Calculus Two: Sequences and Series (Fall 2013) with Jim Fowler at Ohio State U

source: Jim Fowler     2013年11月22日 / list compiled by CosmoLearning
https://stemoutreach.osu.edu/events/mooc-calculus-two-sequences-and-series...
https://www.coursera.org/learn/advanced-calculus
Subscribe at http://www.youtube.com/kisonecat

How can I succeed in this course? - Week 1 Introduction 1:08
What is a sequence? - Week 1 - Lecture 1 4:06
How is a sequence presented? - Week 1 - Lecture 2 5:46
Can the same sequence be presented in different ways? - Week 1 - Lecture 3 3:40
How can we build new sequences from old sequences? - Week 1 - Lecture 4 3:25
What is an arithmetic progression? - Week 1 - Lecture 5 2:19
What is a geometric progression? - Week 1 - Lecture 6 4:27
What is the limit of a sequence? - Week 1 - Lecture 7 4:43
Visually, what is the limit of a sequence? - Week 1 - Lecture 8 1:44
Is it easy to find the limit of a sequence? - Week 1 - Lecture 9 8:04
For some epsilon, how large need N be? - Week 1 - Lecture 10 4:10
How do sequences help with the square root of two? - Week 1 - Lecture 11 3:03
When is a sequence bounded? - Week 1 - Lecture 12 8:28
When is a sequence increasing? - Week 1 - Lecture 13 4:48
What is the Monotone Convergence Theorem? - Week 1 - Lecture 14 1:48
How can the Monotone Convergence Theorem help? - Week 1 - Lecture 15 5:45
Is there a sequence that includes every integer? - Week 1 - Lecture 16 4:47
Is there a sequence that includes every real number? - Week 1 - Lecture 17 5:21
What happens in Week 2? - Week 2 Introduction 1:21
What does sum a_k = L mean? - Week 2 - Lecture 1 3:54
Why does sum (1/2)^k = 2? - Week 2 - Lecture 2 5:21
What is the value of sum r^k for k = m to infinity? - Week 2 - Lecture 3 9:31
What is the value of sum r^k for k = m to infinity? - Week 2 - Lecture 4 7:06
What is sum 1/((k+1) * k)? - Week 2 - Lecture 5 10:11
Why does sum n/(n+1) diverge? - Week 2 - Lecture 6 10:15
Does sum 1/n converge or diverge? - Week 2 - Lecture 7 6:40
Does the series sum (sin^2 k)/(2^k) converge or diverge? - Week 2 - Lecture 8 3:52
What is the comparison test? - Week 2 - Lecture 9 8:27
How can grouping make the comparison test even better? - Week 2 - Lecture 10 6:20
Does sum 1/n^2 converge? - Week 2 - Lecture 11 9:01
In what sense does sum 9 * 10^(-n) equal one? - Week 2 - Lecture 12  5:06
In what sense is sum 9 + 90 + 900 + ... meaningful? - Week 2 - Lecture 13 9:41
What will happen in Week 3? - Week 3 Introduction 1:23
Does sum (n^5)/(4^n) converge? - Week 3 - Lecture 1 13:39
What does the ratio test say? - Week 3 - Lecture 2 7:52
Does the ratio test always work? - Week 3 - Lecture 3 5:35
Does sum (n!)/(n^n) converge? - Week 3 - Lecture 4 9:06
How does n! compare to n^n? - Week 3 - Lecture 5 6:13
Why don't I love the root test? - Week 3 - Lecture 6 3:41
How can integrating help us to address convergence? - Week 3 - Lecture 7 12:27
How else can I show sum 1/n diverges? - Week 3 - Lecture 8 5:06
Does sum 1/n^p converge? - Week 3 - Lecture 9 8:08
Does sum 1/(n log n) converge? - Week 3 - Lecture 10 7:40
How far out can you build a one-sided bridge? - Week 3 - Lecture 11 10:45
What is Week 4 all about? - Week 4 Introduction 1:15
Why have we been assuming the terms are positive? - Week 4 - Lecture 1 3:36
Why do absolutely convergent series just plain converge? - Week 4 - Lecture 2 5:21
Why is absolute convergence an important concept? - Week 4 - Lecture 3 3:38
What is conditional convergence? - Week 4 - Lecture 4 2:52
What is an alternating series? - Week 4 - Lecture 5 4:10
What is the alternating series test? - Week 4 - Lecture 6 11:04
How should I go about checking convergence? - Week 4 - Lecture 7 1:43
Why is monotonicity important for the AST? - Week 4 - Lecture 8 5:44
Why are alternating series important? - Week 4 - Lecture 9 6:10
Why is e irrational? - Week 4 - Lecture 10 8:42
When do two series share the same fate? - Week 4 - Lecture 11 5:54
Why can people get away with writing sum_n a_n? - Week 4 - Lecture 12 4:32
Why is this all so vague\ldots or coarse? - Week 4 - Lecture 13 6:06
What happens when I rearrange the terms in a series? - Week 4 - Lecture 14 7:19
What are power series? - Week 5 Introduction 3:04
For which values does a power series converge? - Week 5 - Lecture 1 3:48
Why does a power series converge absolutely? - Week 5 - Lecture 2 4:54
How complicated might the interval of convergence be? - Week 5 - Lecture 3 5:16
How do I find the radius of convergence? - Week 5 - Lecture 4 3:27
What if the radius of convergence is infinity? - Week 5 - Lecture 5 4:03
What if the radius of convergence is zero? - Week 5 - Lecture 6 3:27
What is a power series centered around a? - Week 5 - Lecture 7 4:07
Can I differentiate a power series? - Week 5 - Lecture 8 3:31
Can I integrate a power series? - Week 5 - Lecture 9 6:19
Why might I believe that sum (x^n)/(n!) is e^x? - Week 5 - Lecture 10 4:14
What happens if I multiply two power series? - Week 5 - Lecture 11 9:28
What happens if I transform 1/(1-x)? - Week 5 - Lecture 12 7:00
What is a formula for the Fibonacci numbers? - Week 5 - Lecture 13 12:13
What is this last week about? - Week 6 Introduction 2:11
What is better than a linear approximation? - Week 6 - Lecture 1 14:13
What is the Taylor series of f around zero? - Week 6 - Lecture 2 10:13
What is the Taylor series of f centered around a? - Week 6 - Lecture 3 4:40
What is the Taylor series for sin x around zero? - Week 6 - Lecture 4 4:37
What is Taylor's theorem? - Week 6 - Lecture 5 11:43
Why is the radius of convergence of 1/(1+x^2) so small? - Week 6 - Lecture 6 9:53
How is Taylor's theorem like the mean value theorem? - Week 6 - Lecture 7 8:05
Approximately, what is cos x when x is near zero? - Week 6 - Lecture 8 8:15
How do Taylor series provide intuition for limits? - Week 6 - Lecture 9 11:04
What is a real analytic function? - Week 6 - Lecture 10 4:55
How are real analytic functions like holograms? - Week 6 - Lecture 11 4:25

