Calculus COMP 3751

At the end of this course, the student will be able to:

General outcomes

• Use mathematical tools to visualize, graph, and represent functions.
• Use mathematical tools as an aid in understanding mathematical concepts and methods.
• Use mathematical tools in the modeling and design of systems (data flow, load modeling).
• Use mathematical tools in physical modeling for algorithm design (e.g. realistic motion for animation).

Mathematical outcomes (using Calculus as an example of the mathematical concepts addressed).

Module 1

• Determine the value of the limit of a function at a point directly and using mathematical tools.
• Determine where a function is continuous.
• Determine rates of change using derivatives.

Module 2

• Differentiate polynomial and trigonometric functions directly and using mathematical tools .
• Find local and global maxima and minima of polynomial functions.

Module 3

• Differentiate using product rule, quotient rule and chain rule.
• Differentiate transcendental functions (exponential, logarithm) directly and using mathematical tools.

Module 4

• Find local and global maxima and minima of functions.
• Solve related rates problems.
• Use differentiation as an aid in modeling or design problems (e.g. load problems).

Module 5

• Use the concept of integration in terms of Riemann sums and in terms of antiderivatives to integrate simple functions.

Module 6

• Integrate definite and indefinite integrals involving polynomials and trigonometric functions directly and using mathematical tools.
• Solve and integral by substitution.
• Find the area between two curves expressed as functions.

Module 7

• Use integration in modeling of systems.
• Use the concept of integration in terms of Riemann sums and in terms of antiderivatives.
• Integrate definite and indefinite integrals involving polynomials, trigonometric functions, and exponentials directly and using mathematical tools.

Module 8

• Integration to determine volumes.
• Use integration in modeling of systems (numerical integration, motion, etc).

Effective as of Fall 2003