MAT 21B: CALCULUS (Fall 2023)
Course Materials
Note. These are sample exams from the last time I taught the course.
Midterm 1 information: Time and place: Wed., Oct. 25.
Here is the list of topics it covers.
Indefinite integral, definite integral, approximating sums,
trapeziodal and Simpson's method, fundamental theorem of calculus,
substitution methods in the definite and indefinite
integral, computing the areas between curves (integration
with respect to x and with respect to y).
This covers Sections 4.8, 8.7, and 5.1-5.6 in the book, first three lecture slide files (labeled week 1-3 above),
homework assignments 1-3, and Discussion
Problems 2-4. Apart from section 8.7, Chapter 8 of the book (for example, material on weeks 4 and 5 lecture slides) will not be on the exam.
For practice, solve the sample
Midterm 1 above.
This midterm will have the same format: four problems of the same type, in the same order.
Details on exam administration have been announced in Canvas.
Midterm 1 solutions.
Midterm 2 information: Time and place: Fri., Nov. 17, in class.
Here is the list of topics it covers.
Integration methods: integration by parts, trigonometric integrals,
trigonometric substitutions, rational functions and partial fractions;
volumes using cross sections (washer method) and cylindrical shells;
arc length; areas of surfaces of revolution.
This covers Sections 8.2-8.5, 6.1-6.4 in the book,
lecture slides for weeks 4-7, homework assignments 4-6, and Discussion
Problems 5-7. Section 6.6 (last part of week 7 slides) will not
be on this exam. The discussion on Thu., Nov. 16 will be devoted to
preparation for the exam.
This exam is (by necessity) computationally intense,
so make sure to practice under a time limit!
For practice, solve the sample Midterm 2 above (solutions).
This midterm will have the same format: four problems of the same type, in the same order (but do not expect
that, say, problem 1(b) on your exam can be solved by exact same integration method as problem 1(b) on the sample
exam). The same trigonometric formulas as on the sample exam will be provided.
For additional practice, you may choose a few problems from
Chapter 6 Practice problems
(e.g., 7, 9, 13, 19, 21, 23; for arc lengths and areas of surfaces of
revolution, concentrate on setting up the integrals,
not computing them) and from
Chapter 8 Practice problems
(e.g., 1, 11, 19, 23, 25, 27, 37, 39, 41, 69, 77, 85, 91, 103, 107).
Details on exam administration are the same as for Midterm 1, but will be announced in Canvas.
Midterm 2 solutions.