Calculus

• The Fundamental Theorem of Calculus states the following

  Let be a continuous real valued function defined on a closed interval . Let be the function defined by

  Then is uniformly continuous on and differentiable on the open interval and

  is the antiderivative of or

  Conversely, Let be a real-valued function on a closed interval and a continuous function on which is an antiderivative of in

  If is Riemann integrable on then

  In simpler terms: The integral and the derivative are inverses of each other.

Topics §

• Differential Calculus
  • Taylor Series
• Integral Calculus
• Differential Equation

Links §

• Linear Algebra - for more on working with vectors.

• MIT 18.02 Multivariable Calculus Fall 2007 - a good series of lectures that discuss multivariate differential and integral calculus.