The world in which we live today could not exist without the explosion in mathematical knowledge which has occurred since the Renaissance. Not only does mathematics make modern technology possible, but mathematical ideas have profoundly changed our views of the structure of the world itself. The ideas which today are grouped under the heading of Calculus lie at the center of this transformation; although some of them can be traced back to Archimedes, the subject is usually considered to have been developed by Newton and Leibniz in the seventeenth century, and its success in solving problems such as planetary motion led to the modern idea of the universe as a complex, but predictable, machine.
In the two semesters of Honors Calculus, MATH 221/222, we will cover material equivalent to the standard three-semester calculus sequence, but our goal is to gain a richer understanding of the material, both of the fundamental concepts and of their use in solving real-world problems. Accordingly, we will study calculus largely by solving realistics and challenging problems, both in class and in smaller work groups. Some of this work will be done by hand, and some using a computer system such as Geogebra or Desmos. A sound knowledge of algebra and trigonometry is required for the course. The key concepts we will cover in the first semester are:
- review of essential functions (exponential, logarithmic, trigonometric, polynomial, rational);
- continuity and limits;
- differentiation—definition, interpretation, short-cuts (basic rules and formulas), and applications (such as linear approximation, optimization, and related rates problems);
- anti-differentiation and integration (including some techniques of integration such as the methods of substitution and integration by parts); applications of integration.
(Note that while we will study all of these topics, we may not study them in the listed order.)
I will try to keep lecturing to a minimum, and devote class time to discussion and problem solving. As a result, you will be expected to read the textbook in a timely fashion, as necessary to participate in the class discussions. When I assign reading for a class, I will often ask you to e-mail me, again in a timely fashion, with one or more questions you have about the reading. I will review those e-mails before the class and prepare a brief lecture or other activity for any common questions, as I feel necessary. I will also save those e-mails; they will be used at the end of the semester as evidence that you were completing the reading assignments, and will count towards the homework portion of your grade.
All class information (homework, class cancellations, etc.) will be posted on the class website, https://sites.uwm.edu/kevinm/math-221-honors-calculus-1/; some will be posted only there. If I find useful and relevant links during the semester, I will post them as well; if you find some yourself, please let me know. You are responsible for any information posted on the website, so please check it frequently.
Your grade for the course will be based on the following factors:
- Homework In addition to the textbook (and possibly other) readings, you will be assigned written homework regularly, some of which you will be expected to hand in. Of the homework you hand in, approximately half will be treated summatively; i.e. you will be given a grade which will contribute to your final grade for the course. (The other half will be treated formatively: I will record that the assignment was handed in, and will provide you with you feedback, but no score.) 20%.
- Class participation You will be expected to contribute to the class discussion, to the extent of leading discussions on topics from the text or homework problems. (For this reason alone, regular class attendance will be essential.) 20%.
- Projects You will complete two projects during the semester, in project groups of 2 or (preferably) 3. These projects will consist of extended applications of the material we study in class. You will be given 3 weeks to complete each project 10% each.
- Exams There will be two exams: a midterm and the final exam. The midterm exam will be given at approximately week 7 of the semester (you will be given at least one week’s notice of the exact date); the final exam will be from 7:30-9:30 AM on Friday, December 20. 20% each.
Average Time Investment
The amount of time that an average student should expect to spend on this class is as follows:
- Classroom time (face to face instruction): 75 hours
- Time taking exams (midterm, final exam): 15 hours
- Time completing reading and other homework assignments: 150 hours
- Time for preparation and study for exams: 10 hours
Total number of hours: 250.
Students with disabilities
If you feel you are a student with a disability, please feel free to contact me early in the semester for any help or accommodation you may need.
You should keep yourself informed of important dates in the University calendar.
The Secretary of the University has a page dedicated to university policies for religious observances, grade appeal procedures, military service and other matters. You should also familiarize yourself with the information on the Dean of Students Office webpage concerning proper student conduct at the university, both academic and non-academic misconduct. You will be held responsible for
the information and policies contained at these links.
Finally, please note that I reserve the right to make changes to this syllabus in the event of a
disruption to normal classroom activities, or other needs that may arise during the semester.