Math 200 - Calculus IV, Spring 2010

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

Syllabus (8th 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.

             Review. Sample problems.

 

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.