Math 31B: General Course Outline
Course Description
31B. Integration and Infinite Series. (4) Lecture, three hours; discussion, one hour. Requisite: course 31A with a grade of C or better. Not open for credit to students with credit for course 3B. Transcendental functions; methods and applications of integration; sequences and series. P/NP or letter grading.
Course Information:
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
The goal of Math31AB is to provide a solid introduction to differential and integral calculus in one variable. The course is aimed at students in engineering, the physical sciences, mathematics, and economics. It is also recommended for students in the other social sciences and the life sciences who want a more thorough foundation in onevariable calculus than that provided by Math 3.
Students in 31AB are expected to have a strong background in precalculus mathematics, including polynomial functions, trigonometric functions, and exponential and logarithm functions. In order to enroll in 31A, students must either take and pass the Mathematics Diagnostic Test at the specified minimum performance level, or take and pass Math 1 at UCLA with a grade of C or better.
Most students entering the 313233 sequence at UCLA have taken a calculus course in high school and enter directly into Math 31B.
The course 31A covers the differential calculus and integration through the fundamental theorem of calculus. The first part of course 31B is concerned with integral calculus and its applications. The rest of the course is devoted to infinite sequences and series.
Singlevariable calculus is traditionally treated at many universities as a threequarter or twosemester course. Thus Math 31AB does not cover all of the topics included in the traditional singlevariable course. The main topics that are omitted are parametric curves and polar coordinates, which are treated at the beginning of 32A.
Ample tutoring support is available for students in the course, including the walkin tutoring service of the Student Mathematics Center.
Math 31A is not offered in the Spring Quarter. Students wishing to start calculus in the Spring may take 31A through University Extension in the Spring or in the Summer.
Please note: Students who are enrolled at UCLA in Spring and wish to enroll in Extension simultaneously should meet with their college counselor about whether they will be able to receive credit for the course because of concurrent enrollment restrictions.
Textbook(s)
J. Rogawski, Single Variable Calculus, (4th Edition) , W.H. Freeman & CO
(a) The inverse trigonometric functions can be limited to the sine, cosine and tangent and the hyperbolic functions to the sine and cosine.
(b) The amount of time devoted to techniques of integration should be determined by the instructor
(c ) The topic of improper integrals is closely related to that of sequences and series, so it makes sense to postpone it until just before the chapter devoted to those subjects
(d) Although the formal definition of the limit is not included in Math 31A, the corresponding topic in the setting of infinite sequences is appropriate for 31B.
Outline update: R. Brown, 3/15
Schedule of Lectures
Lecture  Section  Topics 

1 
Introduction 

2 
7.1 
Derivative of Exponential Function 
3 
7.2 
Inverse Functions 
4 
7.3 
Logarithms and their Derivatives 
5 
7.3 
Logarithms and their Derivatives (cont'd) 
6 
7.7 
L'Hopital's Rule 
7 
7.8 9 
Inverse Trig and Hyperbolic functions (a) 
8 
8.1 
Integration by Parts 
9 
8.1 
Integration by Parts (cont'd) 
10 
8.5 
Method of Partial Fractions (b) 
11 
8.9 
Numerical Integration 
12 
9.1 
Arc Length and Surface Area 
13 
9.4 
Taylor Polynomials 
14 
Midterm 1 (7.1 3; 7.7 9; 8.1; 8.5) 

15 
8.7 
Improper Integrals © 
16 
8.7 
Improper Integrals © (cont'd) 
17 
11.1 
Sequences (d) 
18 
11.1 
Sequences (d) (cont'd) 
19 
11.2 
Summing an Infinite Series 
20 
11.3 
Series with Positive Terms 
21 
11.3 
Series with Positive Terms (cont'd) 
22 
Midterm 2 (8.7; 8.9; 9.1; 9.4; 11.1) 

23 
11.4 
Absolute and Conditional Convergence 
24 
11.5 
Ratio and Root Tests 
25 
11.6 
Power Series 
26 
11.6 
Power Series (cont'd) 
27 
11.7 
Taylor Series 