Calculus One by Jim Fowler at Ohio State U

source: Jim Fowler    2013年5月2日 / list compiled by CosmoLearning
https://zh-tw.coursera.org/learn/calculus1
https://math.osu.edu/people/fowler.291
This course is a first and friendly introduction to calculus, suitable for someone who has never seen the subject before, or for someone who has seen some calculus but wants to review the concepts and practice applying those concepts to solve problems.
Subscribe at http://www.youtube.com/kisonecat

Who will help me? - Week 1 Introduction 1:48
What is a function? - Week 1 - Lecture 1 11:20
When are two functions the same? - Week 1 - Lecture 2 5:58
How can more functions be made? - Week 1 - Lecture 3 3:26
What are some real-world examples of functions? - Week 1 - Lecture 4 6:57
What is the domain of square root? - Week 1 - Lecture 5 15:57
What is the limit of (x^2 - 1)/(x-1)? - Week 1 - Lecture 6 8:49
What is the limit of (sin x)/x? - Week 1 - Lecture 7 6:11
What is the limit of sin (1/x)? - Week 1 - Lecture 8 8:18
Morally, what is the limit of a sum? - Week 1 - Lecture 9 6:15
What is the limit of a product? - Week 1 - Lecture 10 2:14
What is the limit of a quotient? - Week 1 - Lecture 11 9:18
How fast does a ball move? - Week 1 - Lecture 12 16:43
Where are we in the course? - Week 2 Introduction 1:23
What is a one-sided limit? - Week 2 - Lecture 1 3:46
What does "continuous" mean? - Week 2 - Lecture 2 5:02
What is the intermediate value theorem? - Week 2 - Lecture 3 2:25
How can I approximate root two? - Week 2 - Lecture 4 10:21
Why is there an x so that f(x) = x? - Week 2 - Lecture 5 5:13
What does lim f(x) = infinity mean? - Week 2 - Lecture 6 5:25
What is the limit f(x) as x approaches infinity? - Week 2 - Lecture 7 4:44
Why is infinity not a real number? - Week 2 - Lecture 8 6:22
What is the difference between potential and actual infinity? - Week 2 - Lecture 9 2:50
What is the slope of a staircase? - Week 2 - Lecture 10 6:51
How fast does water drip from a faucet? - Week 2 - Lecture 11 5:22
What is the official definition of limit? - Week 2 - Lecture 12 3:35
Why is the limit of x^2 as x approaches 2 equal to 4? - Week 2 - Lecture 13 5:00
Why is the limit of 2x as x approaches 10 equal to 20? - Week 2 - Lecture 14 2:19
What comes next? Derivatives? - Week 3 Introduction 1:38
What is the definition of derivative? - Week 3 - Lecture 1 6:35
What is a tangent line? - Week 3 - Lecture 2 3:29
Why is the absolute value function not differentiable? - Week 3 - Lecture 3 2:39
How does wiggling x affect f(x)? - Week 3 - Lecture 4 3:30
Why is sqrt(9999) so close to 99.995? - Week 3 - Lecture 5 5:44
What information is recorded in the sign of the derivative? - Week 3 - Lecture 6 4:14
Why is a differentiable function necessarily continuous? - Week 3 - Lecture 7 6:02
What is the derivative of a constant multiple of f(x)? - Week 3 - Lecture 8 4:54
Why is the derivative of x^2 equal to 2x? - Week 3 - Lecture 9 12:22
What is the derivative of x^n? - Week 3 - Lecture 10 7:32
What is the derivative of x^3 + x^2? - Week 3 - Lecture 11 5:09
Why is the derivative of a sum the sum of derivatives? - Week 3 - Lecture 12 4:49
What will Week 4 bring us? - Week 4 Introduction 1:22
What is the derivative of f(x) g(x)? - Week 4 - Lecture 1 6:47
Morally, why is the product rule true? - Week 4 - Lecture 2 6:17
How does one justify the product rule? - Week 4 - Lecture 3 6:11
What is the quotient rule? - Week 4 - Lecture 4 4:11
