UGA Bulletin

Course Description

Introductory differential calculus and its applications. Topics include limits, continuity, differentiability, derivatives of trigonometric, exponential and logarithmic functions, optimization, curve sketching, antiderivatives, differential equations, and applications.

Athena Title

Analytic Geometry and Calculus

Prerequisite

MATH 1113 or MATH 1113E

Semester Course Offered

Offered fall, spring and summer

Grading System

A - F (Traditional)

Student Learning Outcomes

Students should understand the concept of limit and the meaning and import of continuity.
Students should understand the concept of the derivative, and be able to calculate the derivatives of algebraic, exponential, logarithmic, and trigonometric functions.
Students are expected to set up and solve maximum and minimum problems using the methods of calculus.
Students should be able to use calculus to make approximations and sketch graphs.
Students should also be able to calculate antiderivatives and solve some elementary differential equations.
Students should, in addition, understand the meaning and application of the derivative in the context of economics.

Topical Outline

Overview of course. Limits and continuity.
Tangent lines, velocity, rules for differentiation; differentiation of trigonometric, exponential, and logarithmic functions. Implicit differentiation.
Rates of change and related rates applications.
Increasing/decreasing functions, concavity, limits involving infinity, extrema of functions, curve sketching.
Optimization applications.
Derivatives and linear approximations.
Business applications.
Antiderivatives, separable differential equations, and applications.

General Education Core

CORE I: Foundation
CORE III: Quantitative Reasoning

Syllabus

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