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 Procedure

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.
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