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Courses: Calculus 1

Differential Calculus Overview

A brief review of inequalities, functions, and plane analytic geometry; limits and continuity; the derivative and the differential; applications of differentiation; L’Hospital’s Rule; introduction to the Riemann integral. Includes differentiation of logarithmic and exponential functions, and indeterminate forms. History of selected topics is studied. Four hours of lecture and one hour of laboratory/recitation. By the end of the course, students will be able to demonstrate an adequate understanding of these topics.

To be successful in this course students must be proficient in precalculus. Students may forgo enrolling in a precalculus course provided they have a strong background in algebra 2  and trigonometry. Please review the prerequisite before enrolling in this course. Students will not be able to complete the course without having a working understanding of these subjects.

Course Description: 

A brief review of inequalities, functions, and plane analytic geometry; limits and continuity; the derivative and the differential; applications of differentiation; L’Hospital’s Rule; introduction to the Riemann integral. Includes differentiation of logarithmic and exponential functions, and indeterminate forms. History of selected topics is studied. Four hours of lecture and one hour of laboratory/recitation. By the end of the course, students will be able to demonstrate an adequate understanding of these topics.


To be successful in this course students must be proficient in precalculus. Students may forgo enrolling in a precalculus course provided they have a strong background in algebra 2  and trigonometry. Please review the prerequisite before enrolling in this course. Students will not be able to complete the course without having a working understanding of these subjects.


PrerequisitePrecalculus or College Algebra and Trigonometry.

Course Topics

  • One-Sided Limits
  • Limit Properties
  • Infinite Limits
  • δ-ε Limit Definition
  • Instantaneous Rate of Change
  • Average Rate of Change
  • Continuity of Functions
  • Discontinuity Types
  • Limit Definition
  • Special Functions
    • Polynomial Functions
    • Exponential Functions
    • Trigonometric Functions
  • Differentiation Rules
    • Product Rule
    • Quotient Rule
    • Chain Rule
    • Implicit Differentiation
  • Mean Value Theorem
  • Rolle’s Theorem
  • Limits
    • Indeteminiate Forms
    • l’Hospitals Rule
  • Numerical Methods
    • Netwon’s Method
  • Related Rates
  • Curve Sketching
  • Optimization
    • Relative Extrema
    • Absolute Extrema
    • Applications
  • Motion
    • Velocity
    • Acceleration 
    • Distance 

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