Checking date: 18/05/2022


Course: 2022/2023

Advanced mathematical methods II
(13708)
Study: Bachelor in Statistics and Business (203)


Coordinating teacher: ALVAREZ ROMAN, JUAN DIEGO

Department assigned to the subject: Department of Mathematics

Type: Compulsory
ECTS Credits: 6.0 ECTS

Course:
Semester:




Requirements (Subjects that are assumed to be known)
Mathematical Methods I Mathematical Methods II Advanced mathematical methods I
Objectives
The goal of this course is to acquaint the student with mathematical tools necessary for an adequate compression of some advanced techniques of statistical analysis: -Complex numbers -Series of functions -Integral transforms -Matrix calculus -Singular value descomposition - Introduction to numerical calculus
Description of contents: programme
T1. PRELIMINARIES - Complex numbers: graph, arithmetic, complex exponential. - Summmation, products, indexed sums. T2. SERIES OF FUNCTIONS - Numerical series, convergence criteria. - Series of fucntions: powers, Taylor, Maclaurin. - Series of functions: Fourier. T3. INTEGRAL TRANSFORMS - Improper integrals. - Fourier transform. - Laplace transform. T4. NUMERICAL ISSUES: CALCULUS - Errors, floating point arithmeticas. - Computer: Newton Method; Trapezoidal Rule. T5. MATRIX CALCULUS - Exponential matrix - Derivatives with scalars, vectors and matrices. - Multidimensional integration. Integration with scalars, vectors and matrices. T6. SINGULAR VALUES DESCOMPOSITION - Singular value descomposition - Moore-Penrose pseudoinverse. - Principal component analysis T7. NUMERICAL ISSUES: LINEAR ALGEBRA - Computer: LU factorization; Power method for approximating eigenvalues.
Learning activities and methodology
The course will be taught mainly on the blackboard, with additional material available in the course webpage. Three written tests will be scheduled, to be performed within the teaching hours along the semester. Besides, there will be at least two deliverables computer homework .
Assessment System
  • % end-of-term-examination 60
  • % of continuous assessment (assigments, laboratory, practicals...) 40
Calendar of Continuous assessment
Basic Bibliography
  • D. Pestana, M. Rodríguez y F. Marcellán. Curso Práctico de variable compleja y teoría de transformadas. Pearson. 2014
  • B.N. Datta. Numerical Linear Algebra and Applications. Brooks & Cole. 1995
  • D. Zill. Ecuaciones diferenciales con aplicaciones de modelado. Thomson. 1997
  • James E. Gentle. Matrix Algebra: Theory, Computation, and Applications in Statistics. Springer. 2007
  • K. Sydsaeter and P. Hammond. Essential Mathematics for economics Analysis. Pearson. 2012
  • L.N. Trefethen & D. Bau. Numerical Linear Algebra. SIAM. 1997
  • Salas, Hille y Etgen. Calculus (I y II). Reverté. 2002
Additional Bibliography
  • D. Higham. Matlab guide, 2nd. ed. SIAM. 2005
  • D. Watkins. Fundamentals of Matrix Computations. Wiley. 2002
  • G. Golub & C. van Loan. Matrix Computations. Johns Hopkins Press. 1996
  • J.W. Demmel. Applied Numerical Linear Algebra. SIAM. 1997

The course syllabus may change due academic events or other reasons.