SE 301-1 Term 002

 Lec Sec Details 1 Overview of numerical methods and grading policy. 2 2.2 Floating point representation 3 2.3 Loss of significance and Programming suggestions 4 1.2 Review of Taylor Series I: Taylor Series, Taylor Theorem, Mean value theorem, Alternating Series 5 1.2 Review of Taylor Series II: Taylor Theorem in terms of h, Mean value theorem, Alternating Series 6 1.2 Review of Taylor Series III: Examples and Programming suggestions 7 3.0 3.1 Locating Roots of equations: the need for solving equations, graphical techniques of estimating the location Bisection method I 8 3.1 Bisection Method II: Error and convergence; Examples 9 3.2 Newton Method I: The algorithm, Interpretation and Examples, 10 3.2 Newton Method II: Convergence, Problems with Newton method and Examples 11 3.3 Secant Method Convergence Analysis and summary of Chapter 3 12 Appendix Linear Algebra; Systems of linear equations. 13 6.1 Naive Gaussian Elimination 14 6.2 Gaussian Elimination with scaled partial pivoting 15 6.2 Examples on Gaussian Elimination with scaled partial pivoting 16 6.3 Tridiagonal and banded systems 17 Programming hints and examples 18 10.1 Least Squares I: Examples of the least squares principles 19 10.3 Least squares II: Examples, extensions, other smoothing approaches 20 Review of Least Squares and more examples 21 Review of Part I of the course 22 4.1 Polynomial interpolation 23 4.1 Polynomial interpolation (Divided Difference Table) 24 4.1 4.2 Errors in Polynomial Interpolation 25 4.3 Numerical Differentiation and Richardson Extrapolation Second Order Derivatives 26 Review of interpolation and more examples 27 5.1 Numerical Integration: Definite Integrals Upper and lower bounds 28 5.2 Trapezoid Rule 29 5.3 Recursive Trapezoid method 30 5.3 Romberg Algorithm 31 5.5 Gaussian Quadrature 32 Review of Numerical Integration and more examples 33 8.0 8.1 Ordinary Differential Equations, First order Taylor series Method (Euler method) 34 8.1 8.2 Highter order Taylor series Methods, Taylor theorem for two independent variable 35 8.2 Runge Kutta Methods (2nd order) 36 8.2 Runge Kutta Methods (2nd and 4th order) and examples 37 9.1 Systems of First Order Ordinary Differential Equations 38 9.2 Higher Order Ordinary Differential Equations 39 9.3 Adams-Moulton Predictor-Corrector Method 40 12.2 Boundary value Problems: Discretization Method 41 Review Ordinary differential equations methods/ more examples 42 13.0 Partial Differential Equations: 43 13.1 Parabolic problems 44 13.2 Hyperbolic problems 45 Review and closing remarks