Math 31A: General Course Outline
Catalog Description
    31A. Differential and Integral Calculus. (4) Lecture, three hours; discussion, one hour. Preparation: at least three and one-half years of high school mathematics (including some coordinate geometry and trigonometry). Requisite: successful completion of Mathematics Diagnostic Test or course 1 with a grade of C- or better. Differential calculus and applications; introduction to integration. P/NP or letter grading.
Textbook
Reviews & Exams

    The following schedule, with textbook sections and topics, is based on 26 lectures. The remaining classroom meetings are for leeway, reviews, and two midterm exams. These are scheduled by the individual instructor. Often there are reviews and midterm exams about the beginning of the 4th and 8th weeks of instruction, plus reviews for the final exam.

    In certain cases (such as for coordinated classes), it may be possible to give midterm exams during additional class meetings scheduled in the evening. This has the advantage of saving class time. A decision on whether or not to do this must be made well in advance so that the extra exam sessions can be announced in the Schedule of Classes. Instructors wishing to consider this option should consult the mathematics undergraduate office for more information.
Schedule of Lectures
Lecture
Sections
Topics
1
2.1
Limits, Rates of Change, Tangent Line (A)
2
2.2 - 2.3
Limits Numerically and Graphically, Limit Laws
3
2.4 - 2.6
Continuity, Evaluating limits, Trigonometric limits(B)
4
3.1
The Derivative
5
3.2 - 3.3
The Derivative as a Function, Product and Quotient Rules
6
3.4 – 3.5
Rates of Change, Higher Derivatives
7
3.6
Trigonometric functions
8
3.7 - 3.8
The Chain Rule,  Implicit differentiation
9
3.9
Related Rates
10
4.1
Linear approximation (C)
11
4.2
Extreme values
12
4.3
The Mean Value Theorem, Monotonicity
13
4.4
Shape of a graph, concavity
14
4.5
Graph sketching
15
4.6
Applied optimization
16
4.8
Antiderivatives
17
5.1
Approximating and Computing area(D)
18
5.2
Definite integral
19
5.3
Fundamental Theorem of Calculus I
20
5.4
Fundamental Theorem of Calculus II
21
5.5
Net Change
22
5.6
Substitution Method
23
6.1
Area between two curves
24
6.2
Setting up integrals
25
6.3
Volumes of Revolution (E)
26
6.4
Method of Cylindrical Shells

Comments

(A) Students may be asked to memorize a small number of proofs for each exams, of which one will actually appear on the exam. Possible proofs are: the geometric proof that  lim sin(x)/x = 1, proof of the Product Rule, proof that local min/max occur at critical points, part of the Fundamental Theorem (e.g., proof that the derivative of the definite integral of f(x) is f(x) itself).

(B) The text formulates the linear approximation without differentials. Differentials should be mentioned only briefly if at all.

(C) Students may be expected to evaluate limits of the right or left endpoint approximations for
linear and quadratic functions f(x). The Midpoint Rule may be omitted.

(D) Suggestion: In the “washer method”, emphasize revolution about arbitrary axes parallel to the x- and y-axes. In Lecture 26, treat  cylindrical shells briefly, stressing revolution about the x- and y-axes only.  This material should take two lectures.

Outline update: 10/10

For more information, please contact Student Services, ugrad@math.ucla.edu.
 

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