Numerical analysis

Related lectures (28)

Covers numerical integration methods, focusing on trapezoidal rules, degree of exactness, and error analysis.

Numerical Integration: Lagrange Interpolation Methods

Covers numerical integration techniques, focusing on Lagrange interpolation and various quadrature methods for approximating integrals.

Gauss-Legendre Quadrature Formulas

Explores Gauss-Legendre quadrature formulas using Legendre polynomials for accurate function approximation.

Numerical Methods: Euler and Crank-Nicolson

Covers Euler and Crank-Nicolson methods for solving differential equations.

System of ODEs

Explores numerical methods for solving ODE systems, stability regions, and absolute stability importance.

Numerical Analysis: Introduction to Computational Methods

Covers the basics of numerical analysis and computational methods using Python, focusing on algorithms and practical applications in mathematics.

Numerical Analysis: Polynomial Interpolation Techniques

Provides an overview of polynomial interpolation techniques in numerical analysis, focusing on Lagrange interpolation and error estimation methods.

Error Analysis and Interpolation

Explores error analysis and limitations in interpolation on evenly distributed nodes.

Numerical Integration: Basics

Covers digital integration, interpolation polynomials, and integration formulas with error analysis.

Numerical Differentiation: Methods and Errors

Explores numerical differentiation methods and round-off errors in computer computations.

Runge Kutta and Multistep Methods

Explores Runge Kutta and multistep methods for solving ODEs, including Backward Euler and Crank-Nicolson.

Numerical Integration: Lagrange Interpolation, Simpson Rules

Explains Lagrange interpolation for numerical integration and introduces Simpson's rules.

Polynomial Approximation: Stability and Error Analysis

Explores challenges in polynomial approximation, stability issues, and error analysis in numerical differentiation.

Computer Arithmetic: Floating Point Numbers

Explores computer arithmetic, emphasizing fixed-point and floating-point numbers, IEEE 754 standard, dynamic range, and floating-point operations in MIPS architecture.

Finite Element Modeling: Dynamics

Introduces the basics of finite element modeling for dynamics and discusses the Newmark method for time integration.

Digital Systems: Fixed-Point and Floating-Point Arithmetic

Provides an overview of fixed-point and floating-point arithmetic in digital systems.

Interpolation of Lagrange: Dualité and Coupling

Explores Lagrange interpolation, emphasizing uniqueness and simplicity in reconstructing functions from limited values.

Numerical Integration: Legendre Polynomials

Explores Legendre polynomials and their role in numerical integration techniques.

Data Science Visualization with Pandas

Covers data manipulation and exploration using Python with a focus on visualization techniques.

Explicit Stabilised Methods: Applications to Bayesian Inverse Problems

Explores explicit stabilised Runge-Kutta methods and their application to Bayesian inverse problems, covering optimization, sampling, and numerical experiments.