2018-03-21
Beginning Scientific Computing by Steve L. Brunton and ?
source: AMATH 301 2016年2月19日
1 49:34 Higher-order Integration Schemes: Higher-order numerical integration schemes are considered along the classic schemes of trapezoidal rule and Simpson’s rule.
2 46:59 Ordinary Differential Equations and Time-stepping
3 39:15 Data Fitting with Matlab
4 57:09 Linear Programming and Genetic Algorithms
5 47:10 Numerical Differentiation Methods
6 43:51 Eigenvalues and Eigenvectors
7 48:56 Unconstrained Optimization (Derivative Methods)
8 47:22 Iteration Methods for Ax-b
9 9:01 Supplement: Using ODE45 & Runge-Kutta methods
10 48:03 PCA for Face Recognition
11 48:55 Eigen-decompositions and Iterations
12 44:39 Least-Squares Fitting Methods
13 44:00 Polynomial Fits and Splines
14 45:21 Higher-order Accuracy Schemes for Differentiation and Integration
15 45:35 Unconstrained Optimization (Derivative-Free Methods)
16 44:49 Error and Stability of Time-stepping Schemes
17 43:40 FFT and Image Compression
18 45:16 General Time-stepping and Runge-Kutta Schemes
19 48:39 Theory of the Fourier Transform
20 48:03 Discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT)
21 44:36 The Singular Value Decomposition (SVD)
22 51:13 Principal Componenet Analysis (PCA)
23 4:40 Supplement: Big systems of ODEs
24 10:10 Supplement: Indexing equations
25 7:45 Supplement: Discrete Fourier Transform
26 5:53 Supplement: Mean Value Theorem
27 29:51 Application of Runge-Kutta to Lorenz Equation
28 41:07 Vectorized Time-step Integrators
29 49:30 Application of Runge-Kutta to Chaotic Dynamics and the Double Pendulum
30 6:07 Supplement: Vector fields and phase-planes
31 41:56 Vectors & Matrices
32 39:25 Logic, Loops, and Iterations
33 41:56 Vectors & Matrices
34 50:59 LU Matrix Decomposition for Ax=b
35 39:40 Gaussian Elimination for Ax=b
36 42:10 Linear Systems of Equations
Data Science for Biologists by Nathan Kutz, Bing Brunton and Steve L. Brunton
source: Data4Bio 2016年6月8日
Course Website: data4bio.com
Instructors:
Nathan Kutz: faculty.washington.edu/kutz
Bing Brunton: faculty.washington.edu/bbrunton
Steve Brunton: faculty.washington.edu/sbrunton
1 2:23 Data Science for Biologists: Introductory Overview
2 19:34 Numerical Calculus: Differential Equations, Part 3
3 10:43 Numerical Calculus: Differential Equations, Part 2
4 8:44 Numerical Calculus: Differential Equations, Part 1
5 8:40 The Basics: Introduction to Matlab, Part 1
6 13:26 The Basics: Introduction to Matlab, Part 3
7 10:17 The Basics: Introduction to Matlab, Part 2
8 10:05 The Basics: Introduction to Matlab, Part 4
9 7:43 Data Fitting: Matlab Implementation, Part 2
10 11:47 Data Fitting: Basic Curve Fitting, Part 3
11 17:55 Dimensionality Reduction: Principal Components Analysis, Part 3
12 5:38 Regression: Linear Regression, Part 1
13 8:24 Plotting and Visualizing Data: Plotting, Part 1
14 20:19 Plotting and Visualizing Data: Data Visualization, Part 1
15 18:50 Clustering and Classification: Introduction, Part 2
16 8:31 The Basics: Loops and Logic, Part 4
17 9:08 The Basics: Loops and Logic, Part 2
18 8:00 The Basics: Loops and Logic, Part 3
19 15:16 The Basics: Loops and Logic, Part 1
20 17:41 Plotting and Visualizing Data: Data Visualization, Part 2
21 13:08 Dimensionality Reduction: Eigenpets, Part 1
22 17:55 Numerical Calculus: Differentiation, Part 2
23 22:42 Dimensionality Reduction: Eigenpets, Part 2
24 8:07 Regression: Linear Regression, Part 3
25 7:59 Numerical Calculus: Integration, Part 2