How can I remember the quotient rule? - Week 4 - Lecture 5 5:58
What is the meaning of the derivative of the derivative? - Week 4 - Lecture 6 11:04
What does the sign of the second derivative encode? - Week 4 - Lecture 7 4:27
What does d/dx mean by itself? - Week 4 - Lecture 8  4:06
What are extreme values? - Week 4 - Lecture 9 7:24
How can I find extreme values? - Week 4 - Lecture 10 9:56
Do all local minimums look basically the same when you zoom in? - Week 4 - Lecture 11 3:56
How can I sketch a graph by hand? - Week 4 - Lecture 12 7:29
What is a function which is its own derivative? - Week 4 - Lecture 13 9:02
Is there anything more to learn about derivatives? - Week 5 Introduction 1:01
What is the chain rule? - Week 5 - Lecture 1 10:33
What is the derivative of (1+2x)^5 and sqrt(x^2 + 0.0001)? - Week 5 - Lecture 2 7:05
What is implicit differentiation? - Week 5 - Lecture 3 5:35
What is the folium of Descartes? - Week 5 - Lecture 4 4:42
How does the derivative of the inverse relate to the original? - Week 5 - Lecture 5 10:21
What is the derivative of log? - Week 5 - Lecture 6 6:56
What is logarithmic differentiation? - Week 5 - Lecture 7 4:26
How can we multiply quickly? - Week 5 - Lecture 8 8:49
How do we justify the power rule? - Week 5 - Lecture 9 11:18
How can logarithms help to prove the product rule? - Week 5 - Lecture 10 3:29
How do we prove the quotient rule? - Week 5 - Lecture 11 5:02
How does one prove the chain rule? - Week 5 - Lecture 12 6:49
What are transcendental functions? - Week 6 Introduction 2:05
Why does trigonometry work? - Week 6 - Lecture 1 3:13
Why are there these other trigonometric functions? - Week 6 - Lecture 2 4:49
What is the derivative of sine and cosine? - Week 6 - Lecture 3 10:05
What is the derivative of tan x? - Week 6 - Lecture 4 9:26
What are the derivatives of the other trigonometric functions? - Week 6 - Lecture 5 5:36
What is the derivative of sin(x^2)? - Week 6 - Lecture 6 4:37
What are inverse trigonometric functions? - Week 6 - Lecture 7 4:33
What are the derivatives of inverse trig functions? - Week 6 - Lecture 8 10:27
Why do sine and cosine oscillate? - Week 6 - Lecture 9 4:40
How can we get a formula for sin(a+b)? - Week 6 - Lecture 10 4:16
How can I approximate sin 1? - Week 6 - Lecture 11 3:27
How can we multiply numbers with trigonometry? - Week 6 - Lecture 12 4:12
What applications of the derivative will we do this week? - Week 7 Introduction 1:23
How can derivatives help us to compute limits? - Week 7 - Lecture 1 9:27
How can l'Hôpital help with limits not of the form 0/0? - Week 7 - Lecture 2 14:44
Why shouldn't I fall in love with l'Hôpital? - Week 7 - Lecture 3 8:16
How long until the gray goo destroys Earth? - Week 7 - Lecture 4 3:47
What does a car sound like as it drives past? - Week 7 - Lecture 5 3:58
How fast does the shadow move? - Week 7 - Lecture 6 5:12
How fast does the ladder slide down the building? - Week 7 - Lecture 7 3:52
How quickly does a bowl fill with green water? - Week 7 - Lecture 8 4:08
How quickly does the water level rise in a cone? - Week 7 - Lecture 9 7:01
How quickly does a balloon fill with air? - Week 7 - Lecture 10 3:46
What sorts of optimization problems will calculus help us solve? - Week 8 Introduction 1:39
What is the extreme value theorem? - Week 8 - Lecture 1 8:57
How do I find the maximum and minimum values of f on a given domain? - Week 8 - Lecture 2 9:07
Why do we have to bother checking the endpoints? - Week 8 - Lecture 3 4:16
