MATH – 10C. Calculus

August, Summer 2021

MWF, 10:00pm-11:50pm.

NEWS HOMEWORK HANDOUTS

Instructor: Professor Vladimir Rotar; e-mail: vrotar@ucsd.edu.

Office hours: MWF, 12:00-12:45. If it is needed, office hours may be run also after 4:00pm. Really short questions may be answered right after the lectures.

Text: Openstax, Volume 3.

Examinations: There will be several quizzes, and a final exam. Homework will be assigned each lecture and posted on the HW site.

SYLLABUS

The list below is rather one of topics than of lectures: the real experience may dictate a slower or faster pace. A slight change of the order of exposition is also possible.

1. Sec. 2.1: Vectors in the Plane.
2. Sec. 2.2: Vectors in Three Dimensions.
3. Sec. 2.3: The Dot Product.
4. Sec. 2.4: The Cross Product.
5. Sec. 2.5: Equations of Lines and Planes in Space.
6. Sec. 3.1: Vector-valued Functions and Curves in Space.
7. Sec. 3.2: Calculus of Vector-valued Functions
8. Sec. 3.4: Motion in Space
9. Sec. 4.1: Functions of Several Variables.
10. Sec. 4.3: Partial Derivatives.
11. Sec. 4.4: Tangent Planes and Linear Approximations.
12. Sec. 4.5: The Chain Rule.
13. Sec. 4.6: Directional Derivatives and the Gradient.
14. Sec. 4.7: Maximum/Minimum Problems s. :
15. Sec. 4.8: Lagrange Multipliers. .
16. Sec. 5.1: Double Integrals over Rectangular Regions.
17. Sec. 5.2: Double Integrals over General Regions.