26 6:37 Regression: Linear Regression, Part 2
27 15:25 Numerical Calculus: Differentiation, Part 1
28 17:56 Numerical Calculus: Integration, Part 1
29 13:10 Regression: Linear Regression, Part 4
30 9:03 Numerical Calculus: Differentiation, Part 3
31 27:08 Clustering and Classification: Introduction, Part 1
32 7:23 Regression: Beyond Linear Regression, Part 3
33 18:19 Fourier Transforms: Image Compression, Part 2
34 10:30 Fourier Transforms: Image Compression, Part 3
35 17:03 Regression: Beyond Linear Regression, Part 2
36 19:21 Clustering and Classification: Introduction, Part 3
37 12:27 Data Fitting: Matlab Implementation, Part 1
38 9:44 Regression: Beyond Linear Regression, Part 1
39 12:10 Fourier Transforms: Image Compression, Part 1
40 8:38 Clustering and Classification: Advanced Methods, Part 4
41 16:19 Dimensionality Reduction: Principal Components Analysis, Part 2
42 13:56 Dimensionality Reduction: Principal Components Analysis, Part 1
43 9:34 Regression: Model Selection and Validation, Part 2
44 12:06 Data Fitting: Basic Curve Fitting, Part 1
45 11:14 Data Fitting: Basic Curve Fitting, Part 2
46 10:10 Fourier Transforms: Discrete Fourier Transform, Part 1
47 27:01 Clustering and Classification: Advanced Methods, Part 1
48 11:59 Fourier Transforms: Fast Fourier Transform, Part 1
49 12:37 Regression: Model Selection and Validation, Part 3
50 9:17 Data Fitting: Basic Curve Fitting, Part 3
51 8:24 Plotting and Visualizing Data: Plotting, Part 2
52 10:20 Fourier Transforms: Fast Fourier Transform, Part 2
53 18:19 Fourier Transforms: Discrete Fourier Transform, Part 3
54 4:15 Data Fitting: Basic Curve Fitting, Part 4
55 16:50 Plotting and Visualizing Data: Plotting, Part 3
56 11:12 Regression: Model Selection and Validation, Part 1
57 16:41 Clustering and Classification: Advanced Methods, Part 2
58 9:29 Fourier Transforms: Fast Fourier Transform, Part 3
59 15:08 Fourier Transforms: Discrete Fourier Transform, Part 2
60 12:45 Dimensionality Reduction: High Dimensional Data, Part 1
61 16:39 Systems of Equations: Eigenvalues and Eigenvectors, Part 2
62 11:36 Systems of Equations: Eigenvalues and Eigenvectors, Part 1
63 11:01 Systems of Equations: Solving Linear Systems, Part 4
64 6:13 Data Fitting: Polynomial Fitting and Splines, Part 3
65 8:56 Systems of Equations: Solving Linear Systems, Part 1
66 17:22 Systems of Equations: Solving Linear Systems, Part 2
67 11:58 Systems of Equations: Eigenvalues and Eigenvectors, Part 4
68 7:35 Data Fitting: Polynomial Fitting and Splines, Part 2
69 11:19 Systems of Equations: Eigenvalues and Eigenvectors, Part 3
70 6:07 Plotting and Visualizing Data: Communicating with Data, Part 3
71 14:51 Plotting and Visualizing Data: Communicating with Data, Part 2
72 9:42 Plotting and Visualizing Data: Communicating with Data, Part 1
73 15:35 Systems of Equations: Modeling with Matrices and Vectors, Part 3
74 12:10 Systems of Equations: Modeling with Matrices and Vectors, Part 2
75 19:03 Clustering and Classification: Support Vector Machines and Decision Trees, Part 1
76 7:54 Clustering and Classification: Support Vector Machines and Decision Trees, Part 3
77 22:00 Clustering and Classification: Support Vector Machines and Decision Trees, Part 2
78 3:08 Data Science for Biologists: Introduction to the Lightboard
79 3:40 Data Science for Biologists: Introduction to Matlab
80 3:04 Data Science for Biologists: Syllabus
Finite-time Lyapunov exponents by Steve Brunton and ?
