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 how to solve problems using Rolle’s Theorem. Step by step tutorial including examples of how to solve problems using Rolle’s Theorem for reference.
Overview
Rolle’s Theorem is a special instance of the Mean Value Theorem, and can be used to prove the Mean Value Theorem. Rolle’s Theorem states that a differentiable and continuous function, which attains equal values at two points, must have a point somewhere between them where the slope of the tangent line to the graph of the function is zero. Mathematically this can be expressed as if a real-valued function f is continuous on a closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists a c in the open interval (a, b) such that f ‘(c) = 0.
Description
A detailed tutorial on the solving of the Mean Value Theorem. Step by step tutorial including several examples of how to solve the Mean Value Theorem for reference.
Overview
You can easily figure out what the Mean Value Theorem is by looking at the word mean – a mean is an average. The Mean Value Theorem states that there is at least one point on the graph of a function where the derivative is equal to the average slope of the entire section of the graph you are looking at. The requirements are that the graph is both continuous and differentiable on the interval [a, b], where a < b. Then there exists some c in (a, b) such that:
f ‘(c) = [f(b) - f(a)] / [b - a]
The Mean Value Theorem is very similar to Rolle’s Theorem, which is a more specific theorem stating the same thing.
