Calculus I Calculus II Linear Algebra

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

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.

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 .