Minerva CS111 Single and Multivariable Calculus

This class cover important all of normal Calculus I, some of Calculus II (including integration and application of integrals), and a bit of multivariable calculus

Concept Notes

Limit & Continuity

• limit
  • L’Hopital’s rule
  • asymptote
• continuity
  • mean value theorem
  • intermediate value theorem

Differentiation

• defining derivative
  • instantaneous rate
  • average rate
  • common derivatives
• differentiability
• rules of differentiation - power rule, chain rule (calculus), product rule
• applications
  • tangent line &
  • critical points
  • related rates using implicit differentiation
  • approximation
  • optimization
  • L’Hopital’s rule

Multivariable Calculus

Resources + Exercises: Ximera OSU, Paul’s Online Notes

• partial derivatives
  • high-order derivatives
• applications
  • tangent plane
  • quadratic approximation
  • local extremum
    • multivariable optimization
  • global extremum
• gradient
  • constrained optimization with Lagrange multipliers
• supplement:
  • geometric vector
    • vector field
  • contour map
    • level curves
• multiple integrals
  • double integral
• differential equation

Resources

• OSU Ximera - Relevant parts of Calculus I, II, and III