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#Numerical Integration

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University of Colorado Boulder

Numerical Analysis

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Explore differential equations, numerical integration, and root-finding methods using software tools. Learn practical techniques for solving complex mathematical problems in engineering and science.
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18 Lesons
1 hour 30 minutes
On-Demand
Free-Video
NPTEL

Power System Dynamics and Control

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This course first introduces a student to power stability problems and the basic concepts of modeling and analysis of dynamical systems. Modeling of power system components - generators, transmission lines, excitation and prime mover controllers - is cov…
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45 Lesons
1 day 18 hours
On-Demand
Free-Video
Jonathan Walters

Numerical Analysis With Matlab

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Learn iterative methods, interpolation, and numerical integration techniques with Matlab implementations for solving complex mathematical problems.
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3 Lesons
4 hours 30 minutes
On-Demand
Free-Video
Steve Brunton

Numerical Integration - Discrete Riemann Integrals and Trapezoid Rule

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Explore numerical integration techniques including Riemann integrals, trapezoidal rule, and Simpson's rule. Learn to approximate definite integrals with Python and MATLAB implementations.
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5 Lesons
30 minutes
On-Demand
Free-Video
Steve Brunton

Chaotic Dynamical Systems

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Explore chaotic dynamical systems, their sensitive dependence on initial conditions, and applications in nature and engineering. Learn to recognize chaos and numerically integrate these complex systems.
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7 Lesons
44 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Introduction to the Finite Element Method: 1D Basis Functions

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Explore 1D basis functions in finite element method. Learn key concepts and applications for numerical analysis and engineering problem-solving.
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1 Lesons
12 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

2D Finite Element Method - Summary of FEM Procedure

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Explore the 2D Finite Element Method procedure, covering key steps and applications in engineering analysis. Gain insights into this powerful numerical technique for solving complex problems.
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1 Lesons
14 minutes
On-Demand
Free-Video
Dot Physics

Why Does the RMS Voltage Have a Square Root of 2?

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Explore the concept of RMS voltage, its relationship to the square root of 2, and the average of sin^2 using Python code examples.
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1 Lesons
10 minutes
On-Demand
Free-Video
Steve Brunton

Chaos in ODEs - Lorenz and the Double Pendulum

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Explore chaos in ordinary differential equations through Lorenz systems and double pendulum examples, examining numerical integration challenges and chaotic dynamics in engineering mathematics.
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11 Lesons
49 minutes
On-Demand
Free-Video
Steve Brunton

Runge-Kutta Integration of ODEs and the Lorenz Equation

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Explore Runge-Kutta integration methods for ODEs and delve into the fascinating Lorenz equation, uncovering its chaotic behavior and applications in engineering mathematics.
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11 Lesons
49 minutes
On-Demand
Free-Video
Professor Leonard

Numerical Integration With Trapezoidal and Simpson's Rule

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Learn to approximate definite integrals using the Trapezoidal and Simpson's Rules, powerful numerical methods for solving complex integration problems.
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1 Lesons
27 minutes
On-Demand
Free-Video
NIOS

Numerical Methods

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Comprehensive exploration of numerical methods covering error analysis, linear systems, interpolation, differentiation, integration, and solving algebraic equations using various techniques.
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37 Lesons
1 day 6 hours
On-Demand
Free-Video
Steve Brunton

Numerical Integration of Chaotic Dynamics - Uncertainty Propagation & Vectorized Integration

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Explore chaos and uncertainty propagation in dynamical systems through numerical integration. Learn efficient vectorization techniques in Python and MATLAB for faster computations.
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1 Lesons
20 minutes
On-Demand
Free-Video
Steve Brunton

Runge-Kutta Integrator Overview - All Purpose Numerical Integration of Differential Equations

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Comprehensive introduction to Runge-Kutta schemes for numerical integration of differential equations, covering RK2 and RK4 methods with intuitive explanations and visual representations.
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1 Lesons
30 minutes
On-Demand
Free-Video
Steve Brunton

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

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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.
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1 Lesons
31 minutes
On-Demand
Free-Video
Steve Brunton

Deriving Forward Euler and Backward-Implicit Euler Integration Schemes for Differential Equations

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Explore Forward and Backward Euler integration methods for ODEs, including derivations, error sources, and stability analysis. Gain insights into numerical integration techniques for solving differential equations.
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1 Lesons
23 minutes
On-Demand
Free-Video
Steve Brunton

Numerical Simulation of Ordinary Differential Equations - Integrating ODEs

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Explore numerical integration of ODEs to analyze nonlinear systems and generate trajectories. Learn techniques for solving complex dynamics where analytic methods fall short.
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1 Lesons
24 minutes
On-Demand
Free-Video
Steve Brunton

Numerical Integration and Numerical Solutions to ODEs

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Explore numerical methods for integration and solving ordinary differential equations, enhancing your computational skills in engineering mathematics.
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1 Lesons
47 minutes
On-Demand
Free-Video
Steve Brunton

Numerical Differentiation and Numerical Integration

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Explore numerical differentiation and integration techniques in engineering mathematics, covering key concepts and practical applications for solving complex problems.
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1 Lesons
49 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Quadrature Rules on Manifolds - Useful Results - Lecture 3

