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5.0 /5
(19)

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Bienvenido al Curso de Métodos Numéricos con Python I
Conoce nuestra trilogía de métodos numéricos
Cómo sacarle el máximo partido al curso
La Comunidad de Discord para Aprender con Amigos
El Repositorio GitHub del Curso
Toma notas de tu curso en tiempo real en Frogames Formación
Introducción
Límites y continuidad
[Avanzado] Teorema de Bolzano Generalizado
Derivabilidad
[Avanzado] Teorema de Rolle Generalizado
Integración
Fórmula de Taylor
Preliminares
Introducción a los errores
Los números binarios
La representación de números en binario
Cómo representa un ordenador de 64 bits en binario
La representación decimal
Error Absoluto y Error Relativo
Aritmética de Dígitos Finitos
Fórmula de propagación del error
Fórmula de propagación del error con n variables
Algoritmos y convergencia
Tipos de algoritmos
Velocidad de Convergencia
Ejercicios de Errores
Solución de la Tarea
Errores
Introducción a la aproximación de ceros de funciones
Método de la bisección
Ejemplo de cálculo de ceros con el método de la bisección
Método del punto fijo
Teorema y algoritmo del punto fijo
Ejemplo del método del punto fijo
Estimación del error cometido
Problemas del método de la bisección y método del punto fijo
Solución de la Tarea
El método de Newton-Raphson
Pseudocódigo y ejemplo del método de Newton Raphson
Estimación del error cometido en Newton-Raphson
El método de la secante
Pseudocódigo y ejemplo del método de la secante
El método de Regula-Falsi
Pseudocódigo y ejemplo del método de Regula-Falsi
Orden de Convergencia
Cálculo de la convergencia de algunos métodos
Ceros múltiples de funciones
La mejora del método de Newton-Raphson para ceros múltiples
Aceleración de la convergencia: Método de Aitken
Diferencias hacia adelante
Ejemplo de aceleración con el método de Aitken
Aceleración de la convergencia: Método de Steffensen
Ejemplo de aceleración con el método de Steffensen
Cálculo de ceros de polinomios
Método de Horner
Cálculo de la derivada
Pseudocódigo y algoritmo del método de Horner
Deflación
El método de Müller
Pseudocódigo y ejemplo del método de Müller
Métodos de la secante y Newton-Raphson, orden de convergencia, ceros múltiples
Solución de la Tarea
Ceros
Introducción a la interpolación
Polinomios de Langrange
El polinomio interpolador
Error de interpolación
Ejemplo de acotación del error de interpolación
Introducción a los métodos tabulares
Método de Neville
Ejemplo del método de Neville
Cómo evaluar los polinomios interpoladores
Método de las diferencias divididas de Newton
Ejercicio: cálculo de coeficientes de interpolación con diferencias divididas
Ejemplo de diferencias divididas
Relación entre las diferencias divididas y la función interpolada
Polinomios de Lagrange y método de Neville
Solución de la Tarea
Nodos equiespaciados
Ejemplo de nodos equiespaciados hacia adelante
Ejemplo de nodos equiespaciados hacia atrás
Interpolación de Hermite
Demostración de la fórmula de Hermite
Ejemplo de interpolación de Hermite
Diferencias divididas en interpolación de Hermite
Ejercicio resuelto: calcular el polinomio de Hermite
Introducción a los splines
Interpolación con splines cúbicos
Construcción de splines cúbicos
Splines Naturales
Ejemplo de Splines Naturales
Splines de Frontera Fija
Ejemplo de Splines de Frontera Fija
Diferencias divididas, interpolación de Hermite y splines cúbicos.
Solución de la Tarea
Interpolación
Introducción a la derivación e integración numérica
Diferencias hacia adelante y hacia atrás
Fórmula general
Fórmulas de los tres puntos
Fórmulas de los cinco puntos
Derivación numérica usando la fórmula de Taylor
Derivadas de orden superior con la fórmula de Taylor
Ejemplo de aproximación de la derivada segunda
Inestabilidad del error de redondeo
Extrapolación de Richardson
Ejemplo de la extrapolación de Richardson
Extrapolación de Richardson con exponentes pares
Problemas de derivación numérica
Solución de la Tarea
Derivación
Introducción a la Integración numérica
La Regla del Trapecio
Regla de Simpson
Precisión de una cuadratura
Fórmulas de Newton-Cotes
Ejemplo de las fórmulas de Newton-Cotes cerradas
Fórmulas de Newton-Cotes abiertas
Ejemplo de las fórmulas de Newton-Cotes abiertas
Integración numérica compuesta
Fórmula de trapecios compuesta
Fórmula de Simpson compuesta
Ejercicio: fórmula de la integración compuesta del punto medio
Ejercicio resuelto: integración con la fórmula de Simpson compuesta
Estabilidad
Integración de Romberg
Polinomios de Legendre y la integración Gaussiana
Cuadratura gaussiana
Ejemplo de Cuadratura gaussiana
Cuadratura gausiana en cualquier intervalo
Problemas de integración
Solución de la Tarea
Integración
Fin de la primera parte del curso de numérico. ¡Nos vemos en la segunda!

