Floating-point arithmetic and rounding errors.
Basic instructions in MATLAB and Octave.
Non-linear equations and systems: Bisection, secant, and Newton methods for scalar equations. Newton for systems.
Linear systems: LU, Cholesky, and QR factorizations. Errors analysis: condition number, a-priori error estimate. Iterative methods: Gradient and Conjugate Gradient methods. Hints to classical iterative methods and to Krylov methods.
Approximation of functions and data: Lagrange interpolation (simple and composite). Spline. Interpolation errors. Linear least squares.
Numerical integration: simple and composite quadrature formulas. Errors analysis. Adaptive Simpson formula. Hints to Gaussian quadrature formulas.
Approximation of initial value problems: forward and backward Euler, Crank-Nicolson schemes. Convergence, consistency, stability. Absolute stability. Runge-Kutta and multistep methods. Predictor-corrector methods.