Application of Differential

Applied Optimization Problems

Preliminary

• To optimize something means to maximize or minimize some aspect of it

• It has many applications in business, engineering, mathematics, physics, and economics.

• The differential calculus is a powerful tool for solving problems that call for maximizing or minimizing a function

Solution

Question

• How do your calculator or computer calculate matrix inverse?

• Or find a root of equation? Or differentiate and Integrate a function?

Math Analysis

1. Analytical methods2. Numerical Methods

Numerical Methods Example

Math Problem Method

Finding roots of equation Secant method, Newton Method, Bisection method

Optimization Gradient method, steepest descent method, Newton method, Quasi Newton method, BFGS method

Solving Non-linear Equation Gauss method, Newton-Raphson method, Gauss-seidel method.

Linear Equation Gauss elimination, Gauss Jordan elimination, LU factorization

Differential Equation Euler method, Runge kutta method

Integration Trapezoid rules

Also well-known as Newton Method. The algorithm Is a method to solve non linear equation f(x)=0.

Another initial point

The important of starting point X0