Revised: January 2015
Limits, continuity, derivative, and integrals of algebraic and trigonometric functions
with applications. Prerequisite: MATH 146. Four semester hours.
Student Learning Objectives
By the end of the course, the student will be able to:
- Use limit rules to calculate various limits
- Calculate the derivative of several basic functions using the definition
- Understand the geometrical meaning of the derivative of a function
- Solve acceleration/velocity/position problems
- Use derivative rules to differentiate functions
- Calculate derivatives of functions defined implicitly
- Determine relative and absolute maximum and minimum values of a function
- Calculate higher derivatives and use them to determine intervals where a function
is increasing/decreasing and concave-up/concave-down
- Solve optimization problems
- Determine simple antiderivatives using the basic rules of differentiation
- Evaluate Riemann sums in order to evaluate definite integrals
- Describe and apply the Fundamental Theorem of Calculus
- Evaluate definite integrals to find areas under and between curves
- Use technology appropriately in the evaluation, analysis and synthesis of information
in problem solving situations.
Calculus: Early Transcendentals, 6th edition, Thomson Brooks/Cole, 2008.
Grading procedures and factors influencing course grade are left to the discretion
individual instructors, subject to general university policy.
Attendance policy is left to the discretion of individual instructors, subject to
- CHAPTER 1 – Functions and Models (4 days)
Selected precalculus topics/summary of chapter (approximately a week) chosen at the
- CHAPTER 2 — Limits and Derivatives (9 days)
Sections 1 - 3, 5 - 8. Section 4 is optional. Limits, continuity, the derivative function,
of the derivative, rates of change, the second derivative, and differentiability.
- CHAPTER 3 — Differentiation Rules (14 days)
Sections 1 - 6, 9 - 10. Sections 7, 8 and 11 optional. Differentiation rules, product
rule, quotientrule, chain rule, implicit differentiation, the linear approximation
of afunction, and related rates.
- CHAPTER 4 — Applications of Differentiation (9 days)
Sections 1 - 5, 7, 9. Sections 6 and 8 optional. Using first and second derivatives,
the mean value theorem, L'Hopital's rule, curve sketching, and antiderivatives.
- CHAPTER 5 —Integrals (5 days)
All sections are to be covered. Definition, interpretations, theorems of the definite
integral, the Fundamental Theorem of Calculus, and the substitution rule.
- CHAPTER 6 — Applications of Integration (2 days)
Section 1. Area between two curves.