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5.0 /5
(19)

  • Avatar
    Javi
    (5)
    Goodbye to calculation headaches

    What I loved most was the patience they show explaining every single step. It doesn't feel like a boring university lecture, but like a super useful tool you can actually apply in the real world

  • Avatar
    Yvonne
    (5)
    Excellent Numerical Calculus course

    Very good explanation

  • Avatar
    Gabriela
    (5)
    It was like unlocking a new level in my career

    Thanks to the numerical calculation course, I now understand better how Python works in the real world. It gave me a solid foundation and I feel ready to face any challenge.

  • Avatar
    María
    (5)
    I finally understood numerical methods

    This course made numerical calculus make sense to me. Python was the ideal tool to visualize and apply each method. I found it very practical, straightforward, and with really well-thought-out examples. I like knowing that now I can solve complex mathematical problems computationally.

  • Avatar
    Giovanni
    (5)
    Solid Foundation

    This numerical calculus course is the perfect introduction to the world of numerical methods; the fundamentals are explained with a patience and detail that you really appreciate. It's helped me understand what actually happens under the hood of the libraries we use every day in Python, giving me a much more critical and analytical perspective.

  • Avatar
    Jorge
    (5)
    The perfect refresher on numerical calculation

    I really liked that they don't just stick to theory, but teach you how to put it into practice with Python in a super efficient way.

  • Avatar
    Nieves
    (5)
    I went from paper and pencil to code that thinks for me

  • Avatar
    Santiago
    (5)
    Excellent course for understanding algorithm stability before diving into large-scale calculations

  • Avatar
    Nicolás
    (5)
    Straight to the point. Perfect for solving equations that would be impossible to do by hand.

  • Avatar
    Rosa
    (5)
    I recommend it

    I learned a lot from this course. I'm going for the next one

  • Avatar
    Gustavo
    (5)
    Numerical Methods with Python I – Numerical Computation: Solve Real Problems with Computational Precision

    This course introduces you to the fundamentals of numerical computation, teaching you how to solve complex mathematical problems through algorithms implemented in Python. You'll learn to model, approximate, and analyze solutions when analytical methods aren't enough, all from a modern computational perspective

  • Avatar
    Jackeline
    (5)
    great course

    It's a very complete course

  • Avatar
    Angel
    (5)
    fundamental algorithms of numerical calculus applied with Python from scratch

    This course introduces you to the fascinating world of numerical methods, teaching you how to solve complex mathematical problems through Python programming. You'll learn to implement classic algorithms for approximation, interpolation, differentiation and integration, essential in engineering, physics, economics and data science.

  • Avatar
    Samuel
    (5)
    It's the perfect foundation to dive into the world of mathematical programming

    The explanations are clear and the practical examples showed me that Python is easier than I thought

  • Avatar
    Carlos
    (5)
    Numerical Computing in Python with Real-World Application

    A must-take course for anyone looking to dive deep into computational mathematics!

  • Avatar
    Joiser
    (5)
    is a great course

    Really comprehensive, practical, and with excellent tips

  • Avatar
    danison
    (5)
    Awesome

    A great course, very comprehensive

  • Avatar
    BORJA
    (5)
    Excellent

    A really comprehensive course, explained really well.

  • Avatar
    Eulogio
    (5)
    Very interesting course

    It's a course that helps you lay the foundations for more advanced courses. Highly recommended to brush up on forgotten math.

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