35007 Real Analysis6cp; 3 hpw (lecture, on campus); 1 hpw (tutorial, on campus)
Requisite(s): 33130 Mathematics 1 OR 33190 Mathematical Modelling for Science OR 37131 Introduction to Linear Dynamical Systems
These requisites may not apply to students in certain courses. See access conditions.
Real Analysis develops the underpinnings of calculus and its extensions. It begins with the structure of the real numbers and the least upper bound axiom. It then develops key ideas involving limits of sequences, continuous functions and the derivative. Applications of the derivative are developed and Taylor series are introduced. The subject then introduces Riemann sums and the Riemann integral. It develops properties of the Riemann integral. It introduces the notion of uniform convergence and study the problem of the convergence of a sequence of Riemann integrals. Throughout the treatment is entirely rigourous. One of the aims of the subject is to teach students how to construct and present a correct proof of a mathematical result.
Detailed subject description.