MTH 263 - Calculus I at Germanna Community College

Course Description

Effective: 2019-08-01

Presents concepts of limits, derivatives, differentiation of various types of functions and use of differentiation rules, application of differentiation, antiderivatives, integrals and applications of integration. This is a Passport Transfer course.
Lecture 4 hours. Total 4 hours per week.
4 credits

General Course Purpose

The general purpose of this first course in a three course sequence is to prepare students for further study in calculus with analytic geometry by providing them with the necessary competencies in finding limits, differentiation and integration.

Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 167 or MTH 161/162 or equivalent with a grade of C or better.

Course Objectives

• Limits
• Differentiate between the limit and the value of a function at a point
• Find the limit of a function by numerical, graphical and analytic methods
• Apply Limit Laws
• Calculate one-sided limit of a function
• Prove the existence of a limit using precise definition of the limit
• Determine the continuity of a function
• Calculate Vertical and Horizontal asymptotes using limits
• Derivatives and Differentiation Rules
• Define Derivatives and Rates of Change
• Compute derivatives of basic functions using the definition of the derivative
• Differentiate polynomial, rational, radical, exponential and logarithmic functions
• Find equation of a tangent line using derivative
• Differentiate trigonometric functions
• Apply product, quotient, chain rules
• Apply implicit differentiation and find derivatives of inverse trigonometric functions
• Apply concept of rates of change to natural and social sciences
• Apply the concept of related rates
• Define hyperbolic functions and their derivatives
• Find linear approximation of a function at a given point
• Applications of Differentiation
• Calculate local and absolute maximum and minimum values of a function
• Apply Rolle's Theorem and Mean Value Theorem to study properties of a function
• Find critical points, and intervals of increasing and decreasing values of a function
• Find points of inflection and intervals of different concavities
• Sketch a curve for a given function
• Apply rules of differentiation to solve optimization problems
• Find antiderivatives for basic functions using knowledge of derivatives
• Integrals
• Relate areas to definite integrals using sigma notation, Riemann Sums, and limits. [Note: L?Hopital?s Rule is in Calc II but may be used for instructional purposes here.]
• Apply Fundamental Theorem of Calculus to find definite integrals and derivatives
• Find indefinite integrals of polynomials and basic trigonometric and exponential function
• Apply Net Change Theorem
• Perform integration using substitution
• Find areas between curves
• Find average value of a function

Major Topics to be Included

• Limits
• Derivatives and Differentiation Rules
• Applications of Differentiation
• Integrals

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