MATH 135 - Calculus of a Single Variable 1

Number of Credits: 4
Examine limits, derivatives, and integrals of functions. Apply these concepts to polynomial, rational, algebraic, and trigonometric functions. Use derivatives to analyze graphs and model real situations involving rates of change. Explore numerical and analytical techniques for integration and apply them to physical situations. Advanced Placement (Calculus AB with a score of 3 or AB sub-score of 3); CLEP (Calculus with a score of 50) accepted. (Fall, Spring & Summer Only) Five hours lecture each week. Four Credits. Four billable hours.

GENERAL EDUCATION Category: Mathematics

Pre-requisite(s): eligibility for ENGL 101, plus MATH 130 with a minimum grade of C or a satisfactory MATH placement measure.
Course Topics:

Limits, derivatives, integrals, and graphs of functions
Solve real-world application problems including related-rates, optimization, distance, area, volume, arc length, surface area, mass, work, and fluid pressure

Course Objectives: Upon successful completion of this course, students will be able to:

Determine limits for functions graphically, numerically, and analytically. (GE3)
Apply the epsilon-delta Precise Definition of Limits. (GE1, GE3)
Apply the Derivative Definition to obtain derivatives of functions. (GE1, GE2)
Differentiate functions using the product, quotient, chain, and implicit rules. (GE3)
Apply differentiation techniques to related-rates and optimization problems. (GE2, GE3)
Sketch curves based on analysis of the function’s limits and derivatives. (GE3)
Apply the Riemann Sums Definition of an Integral to find the definite integral of functions. (GE1, GE3)
Evaluate definite and indefinite integrals using direct and substitution techniques. (GE3)
Apply integration techniques to calculate distance, area, volume, arc length, surface area, mass, work, and fluid pressure. (GE2, GE3)