Numerical Analysis Courses and Certifications

Steve Brunton

What Is Turbulence? - Turbulent Fluid Dynamics Are Everywhere

Explore the fundamental characteristics of turbulent fluid dynamics, their prevalence in nature and engineering, and the role of Reynolds number in controlling complexity.

• YouTube
• 30 minutes
• Self-Paced
• Free Video

Steve Brunton

Runge-Kutta Integration of ODEs and the Lorenz Equation

Explore Runge-Kutta integration methods for ODEs and delve into the fascinating Lorenz equation, uncovering its chaotic behavior and applications in engineering mathematics.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

NumPy: Introduction, Installation, Attributes, and Arithmetic Operations

Master NumPy fundamentals: installation, attributes, and arithmetic operations for efficient numerical computing in Python.

• YouTube
• 20 minutes
• Self-Paced
• Free Video

Wrath of Math

Heron's Method: The Square Root Algorithm They Didn't Teach You in School

Discover Heron's method, an efficient algorithm for computing square roots, including its mathematical proof, historical context, and practical applications in this engaging mathematical exploration.

• YouTube
• 18 minutes
• Self-Paced
• Free Video

Insights into Mathematics

Fundamental Theorem of Algebra Reexamined - Math Foundations 217

Reexamines the Fundamental Theorem of Algebra, proposing new formulations based on rational complex arithmetic and quadrance, avoiding assumptions about continuity and real/complex numbers.

• YouTube
• 28 minutes
• Self-Paced
• Free Video

Let's Code Physics

Numerical Integration for Beginners

Discover numerical integration techniques from Riemann sums to Monte Carlo methods, including midpoint, trapezoidal, Simpson's rules, and double integrals.

• YouTube
• 16 minutes
• Self-Paced
• Free Video

Instituto de Matemática Pura e Aplicada

Numerical Methods for Partial Differential Equations (2022)

Master advanced computational techniques for solving partial differential equations through rigorous mathematical analysis and practical implementation methods.

• YouTube
• 1 day 4 hours 26 minutes
• Self-Paced
• Free Video

The Julia Programming Language

A Mathematical Look at Electronic Structure Theory - JuliaCon 2021 Workshop

Explore density-functional theory and numerical techniques for solving it using Julia. Learn about discretization, solution algorithms, and practical implementation with hands-on coding exercises.

• YouTube
• 3 hours 1 minute
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Cosmological Simulations by R. Angulo

Explore cosmological simulations in this lecture, covering key concepts, techniques, and applications in modern cosmology research for understanding the universe's structure and evolution.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Steve Brunton

Numerical Integration of Chaotic Dynamics - Uncertainty Propagation & Vectorized Integration

Explore chaos and uncertainty propagation in dynamical systems through numerical integration. Learn efficient vectorization techniques in Python and MATLAB for faster computations.

• YouTube
• 20 minutes
• Self-Paced
• Free Video

Steve Brunton

Numerical Integration of ODEs with Forward Euler and Backward Euler in Python and Matlab

Explore Forward and Backward Euler integration methods for ODEs using Python and Matlab. Compare stability, error, and implementation on a spring-mass-damper system with analytic solutions.

• YouTube
• 31 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Panorama of Mathematics - Alfio Quarteroni

Explore reduced order models for solving partial differential equations, focusing on complexity reduction and efficient simulations in multiphysics problems.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Lectures on Standard and Less Standard Asymptotic Methods - Lecture 1

Explore advanced asymptotic methods for evaluating infinite sums and recognizing sequence patterns. Learn techniques from standard to unconventional, with practical examples and high-precision computations.

• YouTube
• 1 hour 29 minutes
• Self-Paced
• Free Video

Society for Industrial and Applied Mathematics

Shock Formation and Vorticity Creation for Compressible Euler

Exploration of shock formation and vorticity creation in compressible Euler equations, featuring constructive proofs, self-similar variables, and analysis of singularities in multiple dimensions.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

Society for Industrial and Applied Mathematics

Rational Functions

Explores recent advances in rational approximation theory for numerical computation, focusing on "AAA" and "lightning" algorithms for solving PDEs in complex domains with singularities.

• YouTube
• 59 minutes
• Self-Paced
• Conference Talk