Why bother considering where the function is not differentiable? - Week 8 - Lecture 4 7:18
How can you build the best fence for your sheep? - Week 8 - Lecture 5 8:50
How large can xy be if x + y = 24? - Week 8 - Lecture 6 5:43
How do you design the best soup can? - Week 8 - Lecture 7 10:33
Where do three bubbles meet? - Week 8 - Lecture 8 12:46
How large of an object can you carry around a corner? - Week 8 - Lecture 9 10:33
How short of a ladder will clear a fence? - Week 8 - Lecture 10 4:04
What is up with all the numerical analysis this week? - Week 9 Introduction 1:35
Where does f(x+h) = f(x) + h f'(x) come from? - Week 9 - Lecture 1 6:00
What is the volume of an orange rind? - Week 9 - Lecture 2 6:42
What happens if I repeat linear approximation? - Week 9 - Lecture 3 10:34
Why is log 3 base 2 approximately 19/12? - Week 9 - Lecture 4 10:22
What does dx mean by itself? - Week 9 - Lecture 5 5:39
What is Newton's method? - Week 9 - Lecture 6 9:56
What is a root of the polynomial x^5 + x^2 - 1? - Week 9 - Lecture 7 6:56
How can Newton's method help me to divide quickly? - Week 9 - Lecture 8 7:26
What is the mean value theorem? - Week 9 - Lecture 9 6:52
Why does f'(x) positive imply that f is increasing? - Week 9 - Lecture 10 5:11
Should I bother to find the point c in the mean value theorem? - Week 9 - Lecture 11 4:28
What does it mean to antidifferentiate? - Week 10 Introduction 2:21
How do we handle the fact that there are many antiderivatives? - Week 10 - Lecture 1 5:27
What is the antiderivative of a sum? - Week 10 - Lecture 2 3:44
What is an antiderivative for x^n? - Week 10 - Lecture 3 7:37
What is the most general antiderivative of 1/x? - Week 10 - Lecture 4 4:15
What are antiderivatives of trigonometric functions? - Week 10 - Lecture 5 5:45
What are antiderivatives of e^x and natural log? - Week 10 - Lecture 6 2:46
How difficult is factoring compared to multiplying? - Week 10 - Lecture 7 5:31
What is an antiderivative for e^(-x^2)? - Week 10 - Lecture 8 4:50
What is the antiderivative of f(mx+b)? - Week 10 - Lecture 9 5:20
Knowing my velocity, what is my position? - Week 10 - Lecture 10 3:18
Knowing my acceleration, what is my position? - Week 10 - Lecture 11 4:25
What is the antiderivative of sine squared? - Week 10 - Lecture 12 3:19
What is a slope field? - Week 10 - Lecture 13 4:57
If we are not differentiating, what are we going to do? - Week 11 Introduction 2:58
How can I write sums using a big Sigma? - Week 11 - Lecture 1 5:11
What is the sum 1 + 2 + ... + k? - Week 11 - Lecture 2 6:12
What is the sum of the first k odd numbers? - Week 11 - Lecture 3 4:16
What is the sum of the first k perfect squares? - Week 11 - Lecture 4 6:48
What is the sum of the first k perfect cubes? - Week 11 - Lecture 5 5:58
What does area even mean? - Week 11 - Lecture 6 7:10
How can I approximate the area of a curved region? - Week 11 - Lecture 7 9:58
What is the definition of the integral of f(x) from x = a to b? - Week 11 5:49
What is the integral of x^2 from x = 0 to 1? - Week 11 - Lecture 9 8:10
What is the integral of x^3 from x = 1 to 2? - Week 11 - Lecture 10 8:37
When is the accumulation function increasing? Decreasing? - Week 11 4:45
What sorts of properties does the integral satisfy? - Week 11 - Lecture 12 4:43
What is the integral of sin x dx from -1 to 1? - Week 11 - Lecture 13 3:16
What is the big deal about the fundamental theorem of calculus? - Week 12 Introduction 2:14
