The course meets in Steacie Lab T107 on Tuesdays and Thursdays from 10:00 to 11:20 and again from 11:30 to 12:50. The course is intended to provide students with the opportunity to continue developing their skills in applying Maple's symbolic and numerical capabilites to solve problems in applied mathematics. The problems dealt with will require slightly more sophisticated mathematics than those considered in MATH2041. In particular, students will be able to test their understanding of ordinary differential equations, optimization problems in more than one variable and the method of Lagrange multipliers, multiple integration, Taylor polynomials and linear algbera. Topics from computer graphics and simulation will also be introduced.

The prerequisite for this course is MATH2041.
The recommended text is *Calculus the Maple Way* by Robert
Israel. Since the course is not based on formal lectures, the text
will be used mostly as a source of examples and exercises.
It is available in the campus book store.

The course mark will be based entirely on the number of assigned projects successfully completed. The possible grades for a submitted assignment are "A" (Acceptable), "B" (Barely acceptable) and "U" (Unacceptable). Although an assignment with a grade of either "A" or "B" will be deemed to have been successfully completed, students receiving a large number of "B" grades may be asked to write a final exam at the end of the term. There will also be two class quizzes. These will not play a role in calculating the final mark except in the case where a student's performance on the quiz does not correspond to marks obtained on submitted assignments. In such cases, the student in question will also be required to write a final examination.

The course requirements for each of the possible grades are outlined in the following marking scheme:

- for a grade of
**D**the following projects must be completed:- Using Taylor series to calculate integrals
- Using splines to draw smooth curves
- Tomography and solving the Challenger puzzle
- The motion of a floating object
- Tracing the motion of points on planetary gears

- for a grade of
**D+**the following projects must be completed:- Using Taylor series to calculate integrals
- Using splines to draw smooth curves
- Tomography and solving the Challenger puzzle
- The motion of a floating object
- Tracing the motion of points on planetary gears
- Designing efficient speed bumps

- for a grade of
**C**the following projects must be completed:- Using Taylor series to calculate integrals
- Using splines to draw smooth curves
- Tomography and solving the Challenger puzzle
- The motion of a floating object
- Tracing the motion of points on planetary gears
- Designing efficient speed bumps
- Calculating the volume of three intersecting cylinders

- for a grade of
**C+**the following projects must be completed:- Using Taylor series to calculate integrals
- Using splines to draw smooth curves
- Tomography and solving the Challenger puzzle
- The motion of a floating object
- Tracing the motion of points on planetary gears
- Designing efficient speed bumps
- Calculating the volume of three intersecting cylinders
- Doing arithmetic with Egyptian fractions

- for a grade of
**B**the following projects must be completed:- Using Taylor series to calculate integrals
- Using splines to draw smooth curves
- Tomography and solving the Challenger puzzle
- The motion of a floating object
- Tracing the motion of points on planetary gears
- Designing efficient speed bumps
- Calculating the volume of three intersecting cylinders
- Doing arithmetic with Egyptian fractions
- How fair is Monopoly?

- for a grade of
**B+**the following projects must be completed:- Using Taylor series to calculate integrals
- Using splines to draw smooth curves
- Tomography and solving the Challenger puzzle
- The motion of a floating object
- Tracing the motion of points on planetary gears
- Designing efficient speed bumps
- Calculating the volume of three intersecting cylinders
- Doing arithmetic with Egyptian fractions
- How fair is Monopoly?
- One of the following
- The Koch Snowflake is a continuous curve with no tangent at any point
- Modelling how falling snow packs
- Placing guards in a modern modern art gallery

- for a grade of
**A**the following projects must be completed:- Using Taylor series to calculate integrals
- Using splines to draw smooth curves
- Tomography and solving the Challenger puzzle
- The motion of a floating object
- Tracing the motion of points on planetary gears
- Designing efficient speed bumps
- Calculating the volume of three intersecting cylinders
- Doing arithmetic with Egyptian fractions
- How fair is Monopoly?
- Two of the following
- The Koch Snowflake is a continuous curve with no tangent at any point
- Modelling how falling snow packs
- Placing guards in a modern modern art gallery

- for a grade of
**A+**the following projects must be completed:- Using Taylor series to calculate integrals
- Using splines to draw smooth curves
- Tomography and solving the Challenger puzzle
- The motion of a floating object
- Tracing the motion of points on planetary gears
- Designing efficient speed bumps
- Evaluating the voting power of provinces under various constitutional proposals
- How fair is Monopoly?
- The Koch Snowflake is a continuous curve with no tangent at any point
- Modelling how falling snow packs
- Placing guards in a modern modern art gallery

A few sample problems along with solutions are available for students to study. These can also be used as guidelines to answer the question: "How much should I put in my solution?". Finally, there is an electronic discussion group set up for this course which is intended to be used by students to exchange thoughts about the assigned problems. Students are encouraged to ask questions here as well as to reply to queries made by other students. I will be looking in on ths group frequently and will add my own comments and answers as well.

## Instructor

Juris Steprans

email address: steprans@mathstat.yorku.ca

Department of Mathematics and Statistics.

Ross 536 North, ext. 33921

York University

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