MTH 263 Calculus I
MTH 263 Calculus I
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MTH 263 Calculus I

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:


  • 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


  • 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


Derivatives and Differentiation Rules

Applications of Differentiation


Applicable School(s)
All Virginia Community Colleges
Course Content Summaries
List of Attachment(s)