Description
A detailed tutorial on saddle-point approximation. Step by step tutorial including several examples of saddle-point approximation for reference.
Overview
Saddle-point approximation is also referred to as the method of steepest descent and Laplace’s method. It is a way of approximating integrals in the form 
Description
A detailed tutorial on the monotone convergence theorem. Step by step tutorial including several examples of the monotone convergence theorem for reference.
Overview
There are several different theorems that the term “monotone convergence” can apply to. However, the most important one, and the one most common called the monotone convergence theorem, is the Lebesgue Monotone Convergence Theorem. This particular monotone convergence theorem deals with calculus, and with integrals and limits specifically. It is a more general form of the other two monotone convergence theorems, which is why it is considered to be the most important.
Description
A detailed tutorial on higher order derivatives. Step by step tutorial including several examples of higher order derivatives for reference.
Overview
A higher order derivative is a derivative with a power other than one – that is, a derivative is referred to as a first derivative, and the higher order derivatives are a second derivative, third derivative, etc. The second derivative is the derivative of the first derivative, and the third derivative is the derivative of the second derivative. When you know all the rules of taking derivatives, taking second and third derivatives are simple. Simply take the derivative and pretend it is another equation. When you go up beyond the third derivative this can get more challenging, as there will be many more parts to the equation.
Description
A detailed tutorial on Leibniz notation. Step by step tutorial including several examples of Leibniz notation for reference. Knowledge of Leibniz notation is mandatory for calculus.
Overview
Leibniz notation is a common notation in calculus that helps to identify derivaties. In Leibniz notation, the terms dx and dy are used for derivatives of x and y. This can be used with any variable. Typically this will be expressed in a fraction form, as dy / dx. This form says that you take the derivative of x in respect to y. This notation can be used for integrals as well as derivatives, although it was first developed for use with derivatives.
