Description:
Matrices, determinants, systems of linear and nonlinear equations, elements of error analysis, real roots of an equation, polynomial approximation by finite difference and least-squares method, and numerical solution on a system of linear and nonlinear equations.
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Topics:
1. Introduction
a. History of Mathematics
b. Overview of Matrices and Determinants
c. Overview of Linear Equations
d. Basic Concepts of Numerical Methods
e. Industrial Engineering Problems and Situations
2. Linear Equations
a. Review of Linear Equations
3. Matrices
a. Definition and Types of Matrices
b. Matrix Addition and Subtraction
c. Matrix Multiplication
d. Transpose of a Matrix
e. Reduced Row Echelon Form
f. Elementary Row Operation
g. Inverse of a Matrix
h. Lower and Upper Triangular Matrices
4. Determinants
a. Definition and Properties of Determinants
b. Methods in Finding the Determinants
c. Cofactor Expression and Inverses
5. Solution of Linear Systems
a. Method of Elimination
b. Gauss-Jordan Reduction Method
c. Inverse Application Methods
d. Cramer's Rule
e. L-U Decomposition Methods
f. Iterative Methods (Numerical Linear Algebra)
g. Gauss-Jacobi, Gauss-Seidel
h. Successive Over Relaxation (SOR)
i. Symmetric Successive Over Relaxation (SSOR)
6. Solving Non-Linear Equations (Root Finding)
a. Interval Methods: Bisection, Regula Falsi, Pegasus
b. Fixed-Point Iteration Method
c. Newton-Raphson Iteration Method
d. Secant Method
7. Solving Systems of Non-Linear Equations
a. Newton's Method
8. Applications in Industrial Engineering
a. Linear Programming in Matrix Form
b. Game Theory
c. Markov Chains
d. Least Squares
e. Polynomial Approximation by Finite Difference
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