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Explore advanced quadrature techniques for manifolds, focusing on key results and applications in harmonic analysis. Gain insights into cutting-edge mathematical approaches.
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1 Lesons
52 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Quadrature Rules on Manifolds - Designs - Lecture 1

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Explore quadrature rules on manifolds and designs in harmonic analysis. Learn about cutting-edge mathematical techniques for solving complex problems in geometry and analysis.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Let's Code Physics

Numerical Integration Methods in Jupyter Notebook - Development Vlog 4

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Explore numerical integration methods using Jupyter Notebook, comparing results and enhancing computational skills for physics research and problem-solving.
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1 Lesons
20 minutes
On-Demand
Free-Video
Let's Code Physics

Jupyter Notebook Assignment - Runge-Kutta Method Development - Vlog 3

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Explore the Runge-Kutta Method in computational physics, comparing it with Euler-Cromer. Develop skills in numerical analysis and scientific computing using Jupyter Notebooks.
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1 Lesons
38 minutes
On-Demand
Free-Video
Inside Livermore Lab

Designing Conservative and Accurately Dissipative Numerical Integrators in Time

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Explore innovative framework for structure-preserving time steppers using finite elements and auxiliary variables. Discover applications in Kepler, Kovalevskaya, Navier-Stokes, and Benjamin-Bona-Mahony problems.
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1 Lesons
56 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Numerical Integration: Simple Numerical Integration

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Learn simple numerical integration techniques for approximating definite integrals, enhancing computational skills in mathematical analysis.
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1 Lesons
20 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Method of Lines for Hyperbolic PDEs

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Explore the Method of Lines technique for solving hyperbolic partial differential equations, enhancing your understanding of numerical methods in applied mathematics.
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1 Lesons
28 minutes
On-Demand
Free-Video
Codeynamics

Integration by Monte Carlo Method Using Python in Jupyter Notebook

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Explore Monte Carlo integration using Python in Jupyter Notebook. Learn to apply this powerful numerical technique for solving complex integrals.
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1 Lesons
11 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Integration Algorithms

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Master integration algorithms for solving complex mathematical problems and enhancing computational skills.
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1 Lesons
15 minutes
On-Demand
Free-Video
Dot Physics

Calculate the Flux Through the Surface of a Wedge - Two Methods

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Learn to calculate flux through a wedge surface using traditional integration and Python-based random number methods, enhancing your vector calculus and computational skills.
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1 Lesons
21 minutes
On-Demand
Free-Video
Prof. Ryan C. Cooper

ME3255 - Verifying Implicit and Explicit Integration Methods for Tsiolkovsky Solution

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Verify implicit and explicit integration methods for Tsiolkovsky solution, enhancing understanding of numerical techniques in aerospace applications.
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1 Lesons
17 minutes
On-Demand
Free-Video
Prof. Ryan C. Cooper

ME3255 - Working on Rocket Problems with Solve_IVP

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Explore rocket problem-solving using solve_ivp in Python. Learn to model and analyze rocket dynamics for advanced engineering applications.
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1 Lesons
33 minutes
On-Demand
Free-Video
Prof. Ryan C. Cooper

Numerical Integration, Root Finding, and Computational Thinking - ME3255

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Explore numerical integration, root finding techniques, and computational thinking principles for solving complex engineering problems.
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1 Lesons
56 minutes
On-Demand
Free-Video
Prof. Ryan C. Cooper

ME3255 - Rocket Equations and Verifying Numerical Integration

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Explore rocket equations and verify numerical integration techniques for aerospace applications. Enhance understanding of propulsion systems and computational methods.
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1 Lesons
26 minutes
On-Demand
Free-Video
Prof. Ryan C. Cooper

Measuring Convergence of Integration Methods: Heun and Runge-Kutta Comparison - Homework 3

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Comparez les taux de convergence des méthodes de Heun et Runge-Kutta pour l'intégration numérique, avec des résultats surprenants.
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1 Lesons
27 minutes
On-Demand
Free-Video
Prof. Ryan C. Cooper

Convergence of Integration Methods and Root Finding with SymPy - ME3255

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Explore integration methods and root finding using Sympy, focusing on convergence analysis for enhanced numerical problem-solving skills.
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1 Lesons
37 minutes
On-Demand
Free-Video
Dyalog User Meetings

Numerical Integration for Forensic DNA Evidence Evaluation

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Explore numerical integration for forensic DNA evidence evaluation, focusing on a novel approach to multi-variable integration that addresses shortcomings in existing methods.
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10 Lesons
31 minutes
On-Demand
Free-Video
Let's Code Physics

Electric Potential Calculation Using Double Integral - Part 1

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Explore numerical integration to calculate electric potential of charged shapes using Scilab, with code examples and practical applications in physics.
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5 Lesons
25 minutes
On-Demand
Free-Video
Let's Code Physics

Calculating Expectation Values - A Journey through Modern Physics

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Explore computational modeling of early 20th-century physics discoveries, focusing on wave functions and expectation values in quantum mechanics through practical examples and numerical integration.
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5 Lesons
22 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Gravitational Wave Parameter Estimation with Compressed Likelihood Evaluations