source: Steve Brunton 2015年9月29日
Finite-time Lyapunov exponent (FTLE) field for an airfoil in a rapid pitch-up maneuver at low Reynolds number. The airfoil pitches up from 0 deg to 32 deg in a fraction of a convective time at Re=300. For more details, see our papers:
1 0:15 FTLE field for a pitching airfoil at low Reynolds number
2 0:15 FTLE field for a pitching airfoil at low Reynolds number (with Force)
3 0:27 Attracting FTLE field for plunging plate in a quiescent fluid
4 0:27 Repelling FTLE field for plunging plate in a quiescent fluid
5 0:27 Vorticity field for plunging plate in a quiescent fluid
6 0:14 FTLE field for a plunging plate at low Reynolds number
7 0:14 FTLE field for a pitching plate at low Reynolds number
8 0:49 FLTE field showing separation bubble bursting for flat plate airfoil
9 0:07 FTLE field for an airfoil in rapid plunge maneuver at low Reynolds number
10 0:10 Validation of forward-time FTLE field for vortex shedding
11 0:10 Validation of backward-time FTLE field for vortex shedding
12 0:41 Particles starting near positive-time LCS attract onto negative-time LCS
13 0:31 Particles starting near positive-time LCS attract onto negative-time LCS (zoom out)
14 0:26 Particle trajectories integrated through the double gyre illustrate heteroclinic tangle
15 0:02 Airfoil pitching about leading-edge (+/- 20 deg, Re=100), with FTLE visualization
16 0:02 Airfoil pitching about quarter-chord (+/- 20 deg, Re=100), with FTLE visualization
17 0:02 Airfoil pitching about mid-chord (+/- 20 deg, Re=100), with FTLE visualization
18 0:02 Airfoil pitching about three-quarter-chord (+/- 20 deg, Re=100), with FTLE visualization
19 0:02 Airfoil pitching about trailing-edge (+/- 20 deg, Re=100), with FTLE visualization
20 0:02 Airfoil pitching about leading-edge (+/- 27.1 deg, Re=100), with FTLE visualization
21 0:02 Airfoil pitching about quarter-chord (+/- 27.1 deg, Re=100), with FTLE visualization
22 0:02 Airfoil pitching about mid-chord (+/- 27.1 deg, Re=100), with FTLE visualization
23 0:02 Airfoil pitching about three-quarter-chord (+/- 27.1 deg, Re=100), with FTLE visualization
24 0:02 Airfoil pitching about trailing-edge (+/- 27.1 deg, Re=100), with FTLE visualization
25 0:02 Airfoil pitching about leading-edge (+/- 43.2 deg, Re=100), with FTLE visualization
26 0:02 Airfoil pitching about quarter-chord (+/- 43.2 deg, Re=100), with FTLE visualization
27 0:02 Airfoil pitching about mid-chord (+/- 43.2 deg, Re=100), with FTLE visualization
28 0:02 Airfoil pitching about three-quarter-chord (+/- 43.2 deg, Re=100), with FTLE visualization
29 3:00 Stirring Faces: Mixing in a Quiescent Fluid
Mechanical Engineering Analysis (Winter 2015) by Steve Brunton | University of Washington
source: Steve Brunton 2016年4月27日
ME565 - Mechanical Engineering Analysis (Winter 2015) by Steve Brunton | University of Washington
Notes: http://faculty.washington.edu/sbrunto...
