Are you interested in learning Calculus 3?
Well, this course is the equivalent of a second-semester course, a continuation of my last series. Don't worry though if you weren't there. This series can be taken by anyone who has completed
the only prerequisite: Calculus 1 (with integration)
and the rest of the necessary background information will be covered or reviewed in the initial sessions.
NOTE: Required reading of about 35 pages a week (for units 2 and 3 only)+ weekly homework (with feedback) + 1 test per unit (inside or outside of class depending on time but always graded with feedback within 2 days)
Sessions are between 1h15m to 1h30m.
Content Covered:
(UNIT I) Single-Variable Integration and Vector Analysis
1. Physical interpretations of the integral and the average value of a function over an interval
2. Finding the area between curves expressed as functions of y
3. Finding the area between curves that intersect at more than two points
4. Volumes with cross sections: squares, rectangles, triangles, and semicircles
5. Volume with the disc and washer method: revolving around x-, y-, and different axes
6. Arc length, distance traveled, and unit calculator practice
7. Defining and differentiating parametric vector-valued functions
8. Finding arc lengths of curves given by parametric equations and solving motion problems
9. Defining polar coordinates and differentiating in polar form
10. Finding the area of a polar region bounded by one and multiple polar curves, and unit calculator practice.
11. Finding the surface area of surfaces or revolution, including in polar coordinates.
(UNIT II) Multivariable Integration and Applications
11. Formulating Riemann sums
12. The Double Integral and Iterated Integral
13. Applications of The Double Integral
14. Triple Integrals
15. The Jacobian and uv-substitution
16. Integration in Polar, Cylindrical, and Spherical Coordinates
17. Applications of Triple Integrals
(Unit III) Multivariable Vector Analysis
18. Scalar-valued Line Integrals
19. Vector-valued line integrals
20. Path Independence
21. Exact Differentials
22. Divergence and Green's Theorem
23 Curl, Stokes' Theorem, and parameterizing surfaces.
24. Flux and Divergence Theorem
25+ (applications to Electrodynamics and other special topics?)
