# Math 31BH: General Course Outline

## Course Description

**31B. Integration and Infinite Series (Honors). (4)**Lecture, three hours; discussion, one hour. Enforced requisite: course 31A with grade of B or better. Honors course parallel to course 31B. 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 one-variable 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.

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.

Single-variable calculus is traditionally treated at many universities as a three-quarter or two-semester course. Thus Math 31AB does not cover all of the topics included in the traditional single-variable 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 walk-in 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 in the College of Letters and Science who will be enrolled at UCLA in Spring and wish to enroll in Extension simultaneously should meet with a College Counselor about whether they will be able to receive credit for the course because of concurrent enrollment restrictions: Concurrent Enrollment Information.

## Textbook(s)

J. Rogawski, *Single Variable Calculus, (2nd Edition)* , W.H. Freeman & CO

Click for information about an electronic version of the book

(A) Instructor should select from the material from Sections 8.3 - 8.5, since it is not possible to cover all integration techniques adequately in two lectures. In Section 8.3, you may require students to know how to integrate powers of (sin x)^m(cos x)^n and otherwise be able to evaluate trigonometric integrals given reduction formulas or a table of integrals. You may limit integration of rational functions to distinct linear factors or at most double linear factors, but require that students recognize the form of a partial fraction expansion in general (without having to find it).

(B) Students should learn to apply the Error Bound for Taylor polynomials.

© Although the :"epsilon-delta" definition of limits in section 2.8 is not covered in Math 31A, the "epsilon-N" definition of limits is appropriate for this course.

Outline update: 8/07, description updated 9/14

## Schedule of Lectures

Lecture | Section | Topics |
---|---|---|

1 |
7.1 |
Derivative of exponential functions |

2 |
7.2 |
Inverse functions |

3 |
7.3 |
Logarithms and their derivatives |

4 |
7.4 |
Exponential growth and decay |

5 |
7.5-7.6 |
Compound Interest, Models involving y' = k(y-b) |

6 |
7.7 |
L'Hopital's Rule |

7 |
8.1 |
Integration by Parts |

8 |
8.2 - 8.3 |
Trigonometric integrals, Trigonometric Substitution(A) |

9 |
8.5 |
Method of partial fractions |

10 |
8.6 |
Improper integrals |

11 |
8.8 |
Numerical integration |

12 |
8.8 |
Error Bounds for Numerical Integration |

13 |
9.1 |
Arc length |

14 |
9.2 |
Fluid pressure and force |

15 |
9.4 |
Taylor polynomials |

16 |
9.4 |
Taylor's Theorem, Error Bound(B) |

17 |
11.1 |
Sequences and Infinite Series(C) |

18 |
11.2 |
Infinite Series |

19 |
11.2 |
Infinite Series (cont'd) |

20 |
11.3 |
Convergence of Series with positive terms |

21 |
11.4 |
Conditional Convergence |

22 |
11.5 |
Ratio and root tests |

23 |
11.6 |
Power Series |

24 |
11.6 |
Power Series (cont'd) |

25 |
11.7 |
Taylor Series |

26 |
11.7 |
Taylor Series (cont'd) |