Course Website: http://faculty.washington.edu/sbrunto...
http://faculty.washington.edu/sbrunton/
Lecture 1: Complex numbers and functions 49:02
2: Roots of unity, branch cuts, analytic functions, and the Cauchy-Riemann conditions 50:19
3: Integration in the complex plane (Cauchy-Goursat Integral Theorem) 50:13
4: Cauchy Integral Formula 47:59
5: ML Bounds and examples of complex integration 50:15
6: Inverse Laplace Transform and the Bromwich Integral 48:49
7: Canonical Linear PDEs: Wave equation, Heat equation, and Laplace's equation 50:18
8: Heat Equation: derivation and equilibrium solution in 1D (i.e., Laplace's equation) 49:28
9: Heat Equation in 2D and 3D. 2D Laplace Equation (on rectangle) 47:16
10: Analytic Solution to Laplace's Equation in 2D (on rectangle) 48:05
11: Numerical Solution to Laplace's Equation in Matlab. Intro to Fourier Series 48:58
12: Fourier Series 50:23
13: Infinite Dimensional Function Spaces and Fourier Series 49:03
14: Fourier Transforms 49:09
15: Properties of Fourier Transforms and Examples 48:22
16: Discrete Fourier Transforms (DFT) 48:39
16 Bonus: DFT in Matlab 7:45
17: Fast Fourier Transforms (FFT) and Audio 48:03
18: FFT and Image Compression 43:40
19: Fourier Transform to Solve PDEs: 1D Heat Equation on Infinite Domain 42:33
20: Numerical Solutions to PDEs Using FFT 50:20
21: The Laplace Transform 49:51
22: Laplace Transform and ODEs 49:48
23: Laplace Transform and ODEs with Forcing and Transfer Functions 49:24
24: Convolution integrals, impulse and step responses 50:25
25: Laplace transform solutions to PDEs 50:23
26: Solving PDEs in Matlab using FFT 50:16
27: SVD Part 1 50:12
28: SVD Part 2 48:46
29: SVD Part 3 47:19
Mechanical Engineering Analysis (Fall 2014) by Steve L. Brunton | University of Washington
source: Steve Brunton 2016年4月25日
ME564 - Mechanical Engineering Analysis (Fall 2014) by Steve L. Brunton | University of Washington
Notes: http://faculty.washington.edu/sbrunto...
Matlab code: http://faculty.washington.edu/sbrunto...
Course Website: http://faculty.washington.edu/sbrunto...
http://faculty.washington.edu/sbrunton/
Lecture 1: Overview of engineering mathematics 41:16 Overview of engineering mathematics and example weather model in Matlab.
2: Review of calculus and first order linear ODEs 48:43
3: Taylor series and solutions to first and second order linear ODEs 53:23
4: Second order harmonic oscillator, characteristic equation, ode45 in Matlab 51:38
5: Higher-order ODEs, characteristic equation, matrix systems of first order ODEs 49:19
6: Matrix systems of first order equations using eigenvectors and eigenvalues 48:07
7: Eigenvalues, eigenvectors, and dynamical systems 46:54
8: 2x2 systems of ODEs (with eigenvalues and eigenvectors), phase portraits 48:42
9: Linearization of nonlinear ODEs, 2x2 systems, phase portraits 48:40
10: Examples of nonlinear systems: particle in a potential well 50:20
11: Degenerate systems of equations and non-normal energy growth 50:15
12: ODEs with external forcing (inhomogeneous ODEs) 49:36
13: ODEs with external forcing (inhomogeneous ODEs) and the convolution integral 49:52
14: Numerical differentiation using finite difference 49:30
15: Numerical differentiation and numerical integration 48:37
16: Numerical integration and numerical solutions to ODEs 46:33
17: Numerical solutions to ODEs (Forward and Backward Euler) 50:24
18: Runge-Kutta integration of ODEs and the Lorenz equation 48:57
19: Vectorized integration and the Lorenz equation 48:12
20: Chaos in ODEs (Lorenz and the double pendulum) 49:00
21: Linear algebra in 2D and 3D: inner product, norm of a vector, and cross product 48:40
22: Div, Grad, and Curl 49:18
23: Gauss's Divergence Theorem 49:29
24: Directional derivative, continuity equation, and examples of vector fields 45:44
25: Stokes' theorem and conservative vector fields 49:52
26: Potential flow and Laplace's equation 45:57
27: Potential flow, stream functions, and examples 54:15
28: ODE for particle trajectories in a time-varying vector field 49:24
Subscribe to:
Posts (Atom)