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Patrick Jones
เข้าร่วมเมื่อ 27 ม.ค. 2016
I'm a mathematics instructor for Cochise College, who has also taught for University of Arizona. The videos on this channel were made for my students, but I chose to share them with everyone to help those interested better understand math.
Differential Equations Taylor Series Solutions to DEs
Cochise College MAT 262 lecture for 12/6/2023. In this lecture we use techniques to manipulate Taylor series to find solutions to higher order linear differential equations with polynomial coefficients.
มุมมอง: 117
วีดีโอ
Differential Equations More on Taylor Series
มุมมอง 5410 หลายเดือนก่อน
Cochise College MAT 262 lecture from 12/4/2023. We continue the review of Taylor series from last time, including re-indexing two Taylor series to add them together.
Differential Equations Review of Taylor Series
มุมมอง 7410 หลายเดือนก่อน
Cochise College MAT 262 lecture from 11/29/2023. Soon we'll be looking at power series solutions to differential equations, and to prepare for that we spend some time reviewing key ideas about Taylor series. (This will continue in the next video.)
Differential Equations Variation of Parameters with Matrices
มุมมอง 9910 หลายเดือนก่อน
Cochise College MAT 262 Lecture from 11/27/2023. In this lecture we discuss how to use variation of parameters to find a particular solution to a nonhomogeneous systems of differential equations, after using eigenvalues and eigenvectors to solve the complementary homogeneous system.
Differential Equations: More on Matrix Systems
มุมมอง 6910 หลายเดือนก่อน
Cochise College MAT 262 lecture from 11/22/2023. In this lesson, we continue to solve systems of homogeneous differential equations using the eigenvalues and eigenvectors of matrices. We discuss both how to solve when there is a repeated root that only has a single eigenvector, and also how to deal with complex eigenvalues and eigenvectors.
Matrix Representations of Homogeneous Systems of Differential Equations
มุมมอง 17410 หลายเดือนก่อน
Cochise College MAT262 lecture from 11/15/2023. In this video we review matrix multiplication and use it to show how a system of DEs can be represented using such a multiplication.
Solving Homogeneous Systems of Differential Equations Using Matrices
มุมมอง 4410 หลายเดือนก่อน
Cochise College MAT 262 Lecture for 11/20. In this lesson, we discuss how to solve a homogeneous system of DEs using eigenvalues and eigenvectors. The techniques shown only work when there are no repeated eigenvalues, and at the end we start moving to closing that gap in our understanding.
Systems of Differential Equations - Elimination Method
มุมมอง 20910 หลายเดือนก่อน
Cochise College MAT 262 Lecture for 11/13/2023. (This is a little shorter than normal due to some exam discussion.) In this lesson we look at systems of differential equations where two functions both use the same independent variable. In order to solve such systems, we make extensive use of differential operators, and eliminate a function in a very similar way to solving an algebra system of e...
Differential Equations: Driven Mass-Spring Systems
มุมมอง 10311 หลายเดือนก่อน
Cochise College MAT 262 lecture from 11/1/2023. Having previously covered both undamped and damped mass-spring systems, we now add a driving force to the system. This results in a non-homogeneous DE, which can then be solved using previous methods.
Differential Equations: Damped Mass-Spring Systems
มุมมอง 4711 หลายเดือนก่อน
Cochise College MAT 262 lecture from 10/30/2023. In this lesson, we discuss combining sin and cos waves into a single trig function with a phase shift, and how to add a damping force to a model for a mass-spring system.
Differential Equations Modelling Undamped Mass-Spring Systems
มุมมอง 4211 หลายเดือนก่อน
Cochise College MAT 262 lecture from 10/25/2023 This lesson primarily covers some physics concepts, which we then apply to a mass-spring system to create a differential equation.
Nonlinear Differential Equations
มุมมอง 10611 หลายเดือนก่อน
The past several videos have been discussing linear differential equations, which have several nice properties. Here, we discuss some tricks and substitutions to attempt to analyze relatively simple second order nonlinear ODEs.
Differential Equations Cauchy-Euler Equations
มุมมอง 5011 หลายเดือนก่อน
Cochise College MAT 262 Lecture for 10/18/2023. In this video we look at our first higher order linear DEs without constant coefficients. In particular, the coefficient functions are all just a constant times a power of x, and the power of x must match the order of the derivative in that term.
Differential Equations Variation of Parameters
มุมมอง 3211 หลายเดือนก่อน
Cochise College MAT 262 lecture for 10/16/2023. In this lesson, we study how to split up a particular solution into two parts for easier solution, and how to use variation of parameters to find a particular solution without having to guess the form.
Differential Equations Superposition Principle and Undetermined Coefficients
มุมมอง 10911 หลายเดือนก่อน
Cochise College MAT 262 lecture for 10/11/2023. In this lesson we discuss how to combine solutions of a complementary homogeneous system with a particular solution to a nonhomogeneous DE. In order to do so, we need to be able to find such a particular solution, which we do by guessing the form of the solution and computing the details.
