**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 |