MATH 135 - Calculus of a Single Variable 1

Number of Credits: 4
Calculus of a Single Variable 1 introduces the initial concepts of both differential and integral calculus. The concept of limits will be introduced both informally and through the formal epsilon-delta process. Derivatives and integrals of polynomial, power and trigonometric functions will be developed as well as general differentiation techniques (such as the chain rule and implicit differentiation). Evaluation of definite integrals will be covered through limits of Riemann Sums, numerical integration techniques, and the Fundamental Theorems of Calculus. Applications of calculus to graphing and to physical situations will be extensively developed. Prerequisite: eligibility for ENGL-101, plus completion of MATH-123/MATH-124 or MATH-130 with minimum grades of C or better or satisfactory scores on the placement test. Credit by exam available. GENERAL EDUCATION (Fall, Spring and Summer) Five hours lecture. Four Credits. Four billable hours.

GENERAL EDUCATION Category: Mathematics

Pre-requisite(s): eligibility for ENGL 101, plus MATH 123/MATH 124 or MATH 130 with minimum grades of C or better or satisfactory scores on the placement test.
Course Objectives: Upon successful completion of this course, students will be able to:

Determine limits for functions graphically, numerically, and analytically. (GE3)
Use the E-& Precise Definition of Limits. (GE1, GE3)
Use The Derivative Definition to obtain derivatives of functions. (GE1, GE2)
Calculate derivatives for functions using the product, quotient, chain and implicit rules. (GE3)
Apply differentiation techniques to related-rate and optimization problems. (GE2, GE3)
Sketch curves based on analysis of the functions’ limits and derivatives. (GE3)
Use the Riemann Sums Definition of an Integral to find the definite integral of functions. (GE1, GE3)
Solve for definite and indefinite integrals using direct and substitution techniques. (GE3)
Apply integration techniques to solve problems in area, volume, arc-length, and curve-length applications. (GE2, GE3)
Apply integration techniques to solve applied problems such as analysis of work, fluid pressure and center-of-mass applications. (GE2, GE3)