MATH 250: Calculus III

March 23, 2012

Test #2 Review Topics

1. Calculus of vector-valued functions

2. Arc length. Speed

3. Arc length parametrization

4. Unit tangent vector. Curvature. Unit normal vector

5. Motion in three-dimensional space. Velocity and acceleration. Finding velocity and path from acceleration

6. Tangential and normal components of acceleration

7. Functions of two variables. Traces. Level curves and contour maps

8. Functions of three variables. Level surfaces

9. Limits and continuity of functions of several variables

10. Partial derivatives. Higher-order partial derivatives. Clairaut’s theorem

11. Linearizations. Linear approximations. Tangent planes to surfaces z=f(x,y)

12. Gradient

13. Chain rule for paths

14. Directional derivatives

15. Significance of gradient: direction and value of maximum rate of increase; normal vector to level surface; finding tangent planes to level surfaces

16. Chain rule for functions of several variables

17. Critical points. Local extrema

18. Global extrema

19. Definition of double integral. Double integral as volume

20. Iterated integrals. Fubini’s theorem