MATH 221 (Fall 2012)

Instructor's contact information

Michael Robinson
226 Gray Hall
michaelr at american {dot} edu
Office hours: Mondays 1:15-2pm, Tuesdays 11:30am-2pm, Wednesdays 9:30-10:15am, Thursdays 9:30-10:15am, or by appointment (please contact me 24 hours in advance to make arrangements)
My research website http://www.drmichaelrobinson.net/
Feel free to contact me with any and all questions (course-related or not)

Quick Links

Course description
Homework assignments
Course schedule
Information about exams
Some useful links
Course policies

Course description

Real numbers; coordinate systems; functions; limits and continuity; differentiation and applications; trigonometric functions; indefinite and definite integration and applications; fundamental theorem of integral calculus. Usually offered every term. Prerequisite: MATH-170 or four years of high school mathematics. Note: Students may not receive credit toward a degree for both MATH-221 and MATH-211.
The overall objectives of this course are to
  1. Examine the unique role of the concepts of derivative and integral in the quantification of change. In so doing, students will be able to explain how any quantitative method involving the measurement of change inevitably leads to these concepts.
  2. Develop quantitative facility with the computational aspects of this theory, with a strong view towards their application, both inside and outside mathematics.
  3. Nurture student comfort in mathematical language, discourse, and thought.

Homeworks

You must staple your assignments before submission; points will be deducted otherwise! Homeworks are due on the dates listed, to be turned in at the beginning of lecture. If you think that you need more practice, just ask! I'll be happy to give you more problems to work, and will also be happy to answer questions about them.

Homework 1, due Wednesday, September 5: 2.2: 4, 12, 20, 29; 2.3: 2, 8, 14, 38; 2.5: 4, 8, 20, 28
Homework 2, due Monday, September 10: 2.5: 44, 48, 54; 2.6: 4, 6, 22, 44; 1.5: 2, 16, 20
Homework 3, due Monday, September 17: 1.6: 2, 14 (explain!), 48; 2.7: 6, 12, 22, 34, 42; 2.8: 2, 4, 14, 18, 38
Homework 4, due Monday, October 1: 3.1: 6, 14, 26, 34, 54, 64; 3.2: 2, 8, 20, 30, 42, 48
Homework 5, due Monday, October 8: 3.3: 2, 22, 34, 40; 3.4: 2, 14, 26, 44, 82; 3.5: 4, 14, 30, 48
Homework 6, due Monday, October 15: 3.6: 2, 6, 26, 44; 3.8: 2, 8, 16; 3.9: 2, 16, 30, 40
Homework 7, due Monday, October 29: 4.1: 4, 22, 40, 60; 4.2: 2, 10, 22, 30; 4.3: 6, 10, 32, 46
Homework 8, due Monday, November 5: 4.4: 8, 18, 24, 44, 58, 88; 4.5: 2, 6, 12, 26, 40; 4.6: 3, 12, 26
Homework 9, due Monday, November 12: 4.7: 4, 12, 32, 24; p. 356-358: 9, 16, 22
Homework 10, due Monday, November 19: 4.9: 2, 6, 32, 43, 54, 74; 5.1: 2, 4, 8, 20, 24
Homework 11, due Monday, December 3: 5.2: 4, 10, 22, 34, 52; 5.3: 4, 10, 18, 34; 5.4: 4, 10, 34, 52; 5.5: 2, 6, 8, 22, 36, 78

Course schedule

The planned course schedule is below; we will not deviate more than a day in terms of the sections covered. The exams, however, will occur on the days listed below.

Unit 1: Limits and derivatives

After this unit, you should be able to
  1. State and explain definitions for the mathematical concepts of limit, continuity, and derivative, as pertains to functions
  2. Use your definitions to compute representative example problems.
  3. Explain why these definitions are important to understanding functions
  4. Give one example (for each definition) illustrating the importance of these definitions outside of mathematics.
August 27: Section 2.2: The limit of a function
August 29: Section 2.3: Limit laws
August 30: Section 2.5: Continuity
September 5: Section 2.6: Limits at infinity
September 6: Section 1.5: Exponential functions
September 10: Section 1.6: Inverse functions and logarithms
September 12: Section 2.7: Derivatives and rates of change
September 13: Section 2.8: The derivative as a function
September 17: Slack day
September 19: Review for Exam 1
September 20: Exam 1

