*Lectures One, Two, Three*:**Chapter ONE**Introduction to numerical computing and floating point numbers. Machine precision, overflow, underflow, normalized numbers and subnormal and the command. Crazy graph of*Lectures Four,Five, Six***Chapter TWO**- finding roots of nonlinear equations. Bisection, Newton, Secant and Halley methods. Rate of convergence and**fzero**command.**Chapter Three Solving****.**Forward and Backward substitutions.*Lecture 8*The Midterm*Lecture 9-11***Chapter Three**Solving the , Gauss elimination and decomposition. Vector and Matrix norms, properties of norms. Condition number of a matrix. Error estimates. Residuals. Solving nonlinear system of equations via Newton iterations. q**Chapter 4**Lectures 12,13 - Eigenvalues, eigenvectors, examples, 'eig' operation in Matlab, Power iterations, Theorem 4.1 and 4.2- Lecture 14, inverse Power iterations, power iterations with the shift.
**Chapter 5**Lectures 15-17, Interpolation. Monomial, Lagrange, piece-wise linear. Example of interpolating- Chapter 6 Lectures 18-22. Numerical Integration: Left sided, Mid Point, trapezoid, Simpson, Gaussian, Adaptive. Special attention to error terms. First lecture: Intro into integration, and numerical integration of by Left-sided, Midpoint, Trapezoid and Simpson quadratures. Second Lecture: error estimates for Left-Sided, Midpoint and composit Midpoint.