Limits and continuity; the Fundamental Theorem of Calculus; definition of the derivative of a function and techniques of differentiation; applications of the derivative to maximizing or minimizing a function; the chain rule, mean value theorem, and rate of change problems; curve sketching; definite and indefinite integration of algebraic, trigonometric, and transcendental functions, with an application to calculation of areas.

Meets NCTC Core Curriculum Requirement.

Upon completion, students will be able to:

  • Develop solutions for tangent and area problems using the concepts of limits, derivatives, and integrals.
  • Draw graphs of algebraic and transcendental functions considering limits, continuity, and differentiability at a point.
  • Determine whether a function is continuous and/or differentiable at a point using limits.
  • Use differentiation rules to differentiate algebraic and transcendental functions.
  • Identify appropriate calculus concepts and techniques to provide mathematical models of real-world situations and determine solutions to applied problems.
  • Evaluate definite integrals using the Fundamental Theorem of Calculus.
  • Articulate the relationship between derivatives and integrals using the Fundamental Theorem of Calculus.

Grade Basis: L
Credit Hours: 4
Lecture hours: 64.0