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Dersin Haftalık Planı

Hafta Konu
1 Week 1: Introduction, Numerical analysis in chemical engineering, Numerical Computing and Computers: Using computers to do numerical analysis, Error in numerical analysis, Introduction to MATLAB
2 Week 2: Solving nonlinear equations: Successive substitution (Fixed point iteration), Interval halving (Bisection), Secant method
3 Week 3: Solving nonlinear equations: Newton’s method, Convergence; Solving Sets of Equations: Matrices and determinants, Systems of linear equations, Cramer method
4 Week 4: Solving Sets of Equations: Gauss elimination method, Gauss-Jordan elimination method, Iterative methods, Jacobi iteration, Gauss-Seidel iteration
5 Week 5: System of nonlinear equations, Successive substitution method, Newton-Raphson method; Interpolating and Curve Fitting: Continuous and discrete functions, Interpolation polynomials, Unevenly spaced points, Divided differences and Newton interpolation polynomial, Lagrange interpolation polynomial, ICPS4, HW4
6 Week 6: Evenly Spaced points, Forward, backward, and central differences and Newton Interpolation Polynomials
7 Week 7: Midterm 1
8 Week 8: Interpolating and Curve Fitting: Approximation methods; Least square approximation, Linear regression, Polynomial regression, Multiple regression
9 Week 9: Numerical Integration and Numerical Differentiation: Newton-Cotes Closed Integration Formulas, The Trapezoid Rule, Simpson Rule
10 Week 10: Numerical Integration and Numerical Differentiation: Newton-Cotes Open Integration Formulas, Numerical integration with unevenly spaced points, Gaussian quadrature and Gauss-Legendre integration formulas, Numerical differentiation
11 Week 11: Numerical Solution of Ordinary Differential Equations (ODEs): First order ODE’s, Review of analytical solutions, Single step methods, Taylor series method, Euler method, Improved Euler and Modified Euler methods, Runge-Kutta methods
12 Week 12: Midterm 2
13 Week 13: Numerical Solution of Ordinary Differential Equations (ODEs): Multistep methods, Use of open integration formulas, Adams-Bashford method, Use of closed integration formulas, Adams-Moulton method, Predictor-corrector methods.
14 Week 14: Systems of first order ODE’s, Higher-order ODE’s, Stability considerations, Stiffness, Initial Value Problems, Boundary Value Problems: Shooting Method
 
 
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