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 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 

• 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