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Calculus I

This course covers in depth the differential calculus portion of a three-course calculus sequence. Topics include limits, continuity, derivatives, and integrals of algebraic and transcendental functions of one variable, with applications. Upon completion, students should be able to apply differentiation and integration techniques to algebraic and transcendental functions.

  • Define and evaluate limits.
  • Define continuity.
  • Determine continuity at a point and on an interval.
  • Limit definition of the derivative.
  • Product, quotient, and chain rules of derivatives.
  • Derivatives of trigonometric functions.
  • Derivatives of exponential and logarithmic functions.
  • Implicit differentiation.
  • Derivatives of inverse trigonometric functions.
  • Integration.
  • Integration by substitution.
  • Apply the Fundamental Theorem of Calculus.

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