
| 27 | Ch.7 §11 | Conservative fields and Green’s theorem; the problem with non-simply connected domains. |
| 28 | Ch.7 §13 | Surfaces and Surface Integrals; flux through a surface. |
| 29 | Ch.7 §14, 15 | Divergence theorem and Stokes’ theorem. |
| 30 | Ch.7 §16 | “∇”, ∇·f, ;∇×f, divergence of curl is zero, curl of gradient is zero. |