MTH 263 Calculus I
Course Title: MTH 263 Calculus I
Course Description
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. Lecture 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
Upon completing the course, the student will be able to:
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 onesided 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

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 rule

Find areas between curves

Find average value of a function
Major Topics to be Included
Limits
Derivatives and Differentiation Rules
Applications of Differentiation
Integrals