Acerca de este Curso
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Nivel intermedio

Basic command of college-level mathematics (linear algebra and calculus). Basic level of programming proficiency: python programming language.

Aprox. 21 horas para completar

Sugerido: 7 weeks of study, 5-6 hours/week...

Inglés (English)

Subtítulos: Inglés (English)

100 % en línea

Comienza de inmediato y aprende a tu propio ritmo.

Fechas límite flexibles

Restablece las fechas límite en función de tus horarios.

Nivel intermedio

Basic command of college-level mathematics (linear algebra and calculus). Basic level of programming proficiency: python programming language.

Aprox. 21 horas para completar

Sugerido: 7 weeks of study, 5-6 hours/week...

Inglés (English)

Subtítulos: Inglés (English)

Programa - Qué aprenderás en este curso

Semana
1
5 horas para completar

Machine arithmetics. Systems of linear algebraic equations.

...
10 videos (Total 60 minutos), 1 reading, 2 quizzes
10 videos
A simple worked example.5m
Machine arithmetics. Representation of real numbers.6m
Machine epsilon. Over- and underflow.8m
A crude estimate of the machine epsilon.2m
Systems of linear equations. Cramer's rule.5m
Gaussian elimination.10m
LU decomposition: the matrix form of the Gaussian elimination.9m
When does the Gaussian elimination work?2m
LU decomposition with pivoting. Permutation matrices.8m
1 lectura
About the course10m
Semana
2
3 horas para completar

Numerical linear algebra.

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12 videos (Total 72 minutos), 1 quiz
12 videos
Sensitivity of a linear system.3m
Vector norms.5m
Matrix norms.3m
Common matrix norms.4m
Sensitivity of a linear system. Condition number.11m
Cholesky decomposition.7m
Banded matrices. Thomas algorithm.3m
Shermann-Morrison formula.8m
QR decomposition.6m
Constructing the QR decomposition: Householder reflections.13m
Constructing the QR decomposition: Givens rotations3m
Semana
3
3 horas para completar

Non-linear algebraic equations.

...
11 videos (Total 71 minutos), 1 quiz
11 videos
Localization of roots. Bisection.4m
Fixed-point iteration.4m
Aside: convergence rates and related technicalities.7m
Back to the fixed-point iteration.11m
Fine-tuning the fixed-point iteration.5m
Newton's iteration.16m
Multiple roots. Modified Newton's method.3m
Inverse quadratic interpolation.4m
Roots of polynomials.3m
Roots of polynomials: the companion matrix.3m
Semana
4
3 horas para completar

Iterative method for linear systems.

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7 videos (Total 46 minutos), 1 quiz
7 videos
Simple iteration for a linear system. Jacobi iteration.8m
Convergence criteria for simple iteration.4m
Seidel's iteration.9m
Successive over-relaxation.3m
Canonic form of two-step iterative methods for linear systems.10m
Variational approaches: minimum residual method.5m
Semana
5
3 horas para completar

Interpolation and approximation. Modeling of data.

...
9 videos (Total 65 minutos), 1 quiz
9 videos
Linear least squares problem.5m
Ordinary least squares: the normal equations.3m
Ordinary least squares: QR decomposition of the design matrix.7m
Global polynomial interpolation.8m
Lagrange interpolating polynomial.6m
Quantifying interpolation errors. Runge phenomenon.7m
Chebyshev nodes.8m
Interpolation of the Runge function.7m
Semana
6
3 horas para completar

Numerical calculus: derivatives and integrals.

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13 videos (Total 80 minutos), 1 quiz
13 videos
Numerical derivatives: finite differences.7m
Truncation and roundoff errors: an interplay.9m
Higher order schemes.4m
Richardson extrapolation.7m
Integration: numeric quadratures.5m
Convergence rates of simple quadratures.6m
Simple geometric quadratures: Trapezoids, Simpson's rule and all that.7m
Error bounds for quadratures. Romberg extrapolation.4m
Integrals with singularities.6m
A check of convergence.4m
Recap: Newton-Cotes vs Gaussian quadratures.5m
Gaussian quadratures.6m
Semana
7
3 horas para completar

Initial value problem for ordinary differential equations.

...
7 videos (Total 64 minutos), 1 quiz
7 videos
Approximation and convergence.10m
Truncation error or Euler-like schemes.6m
Runge-Kutta methods.10m
Asymptotic stability of ODEs. Stiffness.12m
Linear Multistep methods.7m
Zero-stability of linear multistep methods.7m

Instructor

Avatar

Evgeni Burovski

Assistant professor
School of Applied mathematics, MIEM

Acerca de National Research University Higher School of Economics

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communicamathematics, engineering, and more. Learn more on www.hse.ru...

Preguntas Frecuentes

  • Una vez que te inscribes para obtener un Certificado, tendrás acceso a todos los videos, cuestionarios y tareas de programación (si corresponde). Las tareas calificadas por compañeros solo pueden enviarse y revisarse una vez que haya comenzado tu sesión. Si eliges explorar el curso sin comprarlo, es posible que no puedas acceder a determinadas tareas.

  • Cuando compras un Certificado, obtienes acceso a todos los materiales del curso, incluidas las tareas calificadas. Una vez que completes el curso, se añadirá tu Certificado electrónico a la página Logros. Desde allí, puedes imprimir tu Certificado o añadirlo a tu perfil de LinkedIn. Si solo quieres leer y visualizar el contenido del curso, puedes participar del curso como oyente sin costo.

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