Calculus I

Revised: November 2006

Course Description

Introduction to functions, derivatives, and integrals with applications. Four semester hours. Prerequisite: Math 146 or placement.

Objectives

   1. To provide an introduction to functions of one variable.
   2. To provide an introduction to the differential and integral calculus of functions of one variable.
   3. To provide students with problem solving skills using the differential calculus.
   4. To expose students to real-life applications of differential calculus from a variety of fields.

Text

Hughes-Hallet, D. & Gleason, A.M., et al. Calculus, 4th edition, Wiley & Sons, 2005.

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

• CHAPTER 1 — A Library of Functions (6 days)
        Selected precalculus topics/summary of chapter (approximately a week) chosen at the instructor's discretion, plus continuity and limits
• CHAPTER 2 — Key Concept: The Derivative (9 days)
        All sections are to be covered. Limits, the derivative function, interpretations of the derivative, the second derivative, and differentiability
• CHAPTER 3 — Short-Cuts to Differentiation (14 days)
        Sections 1 - 7, 9 - 10 Differentiation rules, the chain rule, implicit differentiation, the linear approximation of a function, and the mean value theorem
• CHAPTER 4 — Using the Derivative (7 days)
        Sections 1 and 7, and selected material from sections 2 - 6. Using first and second derivatives, optimization, L'Hopital's rule, and other topics as time allows (at the discretion of the instructor) Note: Parametric equations (section 4.8) will be covered in MATH 255
• CHAPTER 5 — Key Concept: The Definite Integral (6 days)
        All sections are to be covered Definition, interpretations, and theorems of the definite integral
• CHAPTER 6 — Constructing Antiderivatives (5 days)
        Sections 1 and 2 essential
        Sections 3 and 4 covered if at all possible (strongly recommended)
        Constructing antiderivatives graphically, numerically, and analytically, differential equations (equations of motion), and the second fundamental theorem

* Note: At appropriate places time should be allotted to elaborate on historical aspects relevant to the subject.