What is the fundamental theorem of calculus? - Week 12 - Lecture 1 5:33
How can I use the fundamental theorem of calculus to integrate? - Week 12 - Lecture 2 6:08
What is the integral of sin x dx from x = 0 to x = pi? - Week 12 - Lecture 3 3:33
What is the integral of x^4 dx from x = 0 to x = 1? - Week 12 - Lecture 4 4:16
What is the area between the graphs of y = sqrt(x) and y = x^2? - Week 12 - Lecture 5 6:27
What is the area between the graphs of y = x^2 and y = 1 - x^2? - Week 12 - Lecture 6 6:31
What is the accumulation function for sqrt(1-x^2)? - Week 12 - Lecture 7 8:40
Why does the Euler method resemble a Riemann sum? - Week 12 - Lecture 8 4:30
In what way is summation like integration? - Week 12 - Lecture 9 2:32
What is the sum of n^4 for n = 1 to n = k? - Week 12 - Lecture 10 9:25
Physically, why is the fundamental theorem of calculus true? - Week 12 - Lecture 11 4:01
What is d/da integral f(x) dx from x = a to x = b? - Week 12 - Lecture 12 5:07
How is this course structured? - Week 13 Introduction 2:16
How does the chain rule help with antidifferentiation? - Week 13 - Lecture 1 5:32
When I do u-substitution, what should u be? - Week 13 - Lecture 2 7:11
How should I handle the endpoints when doing u-substitution? - Week 13 - Lecture 3 5:14
Might I want to do u-substitution more than once? - Week 13 - Lecture 4 4:23
What is the integral of dx / (x^2 + 4x + 7)? - Week 13 - Lecture 5 9:05
What is the integral of (x+10)(x-1)^10 dx from x = 0 to x = 1? - Week 13 - Lecture 6 5:37
What is the integral of x / (x+1)^(1/3) dx? - Week 13 - Lecture 7 3:55
What is the integral of dx / (1 + cos x) ? - Week 13 - Lecture 8 4:17
What is d/dx integral sin t dt from t = 0 to t = x^2? - Week 13 - Lecture 9 3:52
Formally, why is the fundamental theorem of calculus true? - Week 13 - Lecture 10 6:14
Without resorting to the FTC, why does substitution work? - Week 13 - Lecture 11 3:49
What remains to be done? - Week 14 Introduction 1:30
What antidifferentiation rule is the product rule in reverse? - Week 14 - Lecture 1 5:06
What is an antiderivative of x e^x? - Week 14 - Lecture 2 4:14
How does parts help when antidifferentiating log x? - Week 14 - Lecture 3 2:03
What is an antiderivative of e^x cos x? - Week 14 - Lecture 4 6:13
What is an antiderivative of e^(sqrt(x))? - Week 14 - Lecture 5 3:26
What is an antiderivative of sin^(2n+1) x cos^(2n) x dx? - Week 14 - Lecture 6 5:51
What is the integral of sin^(2n) x dx from x = 0 to x = pi? - Week 14 - Lecture 7 8:02
What is the integral of sin^n x dx in terms of sin^(n-2) x dx? - Week 14 - Lecture 8 11:34
Why is pi less than 22/7? - Week 14 - Lecture 9 8:26
What application of integration will we consider? - Week 15 Introduction 1:46
What happens when I use thin horizontal rectangles to compute area? - Week 15 - Lecture 1 6:38
When should I use horizontal as opposed to vertical pieces? - Week 15 - Lecture 2 5:47
What does "volume" even mean? - Week 15 - Lecture 3 4:48
What is the volume of a sphere? - Week 15 - Lecture 4 6:04
How do washers help to compute the volume of a solid of revolution? - Week 15 - Lecture 5 5:20
What is the volume of a thin shell? - Week 15 - Lecture 6 7:49
What is the volume of a sphere with a hole drilled in it? - Week 15 - Lecture 7 7:39
What does "length" even mean? - Week 15 - Lecture 8 4:17
On the graph of y^2 = x^3, what is the length of a certain arc? - Week 15 - Lecture 9 4:16
This title is missing a question mark. - Week 15 - Lecture 10 1:16

