This page lists the in-recitation problems worked on during MATH 22 (Calculus 3) in Summer 2012 at MST.

Notational convention: in your textbook, vectors are bolded and look like this: $\textbf{x}$. For better readability on the computer, we use instead the notation $\vec{x}$ for vectors on these pages.

In-class work
5 June 2012 (solutions) - spatial geometry, distance, vector products, sphere equation derivation, angle between vectors, projection of a point

6 June 2012 (solutions) - equations of lines and planes, parallel/intersecting/skew lines

7 June 2012 (solutions) - continuation of yesterday and distance between "things"

8 June 2012 (solutions) - identifying equations of quadric surfaces

12 June 2012 (solutions) - vector functions, limits/derivatives/integrals of vector functions, intersection of surfaces

13 June 2012 - EXAM DAY

14 June 2012 (solutions) - length of space curve, unit tangent vector, unit normal vector, curvature, normal and osculating planes

15 June 2012 (solutions) - position, velocity, acceleration, speed, tangential and normal components of acceleration, projectile problems (not on exam), domain of functions of two variables, level curves

19 June 2012 (solutions) - limits and continuity of functions of two variables

20 June 2012 (solutions) - partial derivatives

21 June 2012 (solutions) - linearizations, differentials, chain rule

22 June 2012 (solutions) - directional derivatives, gradient, tangent planes and normal lines

26 June 2012 (solutions) - local and absolute extrema

27 June 2012 (solutions) - Lagrange multipliers (general type, geometry, and economics examples)

28 June 2012 - EXAM DAY

29 June 2012 - double integrals

3 July 2012 - double integrals in polar coordinates

5 July 2012 - triple integrals

6 July 2012 - triple integrals in cylindrical coordinates

11 July 2012 - EXAM DAY

13 July 2012 - conservative vector fields, line integrals of vector fields, open, connected, and simply-connected sets

17 July 2012 - Green's theorem

18 July 2012 - curl and divergence; parametrization of surfaces

19 July 2012 - parametrization of surfaces; surface integrals

20 July 2012

24 July 2012 - Stokes' theorem

25 July 2012 - final day review