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# MATH 153 Syllabus

### Calculus I

Revised: January 2015

## Course Description

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.

## Text

Steward, James. Calculus: Early Transcendentals, 6th edition, Thomson Brooks/Cole, 2008.

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

## Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to general university policy.
Course Outline

1. CHAPTER 1 – Functions and Models (4 days)
Selected precalculus topics/summary of chapter (approximately a week) chosen at the instructor's discretion.
2. CHAPTER 2 — Limits and Derivatives (9 days)
Sections 1 - 3, 5 - 8. Section 4 is optional. Limits, continuity, the derivative function, interpretations of the derivative, rates of change, the second derivative, and differentiability.
3. 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.
4. CHAPTER 4 — Applications of Differentiation (9 days)
Sections 1 - 5, 7, 9. Sections 6 and 8 optional. Using first and second derivatives, optimization, the mean value theorem, L'Hopital's rule, curve sketching, and antiderivatives.
5. 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.
6. CHAPTER 6 — Applications of Integration (2 days)
Section 1. Area between two curves.