Dynamical Systems by Steve L. Brunton

source: Steve Brunton        2016年4月23日

1 26:44 Sparse Identification of Nonlinear Dynamics (SINDy)--
This video illustrates a new algorithm for the sparse identification of nonlinear dynamics (SINDy).  In this work, we combine machine learning, sparse regression, and dynamical systems to identify nonlinear differential equations purely from measurement data.
From the Paper:
Discovering governing equations from data by sparse identification of nonlinear dynamical systems.
PNAS 113(15):3932—3937, 2016.
Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz  
Code available at: http://faculty.washington.edu/sbrunto...
For more details, see our papers: https://scholar.google.com/citations?...
http://www.pnas.org/content/113/15/3932
http://arxiv.org/abs/1509.03580
2 31:31 Koopman Observable Subspaces & Finite Linear Representations of Nonlinear Dynamics for Control
3 4:38 Koopman Observable Subspaces & Nonlinearization
4 10:18 Koopman Operator Optimal Control
5 30:35 Compressed Sensing and Dynamic Mode Decomposition
6 47:07 Hankel Alternative View of Koopman (HAVOK) Analysis [FULL]
7 22:41 Hankel Alternative View of Koopman (HAVOK) Analysis [SHORT]
8 9:39 Magnetic field reversal and Measles outbreaks: HAVOK models of chaos
9 5:27 Linear model for chaotic Lorenz system [HAVOK]

