MAT 21A: CALCULUS (Winter 2024)

Course Materials




Midterm 1 information: Time and place: Wed., Feb. 7, in class. Bring a pencil and your university ID!

Extra Office Hours: Tue, Feb. 6, 1-2:30pm, in my office (3210 MSB).

Here is the list of topics this midterm covers. Functions: domain, range (only when you can find it from the graph). Limits: computation of limits, one-sided limits, and limits involving infinity. Horizontal and vertical asymptotes and intercepts, and graphing functions using these. Continuous functions, and intermediate value theorem. Derivatives: differentiable functions; rules (power, product, quotient); tangents. This covers Section 1.1, Sections 2.2, 2.4, 2.5, 2.6, and Sections 3.1-3.3 in the book (higher-order derivatives and the derivative of y=ex from Section 3.3 of the book will not be on this midterm). Section 2.3 (the precise definition of a limit) will not be on any exam.

For practice, solve problems 1,2,3,5 on the sample Midterm 1 and problem 2(b) on the first page of 2005 Midterm 1. The exam will have four problems of the same type as problems 1,2,3,5 on the sample exam, in the same order; the only difference is that problem 3 will have three parts, (a), (b), and (c). However, do not expect exact same problems; for example, limit problem 3(a) on the exam may require a different method than the corresponing problem on the sample exam. Discussion problems 1-3 above, as well as the first three homework assignments, are also good practice.
Midterm 1 solutions.



-
Midterm 2 information: Time and place: Wed., Feb. 28, in class. Bring a pencil and your university ID!

Extra Office Hours: Tue, Feb. 27, 1-2:30pm, in my office (3210 MSB).

Here is the list of topics it covers. Derivatives: rules (power, product, quotient, chain); implicit differentiation; derivatives of inverse functions, derivatives of trigonometric, exponential, logarithm, and inverse trigonometric functions; tangents; velocity and acceleration; related rates; extreme values (local and global extrema); Rolle's theorem and mean value theorem. This covers Sections 3.3-3.10, 4.1-4.2 in the book. (You also need to know the relevant material from previous sections.) Section 3.11 (Linearization and Differentials) will not be on any exam.

For practice, solve the latest sample Midterm 2. The exam will again have the same format: five problems of the same type, in the same order (but, again, do not expect exact same problems; for example, the related rates problem 3 on the exam may require a different method than the corresponding problem on the sample exam). Examples from lectures, Discussion problems 4-6 above, as well as homework assignments starting from Section 3.3, are also good practice. The homework and discussion for the midterm week are a review of the exam material and have been posted. Note: Please be very careful when solving routine derivative problems (such as the problems 1 and 2 on the sample Midterm 2). You will receive very little partial credit if you make a differentiation mistake, even a small one.
Midterm 2 solutions.