Calculus MOC

Calculus is study of continuous change.

Limit

• limit
• L’Hospital’s rule
• continuity
• squeeze theorem

Differentiation

• derivative
  • linearity of derivative
  • product rule
  • quotient rule
  • chain rule
• tangent space
• Theorems
  • implicit function theorem
  • inverse function theorem
  • extreme value theorem

Integration

See: integral

• Integration techniques
  • by substitution
  • by parts
  • by using the Euler’s formula
  • trigonometric substitution
• fundamental theorem of calculus
• numerical integration

Series

• sequence and series
• Taylor series
• convergence of series and convergence of sequences

Multivariable Calculus

• multi-index notation

Vector

• level sets
• vector field
• divergence, curl, and Laplacian
• curvature

Derivatives

• partial derivative
• directional derivative
• gradient
• total derivative and Jacobian
• Hessian

Integration

• multiple integrals
  • double integral
  • iterated integral
  • order of integration
  • changing variables in multiple integrals
• line integral
  • contour integration
• surface integral

Theorems

• gradient theorem
• divergence theorem
• Green’s theorem
• Stoke’s theorem

Applications

• mathematical optimization
  • second derivative test
  • critical point
  • Lagrange multiplier

See also

• special functions
• real analysis
• complex analysis
• numerical analysis

References

• MIT OCW Multivariable Calculus
• Calculus Blue