Differential and Integral Calculus III

Math 2934-012, Fall 2016 (http://www.math.ou.edu/~forester/2934F16)

Information about Exam I — Exam I will be held in the usual room at the usual class time, on Tuesday September 20. It will start promptly at the beginning of the class period, so make sure you're on time. The test will cover sections 12.5, 12.6, 13.1-13.3, 14.1, and 14.3. The subsection "Integrals" in 13.2 on page 899 was not covered, and will not be on the exam. The subsection "Partial differential equations" in 14.3 on page 960 was also not covered, and will not be on the exam.

The test will have four or five problems, possibly with several parts each. It will be graded with a total of 60 points. Calculators or other devices will not be allowed.

The following topics are likely to be covered, though the exam is not limited to these topics:

• equations of lines: symmetric equations and vector-valued parametrizations
• equations of planes
• solving geometric problems involving lines and planes, using vectors and their properties
• 3-dimensional surfaces and their equations: cylinders and quadric surfaces; be able to determine a surface from its equation, as in the table on page 877
• visulizing parametrized curves in 3 dimensions
• derivatives of vector-valued functions, velocity vectors of curves
• arc length and curvature, tangent, normal, and binormal vectors
• level curves of a two-variable function; visualizing the graph z=f(x,y) from level curves and traces
• partial derivatives: definition, meaning in terms of slope of a line; second partial derivatives, Clairaut's theorem

Advice: I recommend first reviewing homework problems from each section, perhaps doing a few odd-numbered ones and checking your answers. If you get one wrong, don't skip ahead, but tackle it right away and find out how it works. There may be a similar example worked out in the section, or you can try getting help. I also recommend the "Concept Check" questions at the end of each chapter as a way of finding out where to focus your efforts. There are extra problems there too that are worth trying out.

When it comes time for the test itself, relax and do the best you can. Because you have studied, you know which topics you know best, and can get those problems out of the way quickly. Then you'll have plenty of time to spend on the remaining ones.

Solutions to Exam I

Information about Exam II — Exam II will be held in the usual room at the usual class time, on Tuesday October 25. It will start promptly at the beginning of the class period, so make sure you're on time. The test will cover sections 14.4 - 14.8 and 15.1 - 15.3. The subsection "Tangent planes to level surfaces" on page 994 was not covered, and will not be on the exam.

The test will have four or five problems, possibly with several parts each. It will be graded with a total of 60 points. Calculators or other devices will not be allowed.

The following topics are likely to be covered, though the exam is not limited to these topics:

• using the tangent plane (or linear approximation, or differentials) to estimate the value of a function
• knowing the correct chain rule to use when composing multi-variable functions
• computing the gradient and directional derivatives, and knowing the relationship with level curves
• identifying local maxima and minima using the second derivatives test
• finding absolute maxima and minima on a closed and bounded region, by checking critical points and the boundary
• finding a maximum or minimum using Lagrange multipliers
• computing double integrals over type I and type II regions
• computing double integrals in polar coordinates

My advice is the same as for Exam I. Good luck!

Solutions to Exam II

Information about Exam III — Exam III will be held in the usual room at the usual class time, on Tuesday November 22. It will start promptly at the beginning of the class period, so make sure you're on time. The test will cover sections 15.5 - 15.8 and 16.1 - 16.3.

The test will have four or five problems, possibly with several parts each. It will be graded with a total of 60 points. Calculators or other devices will not be allowed.

The following topics are likely to be covered, though the exam is not limited to these topics:

• calculating surface area
• calculating triple integrals, using rectangular, cyclindrical, and spherical coordinates (including converting between coordinate systems)
• computing line integrals of functions, and line integrals of vector fields
• properties of gradient vector fields, recognizing them, and finding the function from its gradient
• using the fundamental theorem of line integrals to compute the line integral of a vector field

My advice is the same as for Exam I. Good luck!

Solutions to Exam III

Information about the Final Exam — The Final Exam will be held in the usual room on Monday December 12, 8:00 - 10:00 am. It will start promptly at 8:00, so make sure you're on time. The test will cover the same material that was covered in midterms I, II, and III, as well as sections 16.4 - 16.7 and 16.9. Some extra emphasis will be given on the newer material; probably half or more will be on chapter 16.

You are permitted to bring a 4x6 index card with notes on both sides. Think carefully about what to put on your card! As usual, calculators or other devices will not be allowed.

See the advice above for topics to be covered from the first three exams. For the newer material, the following topics are likely to be covered, though the exam is not limited to these topics:

• Green's theorem, applications (e.g. area)
• definitions and properties of gradient, curl, divergence
• parametrizations of surfaces, setting up and computing surface integrals of functions, and of vector fields
• the Divergence theorem, using it to compute a surface integral

The test will not cover Stokes's theorem (section 16.8). It will not cover the subsection "Vector forms of Green's Theorem" on page 1148.

Good luck!

Solutions to the Final Exam