Linear algebra, Calculus I

1. Basic numerical skills to solve problems in Engineering. 2. The use of MATLAB to solve numerical problems. 3. Basic solving skills to solve counting problems. 4. Basic solving skills to solve discrete mathematics.

0: Algorithms and Complexity 0.1 The Growth of Functions 0.2 Complexity of Algorithms 0.3 Representations of Integers 1: Floating-Point Numbers and Errors 1.1 Floating-Point Numbers 1.2 Floating-Point Numbers in Matlab 1.3 Floating-Point Arithmetic 2: Integers 2.1 Divisibility and Modular Arithmetic 2.2 Integer Representations and Algorithms 2.3 Primes and Greatest Common Divisors 2.4 Solving Congruences. The Chinese Reminder Theorem 3: Counting 3.1 The Basics of Counting 3.2 The Pigeonhole Principle 3.3 Permutations and Combinations 4: Linear Equations 4.1 Solving Linear Systems 4.2 LU Factorization 4.3 Pivoting and Permutation Matrices 4.4 Effect of Roundoff Errors 4.5 lutx 5: Interpolation 5.1 The Interpolating Polynomial 5.2 Piecewise Linear Interpolation 5.3 Piecewise Cubic Interpolation 5.4 splinetx y pchiptx 6: Zeros and Roots 6.1 Bisection 6.2 Convergence Rates 6.3 Newton's and Secant methods 6.4 Inverse cuadratic interpolation 6.5 Brent¿s algorithm and fzerotx 7: Quadrature 7.1 Simple and composite quadrature rules 7.2 Adaptive Quadrature. quadtx 7.3 Gaussian Quadrature 8: Least Squares 8.1 Models and Curve Fitting 8.2 Least Squares and QR

There will be two weakly sessions: - Theory sessions: the teacher will explain the fundamental concepts and results of the theory. - Exercise/Lab sessions: the students will work in solving exercises or writing codes to solve problems proposed by the teacher.