Complements of Analysis and Programming

Recommended Prerequisites

Basic knowledge in analysis and differential equations.

Teaching Methods

The teaching methods used in the lectures are focused on a theoretical exposition accompanied by illustrative examples, in fact lectures are designed to articulate theory and discussed examples. Resolution of individual problems is encouraged since it is essential to a proper understanding of the theory. Programming lectures are initiated by brief sessions of theoretical exposition and composed mostly by practical sessions in a computer room, working individually or in groups, under the guidance of the teacher

Learning Outcomes

The student should be able to acquire and apply the mathematical techniques of vector analysis, ordinary differential equations, partial differential equations, in particular its main definitions, properties and applications to economics models. Students must also acquire and apply computational techniques with relevance in quantitative Finance.

Work Placement(s)

No

Syllabus

Elementary concepts of vector analysis and linear algebra. Ordinary differential equations (first order equations and brief introduction to linear n-th order differential equations and systems of first order differential equations). Partial differential equations (classical approach; definitions and fundamental solutions of linear PDEs). Introduction to programming. Programming using interpreted languages (Matlab). Basics of floating point arithmetic, conditioning problems, stability of algorithms, and counting arithmetic operations.  Monte Carlo method  (introduction, implementation and examples). Basic principles of object-oriented programming

Assessment Methods

Assessment
Evaluation consists of an exam (70%), small projects (20%), and problems which the student must solve and submit a report (10%).: 100.0%

Bibliography

M. Braun, Differential Equations and Their Applications: An Introduction to applied Mathematics, quarta edição, Texts in Applied Mathematics, 11, Springer-Verlag, Nova Iorque, 2000.

M. Heath, Scientific Computing, segunda edição, McGraw-Hill, Nova Iorque, 2001.

D. Higham e N. Higham, Matlab Guide, segunda edição, SIAM, Filadélfia, 2005.

C. Moler, Numerical Computing with Matlab,  SIAM, Filadélfia, 2006.

A. Quarteroni, R. Sacco e F. Saleri, Numerical Mathematics, Texts in Applied Mathematics, 37, Springer-Verlag, Berlim, 2000.

M. Taylor, Partial Differential Equations Vol. I-III,, Springer-Verlag, Nova Iorque, 1996.

C. F. Van Loan, Introduction to Scientific Computing – A Matrix-Vector Approach Using Matlab, The Matlab Curriculum Series, Prentice-Hall, Upper Sadlle River, 1997