The test is given in four separate rooms. Please find your recitation in the table below to determine where to go for the test. (The rooms are NOT the same as for midterms.)

The final exam is cumulative and covers Chapters 5 &ndash 8 of Stewart. (The first few sections from Ch. 5 are Calc I material and will not be emphasized.) The series will play an important role on the test (about 40% of the questions will be on Chapter 8). You are also responsible for the material from Calc I and precalculus (properties of functions, differentiation techniques, etc.)

Below is the checklist for Chapter 8. This is the content of Sections 8.1 &ndash 8.7 (with the exception of a few topics we didn't cover). Please refer to the checklists for Midterms I and II for the material of previous chapters.

• Sequences and their limits
• Convergence of series
• Operations with convergent series
• Geometric series and its sum, p-series
• Test for divergence, Integral Test, Comparison Test, Ratio Test
• Absolute convergence
• Power series, radius of convergence and interval of convergence
• Representation of functions by power series
• Taylor and Maclaurin series; series for 1/(1-x), sin x, cos x, e^x
• Differentiating and integrating power series

The best preparation for the exam is to go over past homeworks and midterm exams. For extra practice with series, use the end-of-chapter review material from Chapter 8:

• Concept check: 1, 2, 3, 4, 5abcf, 6
• True-False Quiz (all of it)
• Exercises 1 &ndash 4, 9, 11, 17, 19, 22, 32, 33, 35, 37, 39 &ndash 42, 45

Since series is conceptually the hardest topic we've seen, the concept check and true-false quiz are recommended.

For extra practice of the earlier material, check the review questions for the two midterms. If you did those questions before and want more practice, just pick exercises from sections that seem particularly hard.

Additional office hours will be held by Yasha Savelyev on Monday, Dec 17, 4-7 pm in 3-104.

The material covered by the test is outlined below. You are also responsible for the integration and differentiation techniques as well as the precalculus, but the exam emphasizes differential equations (i.e. there won't be any questions when you have to compute a volume, even though you might need to compute an integral when solving a differential equation). This is the content of Sections 7.1 &ndash 7.5 (with the exception of a few topics we didn't cover), together with the supplementary notes.

• Qualitative analysis of a differential equation, direction fields
• Euler's method
• Solving differential equations: separation of variables
• Orthogonal trajectories
• Exponential model: population growth, radioactive decay, Newton's cooling law
• Logistic Equation
• Second order equations

The difficulty level and the exam policies will be similar to those for Midterm I. The best way to prepare for the test is to go over past homeworks. Non-bold questions are no less important than the bold ones. If a particular topic seems hard, do extra questions from the corresponding section in the book. Additionally, you can do end-of-the-chapter exercises for Chapter 7 (1-13, 16, 17 are all good), as well as the exercises on second order equations in the supplement that were not assigned as homework.

The material you are responsible for is outlined below. (All pages and example numbers refer to Stewart. Reference pages are in the back of the book.) This is the content of sections 5.5 – 5.7, 5.10, 6.1 – 6.5, 6.7 (with the exception of particular topics that we didn't cover), as well as the basics learned in previous courses.

• Precalculus and Calc I: functions and their graphs, limits, basic differentiation and integration, differentiation formulas from reference page 5 (1-8, 9, 11, 13-15, 19-21), integration formulas from reference page 6 (1-4, 6, 7, 17)
• Integration Techniques: substitution, integration by parts, partial fractions
• Improper Integrals (infinite only)
• Areas, length of curves, volumes (disk and washer methods, cross-sections as in Example 8 section 6.2)
• Work
• Average value of a function; probability

The title page of the test detailing the exam rules is here.

The best way to prepare for the test is to go over past homeworks. Non-bold questions are no less important than the bold ones. If a particular topic seems hard, do extra questions from the corresponding section in the book. Additionally, you can use the end-of-chapter questions for Chapters 5 and 6. The following questions provide a good review and some extra practice (they are not supposed to mimic the actual exam questions):

Chapter 5 (p. 435-436): 14, 27, 28, 29, 55, 61
Chapter 6 (p. 494-495): 6, 13, 15, 19, 26, 31