Escalera de Matemáticas · Universidad

Análisis Numérico

Cómo hacen las computadoras cálculo y álgebra lineal: error de punto flotante, búsqueda de raíces, sistemas, interpolación, integración numérica, solución de EDO y valores propios.

0 de 45 temas aprobados

Empezar este curso Mapa de habilidades

Traducción en curso. Algunos temas de este curso todavía aparecen en inglés.

45 temas en 7 unidades. Se apoya en Cálculo 2: Integrales y Series y Cálculo 3: Cálculo Multivariable y Álgebra Lineal y Ecuaciones Diferenciales. ¿No estás seguro de que sea el curso adecuado? Encuentra tu peldaño.

  • Aprobado
  • Toca repasar
  • Aprendiendo
  • Listo para aprender
  • Necesita un tema anterior

Unidad 1 Numbers on a Computer

8 temas

See how a computer stores numbers, where errors come from, and how to tell a hard problem from a bad method.

  1. Absolute and Relative Error
  2. Binary Fractions
  3. Floating-Point Numbers
  4. Round-Off and Cancellation
  5. Truncation Error and Order of Accuracy
  6. Conditioning of a Problem
  7. Stable and Unstable Algorithms
  8. Horner's Method

Unidad 2 Solving Equations

6 temas

Find roots with bisection, fixed-point iteration, Newton's method and the secant method, and measure how fast each one converges.

  1. The Bisection Method
  2. Fixed-Point Iteration
  3. Order of Convergence
  4. Newton's Method: Speed and Failure
  5. The Secant Method
  6. Newton's Method for Systems

Unidad 3 Linear Systems on a Computer

7 temas

Solve Ax = b reliably: the cost of elimination, pivoting, LU, norms and condition numbers, and iterative methods.

  1. The Cost of Elimination
  2. Partial Pivoting
  3. Solving with PA = LU
  4. Vector and Matrix Norms
  5. The Condition Number of a Matrix
  6. Jacobi Iteration
  7. Gauss–Seidel Iteration

Unidad 4 Interpolation

5 temas

Pass polynomials and splines through data points, and see when adding points helps and when it hurts.

  1. Lagrange Interpolation
  2. Newton's Divided Differences
  3. Interpolation Error
  4. Runge's Phenomenon and Chebyshev Nodes
  5. Cubic Splines

Unidad 5 Derivatives and Integrals

7 temas

Approximate derivatives and integrals, choose step sizes, and squeeze out extra accuracy with extrapolation and smart nodes.

  1. Finite-Difference Derivatives
  2. The Best Step Size
  3. Richardson Extrapolation
  4. Error in the Trapezoid and Simpson's Rules
  5. Romberg Integration
  6. Gaussian Quadrature
  7. Adaptive Integration

Unidad 6 Differential Equations

7 temas

Measure the error of ODE solvers, solve systems, keep steps stable, and turn boundary value problems and the heat equation into linear algebra.

  1. Local and Global Error
  2. Systems and Higher-Order Equations
  3. Stability of Euler's Method
  4. Backward Euler and Stiff Equations
  5. Multistep Methods
  6. Boundary Value Problems by Finite Differences
  7. The Heat Equation: An Explicit Scheme

Unidad 7 Least Squares and Eigenvalues

5 temas

Fit data stably with QR, and find eigenvalues by iteration.

  1. Least Squares with QR
  2. The Power Method
  3. Inverse and Shifted Power Methods
  4. Gershgorin Disks
  5. The QR Algorithm