MATH 250: Calculus III

February 18, 2012

Test # 1 Review Topics

1. Parametric equations of curves in the plane; paths versus curves

2. Slope of a tangent line to a curve given in parametric form

3. Arc length of a curve given in parametric form

4. Speed along a parametrized path

5. Polar coordinates; conversions between polar and rectangular coordinates; graphing curves and regions in polar coordinates

6. Arc lengths in polar coordinates

7. Areas in polar coordinates; area between two curves in polar coordinates

8. Conic sections: properties; standard forms; foci, directrix, etc.

9. Vectors in two dimensions; magnitude of a vector; vector algebra; basic properties; triangle inequality

10. Unit vectors, standard basis vectors

11. Vectors in three dimensions; distance formula

12. Parametric equations of a straight line in three dimensions; intersections of straight lines

13. Dot product; basic properties (with proofs); angle between vectors; projection of a vector along another vector

14. Determinants

15. Cross product; basic properties (with proofs)

16. Areas and volumes with the use of cross product

17. Planes in three dimensions; planes through three given points; intersection of a plane and a line; angle between planes; traces of a plane

18. Basic quadric surfaces; traces of quadric surfaces

19. Cylindrical coordinates; conversions between cylindrical and rectangular coordinates; level surfaces; identifying surfaces and regions in cylindrical coordinates

20. Spherical coordinates; conversions between spherical and rectangular coordinates; level surfaces; identifying surfaces and regions in spherical coordinates

21. Vector-valued functions: parametric curves in three dimensions; projections of curves onto coordinate planes