Math 202, CALC III: EXAMS

Math 202, CALC III: EXAMS

Tuesday, May 13: 11 am- 1pm Office Hours. Stop by to see your exam.

MOnday, May 12: Office Hourse Cancelled. I will have office hours on Tue instead. Please contact your TA if you need to see your exam earlier than that.

Sunday, May 11: Right now we are a bit behind the schedule with getting the exams ready for tomorrow, although there is still a good chance that we will make it. I will update this website on Monday, at 10 am, to keep you posted. In any case, I will have additional office hours on Wednesday, May 14, 11 am- 1pm just in case.

Spring 2008 Exam answers.

2005 Exam. Solutions.

MIDTERM II: Friday, April 4, in class.

Solutions to Midterm II (04/04/08)

Preparation: go over the hw problems and lecture notes (especially the examples covered in those); read the textbook; talk to your instructor if you have questions about hw or lectures. Get enough sleep before the exam and make sure you show up in time. Rememeber: there are no make-up exams!

Past midterm exams. Spring 2005. Solutions.

Random practice problems. [no solutions]

Exam material:

1. Gradients, directional derivatives, chain rule.

2. Hessian.

3. Critical points. Local maxima and minima (second derivative test).

4. Lagrange method: in R^2 (one constraint) and R^3 (one or two constraints).

5. Global maximum and minimum on a region with boundary (optimization).

6. Double and triple integrals by iteration. Area. Volume. Cavalieri principle.

7. Change of variable in R^2.

MIDTERM I: Friday, February 29, in class.

Practice problems. (Practice exam to be added later this afternoon; we will discuss it in class if time permits.)

Midterm exam: answers

Exam material:

1. Vectors in R^2, R^3 (R^n)

standard basis, addition, subtraction, scalar multiplication (know how to represent this geometrically), norm of a vector.
inner product: a) algebraic formula; b) geometric meaning (angle between two vectors); c) orthogonality
cross product: a) algebraic formula; c) geometric meaning (a x b orthogonal on a, b; ||a x b||=area of parallelogram spanned by a, b)
use of vectors to find equations of : lines; planes.

2. Graphs and level sets.

definition
what is the difference between level curves and level surfaces?
know what the equation of a: parabola, circle, ellipse (R^2); sphere (R^3) look like.
Equation of a tangent plane to the graph of f(x,y).

3. Paths and curves (what is the difference between the two?). Velocity.

5. Limits and continuity.

definition of D_r(x); open sets.
know how recognize continuous functions.
know how to prove that a function is *not* continuous (or that a limit doesnt exist) in some simple examples (as in class)

4. Differentiation.

partial derivatives of a scalar function
gradient of a scalar function
the matrix of partial derivatives of a vector-valued function
Chain Rule
Special case of chain rule: d/dt F(c(t))=grad F(c(t)) * v(t)

5. Differentiable (smooth) functions

know how to check that a function is smooth (Theorem)
linear approximation: when does it apply? (know how to apply in a concrete situation: hw exercise).

MIDTERM II: Friday, April 4, in class.

FINAL EXAM: Thursday, May 8, 9-12 Noon. Location TBA.