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Explore advanced techniques for efficient gravitational wave parameter estimation, focusing on Reduced Order Quadratures (ROQs) to accelerate likelihood evaluations and improve Bayesian inference in GW astronomy.
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26 Lesons
42 minutes
On-Demand
Free-Video
Let's Code Physics

Rope Simulator - Building a Simple Rope Model - Episode 1

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Explore the physics of ropes in video games by building a simple rope simulator using three atoms and two springs. Learn about the Euler-Cromer Method and VPython programming.
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1 Lesons
21 minutes
On-Demand
Free-Video
Let's Code Physics

Jupyter Notebook Assignment - Euler-Cromer Method Development - Part 2

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Explore the Euler-Cromer Method for computational physics through a guided Jupyter notebook project. Learn to implement and analyze this numerical integration technique for solving differential equations.
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1 Lesons
39 minutes
On-Demand
Free-Video
Let's Code Physics

Potential Integrator 5 - Fun with Shapes: Exploring Electric Potential of Various Charged Objects

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Explore electric potential of various charged shapes through numerical integration. Hands-on coding with Scilab to visualize and analyze electrostatic phenomena beyond simple rectangles.
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1 Lesons
23 minutes
On-Demand
Free-Video
Let's Code Physics

Graphing Electric Potential in 3D - Potential Integrator Series Part 4

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Explore 3-D visualization of electric potential using numerical integration. Learn to graph potential against x and y coordinates for various charged object shapes.
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1 Lesons
18 minutes
On-Demand
Free-Video
Let's Code Physics

Potential Integrator - Checking Multipoles Against Electric Potential Code - Part 3

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Explore numerical integration for electric potential of charged objects, comparing results with multipole expansion to verify accuracy.
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1 Lesons
17 minutes
On-Demand
Free-Video
Let's Code Physics

Graphing Electric Potential vs Distance - Potential Integrator Series Part 2

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Visualize electric potential through numerical integration, exploring various charged object shapes. Learn to graph V vs x using Scilab in this physics coding tutorial.
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1 Lesons
20 minutes
On-Demand
Free-Video
Let's Code Physics

Calculating Expectation Values in Computational Quantum Mechanics - Lecture 6

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Explore computational methods for calculating quantum expectation values, visualizing wave functions, and understanding the connection between quantum and classical mechanics.
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1 Lesons
21 minutes
On-Demand
Free-Video
Let's Code Physics

Building Wave Functions with Fourier - Computational Quantum Mechanics Lecture 5

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Learn to construct and deconstruct wave functions using Fourier's method in computational quantum mechanics. Visualize quantum behaviors through computer animations with VPython.
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1 Lesons
21 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Numerical Integration of Loop Amplitudes in Momentum Space

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Explore numerical integration techniques for loop amplitudes in momentum space, focusing on singularities, thresholds, and local cancellation methods.
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15 Lesons
47 minutes
On-Demand
Free-Video
Centrum Fizyki Teoretycznej PAN

Cyclic Projective t-Designs and How to Find Them

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Explore complex projective t-designs in quantum states and their applications in optimal quantum tomography, focusing on cyclic designs generated through unitary operations.
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1 Lesons
47 minutes
On-Demand
Free-Video
Dot Physics

Python Physics: Finding the Height of an Elevator From Acceleration

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Estimate elevator height using smartphone acceleration data and Python for numerical integration. Learn practical physics application.
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1 Lesons
22 minutes
On-Demand
Free-Video
Dot Physics

Quantum Python: Numerical Integration to Normalize a Wave Function

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Explore numerical integration techniques to normalize wave functions in quantum mechanics using Python, enhancing understanding of computational approaches in physics.
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1 Lesons
15 minutes
On-Demand
Free-Video
Dot Physics

Python Lists for Physics: Creating, Manipulating, and Visualizing Data

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Explore Python lists for physics applications, covering creation, manipulation, and visualization of data, including integration and animated graphing.
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1 Lesons
17 minutes
On-Demand
Free-Video
Dot Physics

Derivation of the Gravitational Potential Energy - Plus Numerical Integrals with Python

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Derive gravitational potential energy through work calculations and explore numerical integration using Python for practical applications.
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1 Lesons
20 minutes
On-Demand
Free-Video
Dot Physics

Numerical Line Integrals with Python

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Explore numerical line integrals using Python to calculate work done in force fields. Gain practical coding skills for solving complex physics problems.
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1 Lesons
22 minutes
On-Demand
Free-Video
Prof. Ryan C. Cooper

Using Timers, Numerical Integration, and Other Programming Tips - HW_01

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Explore timers, numerical integration, and coding tips while learning about error fixing, Linux, and numerical modeling techniques.
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8 Lesons
21 minutes
On-Demand
Free-Video
Inside Livermore Lab

Sparse, Approximate Quadrature for Acceleration of Isogeometric Analysis and ROMs

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Explore advanced numerical integration techniques for accelerating isogeometric analysis and reduced order models through sparse quadrature methods in finite element computations.
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1 Lesons
30 minutes
On-Demand
Free-Video