MATH 171B Syllabus
(Integral Calculus – Spring 2012)
Instructor:
Prof. Aba Mbirika
Searles 102, Phone: 725-3131
Email: ambirika@bowdoin.edu
Webpage: www.bowdoin.edu/~ambirika
Textbook: Calculus: Single Variable (Fifth Edition, Wiley, 2009) by Hughes-Hallett, Gleason,
McCallum, et al.
Course Information:
Lectures: Mondays and Wednesday 11:30am – 12:55pm in Searles 113
Lab: Thursdays 2:30pm – 4:25pm in Searles 216
Office Hours: Mondays, Tuesdays, and Wednesdays 2:30pm – 3:30pm
Course Website: Go to http://blackboard.bowdoin.edu and click on the “Courses” tab.
Final Exam: May 15th, 2012, at 9:00am
Do NOT plan to leave for break before this date!!!
Course Description: As suggested by the course title, this is a calculus course stressing the
concept of integration. We will cover the definite integral, the fundamental theorem of
calculus, improper integrals, techniques of integration, practical applications of the definite
integral, and sequence and series. We will use infinite series to approximate functions and
compute the error in these Taylor polynomial approximations. Time permitting, we will
conclude with a brief introduction to differential equations.
Homework/Labs: Homework (20%) will be assigned weekly and assignments will be posted
on Blackboard. Labs (5%) will occur sporadically. Doing the assigned homework is the BEST
way to learn the material. BOTTOMLINE: Homework is the most important part of the course!
Many of the problems on the exams will be based on problems you will see in the homework.
Quizzes/Midterms: There will be many reading comprehension short quizzes at the start
of most classes (10%), two midterms (each worth 20%), and one final exam (25%) this
semester. The quizzes are meant to motivate the readings and make sure we are all on the
same page. The midterms will occur during the lab period in our classroom Searles 217. Here is
the (tentative) schedule:
 Midterm 1: February 23
 Midterm 2: April 19
Weekly Review Session: One night per week (to be determined still), an advanced math
major Michael Ben-Zvi will hold a review session geared just for our class. I encourage you to
attend these sessions to increase your understanding of the course material. Ben-Zvi will run a
series of review sessions at the beginning of the semester, and a review class before each
exam. He’s a very friendly and clever math guy. Plus, he plays frisbee!
Knowing your fellow classmates, collaborating with them, and academic
honesty: You are encouraged to work with others on homework. However, it is VERY
IMPORTANT for each student to write up their own solutions when it comes to turn-in work.
Remember your Bowdoin Honor Code!!! The work that you write down should be the result of
your own understanding, and a direct copying of other’s work is strictly forbidden.
We will be INTERACTIVE in the class (translate that as “I will ask you what YOU would do on a
certain problem or what YOU think might work”). Occasionally we will get into groups and
work on exercises together on the board. Then one or more people in the group will present to
the class. Hopefully you will all know each other very well by the 1st couple of weeks. MAIN
OBJECTIVE: Have fun, enjoy the course, and learn that integral calculus can be a lot of fun.
SOME RULES / REGULATIONS / REMINDERS
HOMEWORK PRESENTATION: Homework papers must be STAPLED, have NO FRAYED
EDGES (i.e., don’t just rip it out your spiral notebook, pleaseeee), the individual cover sheet
(found on blackboard) must be the FIRST page of every assignment. Please do not deviate
from these rules. Neatness and presentation help the grading AND the learning (especially
when you can clearly see what you have written). Pen users – PLEASE USE TAPE WITE-OUT
instead of SCRIBBLING OUT a mess of ink. Graders and teachers abhor large continents of
scribble (we call it scratch work, not turn-in homework).
FINAL EXAM: May 15th, 2012, at 9:00am
CLASS CONDUCT: Here are the simple 3 rules:
(1) Try to come to class on time. However if you are running very late, don’t hesitate to
come. Better late than absent! Attendance is closely monitored as you’ll notice.
(2) TURN OFF THE CELL PHONES. Pretend you are on an airplane after take-off.
(3) Love thy neighbor and all that groovy stuff.
Approximate Course Outline
Basic concepts of integrals:
 Definite integral from Riemann sums, area under a curve (5.1, 5.2)
 Fundamental theorem of calculus (5.3)
 Properties of the definite integral (5.4)
 Anti-derivatives and basic differential equations (6.1 – 6.3)
 Second fundamental theorem of calculus (6.4)
Computing and/or approximating integrals:
 Integration by substitution (7.1)
 Integration by parts (7.2)
 Table of integrals (7.3), trig substitutions and partial fractions (7.4) [Please
review these topics on your own as needed!]
 Approximating the definite integral (7.5)
 Approximation errors and Simpson’s rule (7.6) [most likely a lab]
 Improper integrals (7.7, 7.8)
Real-world applications [we will pick a subset of the choices below]
 Areas and volumes (8.1)
 Applications to geometry (8.2)
 Density and center of mass (8.4)
 Applications to physics (8.5)
 Statistical analysis (8.7, 8.8)
Towards the very cool realms of the infinite!!!
 Sequences and convergence (9.1)
 Geometric series (9.2)
 Does my infinite series blow up?? (See the next two topics)
 Properties of convergence (9.3)
 Convergence tests (9.4)
Brook Taylor
 Power series (9.5) WE GOT THE POWER!!!
1685 – 1731
Approximating functions using series
 Taylor polynomials (10.1)
 Taylor series (10.2, 10.3)
 Computing error bounds in Taylor approximations (10.4)
An obligatory back page2
(I add this since the syllabus is double-sided, and this page will show up blank otherwise)
For extra credit, please do the Sudoku above. By semester’s end, you should be
able to solve any of the calculus problems in the boxes above. In row 8 and
column 1, the notation asks you just to compute the length of the line from (0,0)
to (4 ,2). The value at which to evaluate the derivative in row 6 and column 8 is
cut off, but it should read
. The letters POI in row 7 and column 1 mean
“point of inflection”. Do not work on this with others. This is a SOLO project!
2
Credit for the images on this page goes to Lesley Britton Eygabroad.