Instructor: Anatolii Grinshpan

Office hours: MTW 12-1, Korman 247, or by appointment, Korman 253

Syllabus (8^{th} ed. variant)
Calculus
root page Greg Naber’s notes Academic calendar Math resource center

Mar 29. Introduction to the course. Three-dimensional space.

Mar 30. Vectors. Coordinate representation of vectors.

Mar 31. Orthogonal unit frame. Examples.

Apr 1. Quiz 1 (11.1, 11.2). Dot product.

Apr 5. Orthogonal projection. Direction cosines.

Apr 6. Orthogonal projection. Examples.

Apr 7. Cross product.

Apr 8. Quiz 2 (11.3). Lines in 3D.

Apr 12. Lines and planes in 3D.

Apr 13. Review. Sample problems.

Apr 14. Midterm 1: 8-8:50 AM, CAT
61. (answers)

Regular class: parametric curves in 3D.

Apr 15. Vector functions. Quiz 3 (due Monday, in class). (answers)

Apr 19. Functions of several variables. Cross-sections and level sets.

Apr 20. Quadric surfaces.

Apr 21. Quadric surfaces.

Apr 22. Quiz 4 (13.1, 11.7). Quiz discussion.

Apr 26. Partial derivatives.

Apr 27. Partial derivatives.

Apr 28. Midterm 2: 8-8:50 AM, CAT 61. (answers)

Regular class: local linear approximation.

Apr 29. Local linear approximation. Chain rule.

Quiz 5 (due Monday, in class). (answers)

May 3. Implicit Function Theorem.

May 4. Directional derivative and gradient.

May 5. Directional derivative and gradient.

May 6. Quiz 6 (13.6). Quiz discussion.

May 10. Tangent planes and normal lines.

Critical points. Points of local extremum.

May 11. Review. Sample problems. (answers)

Critical point analysis: an example.

Notes on the Second Partials Test.

May 12. Midterm 3: 8-8:50 AM, CAT 61. (answers)

Regular class: absolute extremum.

May 13. Double integrals.

Quiz 7 (due Monday, in class). (answers, plot)

May 17. Integrals over 2D regions.

May 18. Examples of integration over 2D regions.

May 19. Double integrals in polar coordinates.

May 20. Quiz 8 (14.2). Polar integrals.

May 24. Cylindrical and spherical coordinates.

May 25. Surface area of a graph.

May 26. Area of a parameterized surface.

*Makeup exam: 8-9AM, CAT 61**. (answers)*

May 27. Triple integrals.

Quiz 9 (due Tuesday, in class). (answers)

June 1. Triple integrals. Interchange of integrals: an example.

June 2. Change of variables. Examples.

Notes: change of variables in 2D.

June 3. Change of variables: examples.

Quiz 10 (due Monday, in class). (answers)

June 7. Review. Old finals: S08, S09.

*Office hours: 10-11, 12-1 (Korman
247).*

June 8: Final Exam 10:30-12:30, Main Auditorium. (answers)

Decomposition
of a parallelepiped.