Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living cells in medicine and biology. Before modern computers, numerical methods often relied on hand interpolation formulas, using data from large printed tables. Since the mid 20th century, computers calculate the required functions instead, but many of the same formulas continue to be used in software algorithms. The numerical point of view goes back to the earliest mathematical writings. A tablet from the Yale Babylonian Collection (YBC 7289), gives a sexagesimal numerical approximation of the square root of 2, the length of the diagonal in a unit square. Numerical analysis continues this long tradition: rather than giving exact symbolic answers translated into digits and applicable only to real-world measurements, approximate solutions within specified error bounds are used. (Wikipedia).
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
Integration 10 Numerical Integration Video 1 Part 1.mov
Discussion on numerical integration using Riemann Sums.
From playlist Integration
Numerical Aperture in Fourier Optics
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From playlist Fourier Optics
An introduction to the idea of Dimensional Analysis
From playlist Mathematical Physics I Uploads
Lecture: Numerical Differentiation Methods
From simple Taylor series expansions, the theory of numerical differentiation is developed.
From playlist Beginning Scientific Computing
Eva Darulova : Programming with numerical uncertainties
Abstract : Numerical software, common in scientific computing or embedded systems, inevitably uses an approximation of the real arithmetic in which most algorithms are designed. Finite-precision arithmetic, such as fixed-point or floating-point, is a common and efficient choice, but introd
From playlist Mathematical Aspects of Computer Science
An introduction to multilevel Monte Carlo methods – Michael Giles – ICM2018
Numerical Analysis and Scientific Computing Invited Lecture 15.7 An introduction to multilevel Monte Carlo methods Michael Giles Abstract: In recent years there has been very substantial growth in stochastic modelling in many application areas, and this has led to much greater use of Mon
From playlist Numerical Analysis and Scientific Computing
We introduce the idea of dimensional analysis and its use in finding unknown quantities' dependence on relevant dimensionful variables.
From playlist Mathematical Physics I Uploads
Mod-01 Lec-21 Vector and Matrix Norms
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
Mod-01 Lec-01 Introduction and Overview
Advanced Numerical Analysis by Prof. Sachin C. Patwardhan,Department of Chemical Engineering,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Bombay: Advanced Numerical Analysis | CosmoLearning.org
Time domain modeling and computation for waves in some complex mediums
Liwei Xu University of Electronic Science and Technology of China, China
From playlist 2018 Modeling and Simulation of Interface Dynamics in Fluids/Solids and Their Applications
Dynamics, numerical analysis and some geometry – Christian Lubich – ICM2018
Plenary Lecture 18 Dynamics, numerical analysis and some geometry Christian Lubich Abstract: Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we revi
From playlist Plenary Lectures
Professor Kostas Zygalakis, University of Edinburgh
Bio He received his PhD in computational stochastic differential equations from University of Warwick at 2009 and held postdoctoral positions at the Universities of Cambridge, Oxford and the Swiss Federal Institute of Technology, Lausanne. In 2011 he was awarded a Leslie Fox Prize (IMA UK
From playlist Short Talks
Python for Data Analysis: Preparing Numeric Data
This video examines a variety of techniques for preprocessing and preparing numeric data for analysis in Python. It covers centering and scaling data, dealing with skewed data, identifying and dealing with highly correlated features and imputing missing data with the sklearn package. Subs
From playlist Python for Data Analysis
How I'm Learning AI and Machine Learning
For the past 6 months or so, I have been teaching myself about artificial intelligence. In this video, I describe some of the places I learned from and a few of the things I've done with my new found knowledge. MIT OpenCourseware videos: http://ocw.mit.edu/courses/electrical-engineering-a
From playlist Machine Learning
Analysis of an instability in stratified fluid flow by Vishal Vasan
Summer school and Discussion Meeting on Buoyancy-driven flows DATE: 12 June 2017 to 20 June 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru Buoyancy plays a major role in the dynamics of atmosphere and interiors of planets and stars, as well as in engineering applications. This field
From playlist Summer school and Discussion Meeting on Buoyancy-driven flows
Short-Scale Instabilities of Internal Wave Beams: From Floquet Analysis... by Triantaphyllos Akylas
DISCUSSION MEETING WAVES, INSTABILITIES AND MIXING IN ROTATING AND STRATIFIED FLOWS (ONLINE) ORGANIZERS: Thierry Dauxois (CNRS & ENS de Lyon, France), Sylvain Joubaud (ENS de Lyon, France), Manikandan Mathur (IIT Madras, India), Philippe Odier (ENS de Lyon, France) and Anubhab Roy (IIT M
From playlist Waves, Instabilities and Mixing in Rotating and Stratified Flows (ONLINE)
Lec 8 | MIT Finite Element Procedures for Solids and Structures, Linear Analysis
Lecture 8: Numerical integrations, modeling considerations Instructor: Klaus-Jürgen Bathe View the complete course: http://ocw.mit.edu/RES2-002S10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT Linear Finite Element Analysis
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Discussion on numerical integration using Trapezoidal Sums.
From playlist Integration
On effective numerical methods for phase-field models – Tao Tang – ICM2018
Numerical Analysis and Scientific Computing Invited Lecture 15.10 On effective numerical methods for phase-field models Tao Tang Abstract: In this article, we overview recent developments of modern computational methods for the approximate solution of phase-field problems. The main diffi
From playlist Numerical Analysis and Scientific Computing