# Lecture-by-lecture Outline, Spring 2019

1. Chapter 1. Introduction, Errors, representing numbers in a computer. Numerical errors.
2. Floating Point Arithmetic, machine precision, NaN, Inf, overflow, underflow
3. Arithmetical operations in Floating Points. Chapter 2 Solving nonlinear equations, rate of convergence, Bisection method, fixed point iterations.
4. Newton Method, rate of convergence.
5. Stopping criteria, hybrid methods, overview. Secant Method 3 Chapter 3, Linear system of equations . Existence and uniqueness of solutions.
6. S19 Forward and Backward substitution, Gauss Elementary elimination matrices and LU decomposition. Partial and Complete pivoting.
7. F24 Vector and Matrix norms. Condition number of a matrix. Properties of vector and matrix norms. Properties of condition numbers.
8. F28 Absolute and relative residual. Error Estimates. Newton method for solving nonlinear system of equations.
9. S29
10. O3
11. O6
12. O11
13. O13 Introduction to interpolation. Formulation of a problem, monomial interpolation.
14. O17 Interpolation - Lagrange interpolation, wiggles, Piece wise linear interpolation.
15. O20
16. O24 Midterm
17. O27
18. O31
19. N3
20. N7
21. N10
22. N14
23. N17
24. N21 Midterm
25. N28
26. D1
27. D5 Matlab Lab
28. D8 concluding Remarks