Unit 2: Computing derivatives

After this unit, you should be able to
  1. Compute derivatives of compositions of elementary functions (polynomials, exponentials, logarithms, and trigonometric functions)
  2. State the properties of derivatives or limits that you used in making these computations
  3. Explain why these properties desirable in a tool that describes rates of change
  4. Use these properties to solve problems outside of mathematics pertaining to rates of change and approximation
September 24: Section 3.1: Derivatives of exponentials and polynomials
September 26: Section 3.2: The product rule
September 27: Section 3.3: Derivatives of trigonometric functions
October 1: Section 3.4: The chain rule
October 3: Computing derivatives using combinations of rules
October 4: Section 3.5: Implicit differentiation
October 8: Section 3.6: Derivatives of logarithms
October 10: Section 3.8: Exponential growth and decay
October 11: Section 3.9: Related rates
October 15: Section 3.10: Linear approximants
October 17: Review for Exam 2
October 18: Exam 2

Unit 3: Applications of derivatives

After this unit, you should be able to
  1. Sketch the graph of compositions of elementary functions that captures extrema, concavity, and inflection points
  2. Compute indeterminate limits of functions by using derivatives
  3. Use extrema and concavity to solve optimization problems that arise outside of mathematics
October 22: Section 4.1: Maximum and minimum values
October 24: Section 4.2: The mean value theorem
October 25: Section 4.3: Derivatives and graphing
October 29: Section 4.4: L'Hospital's rule
October 31: Section 4.5: Curve sketching
November 1: Section 4.6: Graphing using electronics
November 5: Section 4.7: Optimization problems
November 7: Slack day
November 8: Review for Exam 3
November 12: Exam 3

Unit 4: Integrals

After this unit, you should be able to
  1. Explain the definition of an integral (as a limit)
  2. Use this definition to compute example definite integrals
  3. Explain the fundamental theorem of calculus, and how it connects integration and antidifferentiation
  4. Use the fundamental theorem of calculus (and by extension, the derivative rules) to evaluate integrals
November 14: Section 4.9: Antiderivatives
November 15: Section 5.1: Areas and distances
November 19: Section 5.2: The definite integral
November 26: Section 5.3: The Fundamental theorem of calculus
November 28: Section 5.4: Indefinite integrals
November 29: Section 5.5: The substitution rule
December 3: Slack day
December 5: Review for final
December 6: Review for final

Final exam: December 13, 8:55am-11:25am

Course policies

A typical course meeting

On most non-exam days, there is a usual cadence to the classes, which goes something like this...
  1. At the beginning, I will take attendence
  2. I will either give you a quick quiz or select students to present specific problems (which I choose) from the homework that pertain to the section covered in the previous class. (Come prepared to at least attempt all the problems!) If you have trouble articulating your solution (or you get stuck), that's OK! The rest of the class and I will help you!
  3. I will present the new section. Taking notes and asking questions is encouraged!
  4. Depending on the nature of the material, we will walk through some representative problems afterwards, either as a class, or in smaller groups.

Absences

You are expected to attend all the class meetings. I will take attendence, usually as roll call at the beginning of class. There may be unexpected quizzes, and you may not take these at a different time! Please contact me in advance if you cannot attend (this includes both religious observances as well as sporting obligations), especially in the case of an exam. Missing an exam without appropriate (prior in all but a few situations) authorization is cause for a zero on that exam!

Late homeworks are not accepted without a University-approved excuse. You have the schedule in front of you now; turn assignments in early if you plan to be absent.

Exams

For each exam, you will be permitted to bring one double sided hand written 8.5 x 11 sheet with handwritten notes on it. Electronic calculators will not be permitted. However, mechanical calculators (such as this or these) are fine.
Missing an exam without appropriate (prior in all but a few situations) authorization is cause for a zero on that exam!

Grading

The course grade will be determined from the following components. You'll accumulate points for each of these over the course of the semester.
10% Homework
20% Exam 1
20% Exam 2
20% Exam 3
30% Final exam

Here's how to associate letter grade equivalents to the percentage of points you've gotten (weighted as above):
A = 93 or above
A- = 88 to 92.9 < Minimum grade to be recommended as a tutor!
B+ = 85 to 87.9
B = 82 to 84.9
B- = 78 to 81.9
C+ = 75 to 77.9
C = 72 to 74.9
C- = 68 to 71.9
D = 60 to 67.9
F = below 60

Academic dishonesty

Academic dishonesty is a serious offense. Read our University policies. As applied to this course, you may work together on homeworks, but the work you turn in must be your own. I'm happy to answer any questions you have about these policies.