MATH 105A: NUMERICAL ANALYSIS I

In this class, we study numerical methods for mathematical problems in Calculus and Linear Algebra. We start to understand how computers recognize numbers and do arithmetic. In order to solve mathematical problems using computers, we apply some discrete methods and check their accuracy or convergence. As a typical problem, we consider a nonlinear equation 'f(x)=0' and try to find its roots. We learn several numerical methods to approximate the roots from a simple algorithm to faster ones: Bisection method, Fixed-Point iteration, Newton’s method, and Secant method. Especially, we check how they are derived and how they work. Moreover, various massive computations in Linear Algebra can be performed by computers. We learn matrix decompositions and iterative techniques to numerically solve a system of linear equations denoted as 'Ax=b'. We also cover the power methods to approximate eigenvalues of matrices.

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