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Calculus and Analytical Geometry: Course Outline

Calculus is the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.

Course Outline

  • Absolute value
  • Coordinates plane and graphs
  • Distance & circles
  • Quadratic equations
  • Limits & continuity
  • Differentiation
  • Tangent lines
  • Rates of change
  • The derivative
  • Derivatives of trigonometric functions maximum and minimum values of functions
  • Newton's method
  • Roll's theorem and the mean value theorem
  • Integration by substitution
  • Sigma notation
  • Definite integral
  • First and second fundamental theorem of calculus
  • Applications of the definite integral
  • Area between two curves
  • Volumes by cylindrical shells
  • Length of plane curves
  • Improper integral
  • L'hopital's rule
  • Improper integral
  • Infinite series
  • Sequence and monotone sequences
  • Alternating series
  • Conditional convergence
  • Taylor and Maclaurin series

Text Books