# Calculus

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## Calculus

Each of the courses, in the flow chart above (excluding Precalculus) has two hours of workshop per week. The academic content of a workshop depends on the particular educational objectives of the course to which it's attached; all workshops, regardless of the course they support, are organized around cooperative study, interaction, and participation in the problem-solving process. They are not traditional recitations, nor are they a time for students to do or discuss homework from lecture.

Here are some examples of topics from worksheets in the project-based calculus sequence:

- Using the derivative to examine the reflective properties of parabolic dishes, elliptical couplers, and hyperbolic mirrors
- Using the integral to calculate the net total of distributed quantities such as mass, energy, and charge
- Using sequences to predict the evolution of social and natural systems
- Using the improper integral to interpolate the factorial

Worksheets are written to be relevant to students' lives (either personally or professionally) and often introduce students to "real" problems. Of course, "real" problems are "real" hard. To help students make the transition to collegiate level thinking and ability, each workshop is supported by both a faculty member and a Workshop Leader; they attend workshop to help facilitate student group discussions.

Each course in the Project Based Calculus sequence has, as you might expect, a term project. These projects vary from semester-to-semester, and from instructor-to-instructor. Students are expected to solve the given problem, and to write a clear, concise, technical report in which they delineate the process by which they found the solution.

Some recent topics for projects are given below.

- Bezier curves, such as those used by Adobe Illustrator and other vector graphics programs
- Mathematical models of toxins in the body
- Satellite positions and orbital transfer
- Kepler's Laws of planetary motion

The final exam for each section of each calculus course is given in two parts:

- A multiple-choice "common core" in which students are asked to demonstrate basic skills and knowledge that are fundamental to the subject
- A free-response part written by the individual instructor in which students demonstrate skills and knowledge particular to that section and instructor

The School of Mathematical Sciences prohibits calculators on the final exam of calculus (and other first-year) courses. Many professors prepare students for this by prohibiting calculators on exams during the term.

Common sense points to adequate preparation as an important element in student success. Particularly when courses are in sequence, demonstrated competence in one course provides the best foundation for success in the next. For this reason, students in calculus must earn a letter grade of at least "C-" before continuing on to subsequent courses.

## Calculus Bridge Exam

Students bridge from MATH-171 to MATH-182A by taking the Bridge Exam as a Credit by Examination/Experience during final exam week.

A score of at least 80% on the Bridge Exam is required to receive 1 credit for MATH-180 (Calculus Bridge) and thus move onto MATH 182A.

- Grade level of A or A- in MATH-171 (for 2181 term)
- Score of at least 80% on the Calculus common core exam (for 2181 term)
- Students typically have previous exposure to the exam topics, for example: high school course from which they earned no college credit

- Free response written exam
- Approximately 10 questions, 90 minutes long
- Students must show proficiency in both MATH-171 and MATH-181A content

**TOPICS FROM MATH-181A THAT ARE NOT INCLUDED IN MATH-171:**

- Newton's Method
- Integration:
- Estimating area
- Sigma notation and Riemann sums
- The definite integral
- Antiderivatives
- The Fundamental Theorem of Calculus
- Indefinite integrals
- The substitution technique of integration
- The definition of a logarithm in terms of integrals