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

Homework assignments

Course schedule

Information about exams

Some useful links

Course policies

The overall objectives of this course are to

- 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. - Develop quantitative facility with the computational aspects of this theory, with a strong view towards their application, both inside and outside mathematics.
- Nurture student comfort in mathematical language, discourse, and thought.

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

- State and explain definitions for the mathematical concepts of limit, continuity, and derivative, as pertains to functions
- Use your definitions to compute representative example problems.
- Explain why these definitions are important to understanding functions
- Give one example (for each definition) illustrating the importance of these definitions outside of mathematics.

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

- Compute derivatives of compositions of elementary functions (polynomials, exponentials, logarithms, and trigonometric functions)
- State the properties of derivatives or limits that you used in making these computations
- Explain why these properties desirable in a tool that describes rates of change
- Use these properties to solve problems outside of mathematics pertaining to rates of change and approximation

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

- Sketch the graph of compositions of elementary functions that captures extrema, concavity, and inflection points
- Compute indeterminate limits of functions by using derivatives
- Use extrema and concavity to solve optimization problems that arise outside of mathematics

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

- Explain the definition of an integral (as a limit)
- Use this definition to compute example definite integrals
- Explain the fundamental theorem of calculus, and how it connects integration and antidifferentiation
- Use the fundamental theorem of calculus (and by extension, the derivative rules) to evaluate integrals

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**

- At the beginning, I will take attendence
- 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!
- I will present the new section. Taking notes and asking questions is encouraged!
- Depending on the nature of the material, we will walk through some representative problems afterwards, either as a class, or in smaller groups.

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.

Missing an exam without appropriate (

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