1. Application of Differential Applied Optimization Problems

2. 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

8. Solution

12. Question How do your calculator or computer calculate matrix inverse? Or find a root of equation? Or differentiate and Integrate a function?

13. Math Analysis 1.Analytical methods 2.Numerical Methods

14. Numerical Methods Example Math ProblemMethod Finding roots of equationSecant 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 EquationGauss elimination, Gauss Jordan elimination, LU factorization Differential EquationEuler method, Runge kutta method IntegrationTrapezoid rules

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

20. Another initial point

22. The important of starting point X 0