Math 200 - Calculus IV, Spring 2011

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Instructor: Anatolii Grinshpan
Office hours: WR 4-5, Korman 247, or by appointment, Korman 253

Syllabus  Wiley+  Math 200 root page   Greg Naber’s notes   Academic calendar   Math resource center   

Mar 28. Introduction to the course. Three-dimensional space.

Mar 29. Planes parallel to coordinate planes. Distance between two points. Spheres.

Mar 30. Vectors in space.  Properties of length. Orthogonal unit frame.

Mar 31. Quiz 1 (11.1). Dot product.

Apr 4. Dot product. Direction cosines.

Apr 5. Orthogonal projection. Shortest distance.

Apr 6. Quiz 2 (11.2, 11.3). Lines in 3D.

Apr 7. Lines and planes in 3D.

Apr 11. Cross product.

Apr 12. Review guide. Practice problems. Old midterm. (answers)

Apr 13. Midterm 1: 8-8:50 AM, Main Auditorium.

             Regular class: vector functions.

 

Apr 14. Quiz 3 (take-home, due Monday). Parametric curves in 3D. 

 

Apr 18. Tangent line equation. Traces and level sets of surfaces.

 

Apr 19. Quadric surfaces.

 

Apr 20. Quadric surfaces.

 

Apr 21. Quiz 4 (11.7). Functions of two and three variables.

 

Apr 25. Partial derivatives.

 

Apr 26. Review guide. Practice problems. Old midterm. (answers)

 

Apr 27. Midterm 2: 8-8:50 AM, Main Auditorium.

             Regular class: The dot and the line. Local linear approximation. 3D plotter.

 

Apr 28. Local linear approximation: total differential and approximate error. Tangent plane and normal line.

             Quiz 5 (take-home, due Monday).

 

May 2. Contour map. Gradient. Directional derivative.

 

May 3. Contour map. Gradient. Directional derivative.

 

May 4. One, two, and three variables: comparison. Gradient as a normal.     

            Notes: directional derivatives.

 

May 5. Quiz 6 (13.5, 13.6) (answers). Stationary (critical) points.

 

May 9. Points of local and absolute extremum.

            Notes: second partials test. Example from class.

 

May 10. Review guide. Practice problems (answers). Old midterm (answers).

 

May 11. Midterm 3: 8-8:50 AM, Main Auditorium.

              Regular class: Cavalieri’s principle.

 

May 12. Double integral and iterated integral.

 

May 16. Double integral and iterated integral. Quiz 7 (take-home, due Wednesday).

 

May 17. Examples of integration.

 

May 18. Double integral in polar coordinates.

 

May 19. Quiz 8 (14.3). Cylindrical and spherical coordinates.

 

May 23. Surface area of a graph.

 

May 24. Area of a parameterized surface.

 

May 25. Examples on surface area.

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

 

May 26. Quiz 9 (11.8, 14.4).

 

May 30. Memorial Day.

 

May 31. Triple integral. Volume and total mass. Interchange of integrals.

              Archimedes on volumes. Volume of a sphere via Cavalieri. On average value, volume, and probability.

 

June 1. Triple integral in Cartesian, cylindrical, and spherical variables.

 

June 2. Quiz 10 (14.5, 14.6). Change of variables in 2D. Jacobian. Examples.

 

June 6.  Review guide. Old final (answers).

 

June 7.  Office hours: 12-2 (Korman 247).

 

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

 

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