Exams

Midterm I                 Wed October 1                4.00 pm - 5.20 pm        Library E4320

The first midterm exam will cover the materials of Chapters 1, 2 and 4 in the textbook with the exclusion of: section 6 in Chapter 1; section 1B in Chapter 2; sections 1E, 2C, 4C in Chapter 4.

There will be three problems in the exam.

One is about lines, planes and vectors: parametric representations and equations of lines and planes; calculation of projections, distances and angles using the dot product.

A second problem is about systems of linear equations: study the set of solutions using row operations, determinants, inverses, etc.

A final problem is about parametrized curves and surfaces: curves on surfaces, partial derivatives, tangent lines and tangent planes, length of curves, etc.

Some suggestions to prepare for the exam are: review your notes, the textbook and the homework assignments. Work through the examples in the textbook and your notes on your own, make sure you understand homework corrections. Most important of all, do plenty of exercises (there are extra exercises at the end of every chapter in the textbook).

Midterm II                Wed November 12           4.00 pm - 5.20 pm        Library E4320

The exam will cover Chapters 5, 6 and 7 and section 8.1. A more detailed description of what will be in the exam and what sections in each chapter you can skip is given below. I have also indicated exercises in the textbook which might be useful. Of course you are not required to do all of them, but it is a good idea to solve as many as possible. In order to prepare well for the exam, you should also review the textbook, your notes and past homework assignments. You are encouraged to meet me or Shalin during office hours next week for any doubt and to come to the lecture and recitation on Monday Nov 10 ready to ask plenty of questions.

Chapter 5.

Limits. Continuity. Differentiability. Directional derivatives.

Section 5 is not included in the exam.

Exercises from the Review of Chapter 5 (pp. 250-251): 10-34.

Chapter 6.

Interpretation of the gradient of a function. The chain rule. Implicit differentiation. Critical points of a function and second derivative criterion to find extreme points. Method of Lagrange multipliers. Change of coordinates: polar, spherical and cylindrical coordinates; the Jacobian matrix.

Sections 1D and 4F are not included in the exam.

Exercises from the Review of Chapter 6 (pp. 309-311): 1-6, 9, 15, 18-22, 24-27, 29-38, 40-44, 46.

Chapter 7.

Iterated integrals. Definition of integrals as limits of Riemann sums. Change of variables. Improper integrals.

Section 7 is not included in the exam.

Exercises from the Review of Chapter 7 (pp. 363-366): 1-39, 46-61.

Section 8.1.

Definition of line integrals. Fundamental Theorem of Calculus and its consequences.

You can skip the section “Equivalent parametrizations” on p. 373.

Exercises 1-16 on p. 376.

Final Exam               Tue December 9              8.30 pm - 11.00 pm        Library E4320

The final exam is cumulative, covering everything we have studied during the semester. However, extra emphasis will be given to Chapters 8 and 9.

See the info about midterm exams for what you can skip in Chapters 1, 2, 3, 5, 6 and 7, with one change: section 6 in Chapter 1 (the cross product) is a prerequisite for some of the material in Chapter 9, so you should be familiar with it.

Chapter 8.

Definition of line integrals. Fundamental Theorem of Calculus and its consequences. Arc-length parametrization. Curvature. Divergence and curl of a vector field.

Chapter 9.

Green’s theorem. Path independence principle. Gauss’s and Stokes’s Theorems in the plane. Area of a surface. Integral of a vector field on a surface. Gauss’s Theorem. Stokes’s Theorem.

You can skip section 3D and the whole of section 6.

Here’s a list of exercises from the REVIEW at the end of each chapter which might be useful to do before the exam:

Chapter 1 (pp. 44-45): 17-26 and 31-35.

Chapter 2 (pp. 99-101): 21-24, 29-32, 43-44.

Chapter 4 (pp. 214-215): 1-10, 24.

Chapter 5 (pp. 250-251): 10-34.

Chapter 6 (pp. 309-311): 1-6, 9, 15, 18-22, 24-27, 29-38, 40-44, 46.

Chapter 7 (pp. 363-366): 1-39, 46-61.

Chapter 8 (pp. 395-396): 1-8, 21-22.

Chapter 9 (pp. 457-459): 1-3, 5, 7-8, 10, 12, 14, 16-17.

I will hold office hours as follows:

Fri Dec 5, 11am-2pm in my office Math 2-121;

Tue Dec 9, 11am-noon in the MLC, noon-1pm in my office.

Office hours on Monday Dec 8 at 3pm are cancelled.

Writing an email to ask a quick question or to schedule an appointment outside of these hours is also possible.

Shalin also will hold exceptional office hours:

Mon Dec 8, 3-6pm in the MLC.

He will also take part in a tutoring session organised by the Math Club:

Tue Dec 9, 5-8.30pm in P-131 in the Math Tower.

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Exam Rules:

Calculators are not allowed.

All electronic devices (except watches) must be turned off. In particular, cell phones are not allowed. If you take your cellphone out for any reason (even just to check the time), you will be asked to turn in your exam paper and to leave the room.

Notes, textbooks, etc. are not allowed. Only the test paper and pens/pencil/eraser should be on your desk.

No consultations with others. Please raise your hand if you have any question.

No bathroom brakes are allowed. Please use the restroom before the test starts.