Koopman Analysis by Steve L. Brunton

source: Steve Brunton    2015年10月22日


1 31:31 Koopman Observable Subspaces & Finite Linear Representations of Nonlinear Dynamics for Control--
This video illustrates the use of the Koopman operator to simulate and control a nonlinear dynamical system using a linear dynamical system on an observable subspace.
From the Paper:
Koopman observable subspaces and finite linear representations of nonlinear dynamical systems for control
by Steven L. Brunton, Bingni W. Brunton, Joshua L. Proctor, and J. Nathan Kutz
For more details, see our papers:
https://scholar.google.com/citations?...
http://arxiv.org/abs/1510.03007
http://arxiv.org/abs/1509.03580
2 4:38 Koopman Observable Subspaces & Nonlinearization
3 10:18 Koopman Operator Optimal Control
4 30:35 Compressed Sensing and Dynamic Mode Decomposition
5 47:07 Hankel Alternative View of Koopman (HAVOK) Analysis [FULL]
6 22:41 Hankel Alternative View of Koopman (HAVOK) Analysis [SHORT]
7 9:39 Magnetic field reversal and Measles outbreaks: HAVOK models of chaos
8 5:27 Linear model for chaotic Lorenz system [HAVOK]

Control Bootcamp by Steve L. Brunton

source: Steve Brunton    2017年1月23日
This course provides a rapid overview of optimal control (controllability, observability, LQR, Kalman filter, etc.). It is not meant to be an exhaustive treatment, but instead provides a high-level overview of some of the main approaches, applied to simple examples in Matlab.
These lectures follow Chapters 1 & 3 from: Machine learning control, by Duriez, Brunton, & Noack https://www.amazon.com/Machine-Learni...
Chapters available at: http://faculty.washington.edu/sbrunto...
Other great references: 
A course in robust control theory. Dullerud & Paganini: https://www.amazon.com/Course-Robust-...
Mathematical treatment based on linear algebra.
Multivariate feedback control. Skogestad & Postle thwaite
https://www.amazon.com/Multivariable-...
Applied treatment with an emphasis on design and practical considerations.

1 19:32 Overview: Overview lecture for bootcamp on optimal and modern control. In this lecture, we discuss the various types of control and the benefits of closed-loop feedback control. 
2 24:47 Linear Systems
3 19:30 Stability and Eigenvalues
4 30:46 Linearizing Around a Fixed Point
5 32:30 Controllability
6 10:49 Controllability, Reachability, and Eigenvalue Placement
7 5:47 Controllability and the Discrete-Time Impulse Response
8 15:24 Degrees of Controllability and Gramians
9 13:34 Controllability and the PBH Test
10 6:57 Cayley-Hamilton Theorem
11 10:30 Reachability and Controllability with Cayley-Hamilton
12 15:09 Inverted Pendulum on a Cart
13 12:55 Eigenvalue Placement for the Inverted Pendulum on a Cart
14 13:04 Linear Quadratic Regulator (LQR) Control for the Inverted Pendulum on a Cart
15 11:03 Motivation for Full-State Estimation
16 8:03 Observability
17 11:38 Full-State Estimation
18 6:11 Kalman Filter
19 8:20 Observability Example in Matlab
20 11:08 Observability Example in Matlab (Part 2)
21 22:12 Kalman Filter Example in Matlab
22 8:34 Linear Quadratic Gaussian (LQG)
23 13:26 LQG Example in Matlab
24 8:13 Introduction to Robust Control
25 12:16 Three Equivalent Representations of Linear Systems
26 18:30 Example Frequency Response (Bode Plot) for Spring-Mass-Damper
27 19:15 Laplace Transforms and the Transfer Function
28 14:47 Benefits of Feedback on Cruise Control Example
29 11:12 Benefits of Feedback on Cruise Control Example (Part 2)
30 23:17 Cruise Control Example with Proportional-Integral (PI) control
31 11:20 Sensitivity and Complementary Sensitivity
32 8:27 Sensitivity and Complementary Sensitivity (Part 2)
33 7:22 Loop shaping
34 12:21 Loop Shaping Example for Cruise Control
35 9:56 Sensitivity and Robustness
36 9:02 Limitations on Robustness
37 5:19 Cautionary Tale About Inverting the Plant Dynamics