MAT 272 Topics

1. Coordinates in the space, vectors, dot product and cross product;

2. Lines and planes in the space;

3. Vector functions, derivatives and integrals, tangent lines;

4. Arc length and curvature;

5. Velocity, acceleration, components of acceleration;

6. Limits of functions of several variables;

7. Partial derivatives;

8. Tangent planes and linear approximation;

9. Chain Rule and implicit differentiation;

10. Directional derivatives and gradient;

11. Relative maximum and minimum;

12. Absolute max/min in a region;

13. Max/min under constraint (no Lagrange multipliers);

14. Double integrals: rectangles, type 1, type 2, changing order;

15. Double integrals in polar coordinates;

16. Mass and center of mass;

17. Triple integrals;

18. Line integral of a function, line integral of a vector field;

19. Fundamental Theorem;

20. Green's Theorem;

21. Curl and divergence;

22. Determining if a given vector field is a gradient;

23. Area of a surface;

24. Surface integral of a function, surface integral of a vector field.