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.