Homogeneous Differential Equations with Constant Coefficients
มุมมอง 67ปีที่แล้ว
Homogeneous Differential Equations with Constant Coefficients
Differential Equations Reduction of Order
มุมมอง 73ปีที่แล้ว
Differential Equations Reduction of Order
Differential Equations Higher Order Linear Initial Value Problems
มุมมอง 79ปีที่แล้ว
Differential Equations Higher Order Linear Initial Value Problems
Differential Equations Theory of Initial Value Problems
มุมมอง 64ปีที่แล้ว
Differential Equations Theory of Initial Value Problems
First Order Linear Differential Equations
มุมมอง 75ปีที่แล้ว
First Order Linear Differential Equations
Numerical Analysis 12.4.1 SVD and Compression
มุมมอง 3514 ปีที่แล้ว
Numerical Analysis 12.4.1 SVD and Compression
Numerical Analysis 12.3.3 More on the Singular Value Decomposition
มุมมอง 2554 ปีที่แล้ว
Numerical Analysis 12.3.3 More on the Singular Value Decomposition
Numerical Analysis 12.3.2 Performing the Singular Value Decomposition
มุมมอง 5494 ปีที่แล้ว
Numerical Analysis 12.3.2 Performing the Singular Value Decomposition
Numerical Analysis 12.3.1 Introduction to Singular Values
มุมมอง 3514 ปีที่แล้ว
Numerical Analysis 12.3.1 Introduction to Singular Values
Numerical Analysis 12.2.4 Upper Hessenberg Form
มุมมอง 9K4 ปีที่แล้ว
Numerical Analysis 12.2.4 Upper Hessenberg Form
Numerical Analysis 12.2.3 Review of Householder Reflectors
มุมมอง 6804 ปีที่แล้ว
Numerical Analysis 12.2.3 Review of Householder Reflectors
Thankyou so much!
I appreciate you putting these up, you are wonderful at explaining
I'm glad you're finding them useful. Not many people want to watch a full lecture on a topic, so I'm always glad to hear from someone that takes the time to do so.
w teacher, lowkey sounds like the Khan Academy guy
I've heard that from several people. I have no connection to Khan Academy, but I don't mind the comparison at all.
Now prove there’s an inverse 😢
Thank you great video explaining how quotients in polynomial rings actually works.
Just taken aback for a second here, because every time I've seen the unique identity proof before the "two" possible identity elements have been denoted as e and f.
Wow 👌 great explanation 😅
WHY DON'T WE DIRECTLY WRITE THAT WE TOOK DISJOINT COSETS...WHY WE INVOLVE DISTINCT.
distinct and disjoint are the same thing for cosets. (which is not true for sets in general - distinct sets can have some common elements so A = {1,2,3} and B = {2, 3, 4} are distinct sets ( A /= B) that are not disjoint)
thank you patrick
Excellent video! After so many videos on youtube that explained this concept in a really unclear way, I understood it immediately with this one. Thank you
gcd 2 and 12 is not 1?
How you find the factor in first step
After using 1 why didn't you use 2 instead of 3
you are trying to find the cycle, so once you find that 1 goes to 3, you then have to find what 3 goes to, and keep going till you get something that goes back to 1.
Thanks
Hello Professor, Thanks a lot for making this video. Watching this video from a very small town in 🇮🇳 and cannot be more grateful.
You are very welcome. I live in a small town myself, and I know how frustrating it can be to find resources. I wish you well with your education.
Thank you, these videos are extremely helpful.
You are welcome. I'm glad these videos are still helping people.
I understood how, but I don't understand why, whatever helps me raising my gpa i guess.
Why encrypt a message? That is mainly a history question rather than a math question, but any time you need to transmit information and make it difficult/impossible for anyone that intercepts the message to make use of that information. In modern times we think mainly of digital encryption of data such as credit card numbers, which often have to be transmitted through non-secure servers, but you absolutely don't want anyone other than a trusted recipient to have that number. This would be a poor way to encrypt such a thing, but this video is only the briefest glimpse into a huge field of mathematics.
Maybe there is a mistake with Z2 example , May you please check it again
Thankyou sir❤
🎉
Thank you for leaving these up over the years! They've been super helpful to me this semester while I'm taking an online Abstract Algebra course!
That was a really helpful demonstration thank you
Thank you sir❤
Great Lecture.
thank u a lot
Thank you soo much for cleaning my dought's 😊 I need this
Thank you sir... because of you only I learned this topic...but, I have one doubt...In last example (3,6 ) ... How order of 3 is 2…. 3² =9 .. then in Z₆ it will go to 2 only... Please explain... I am right or wrong...
The group operation is addition (mod 6), not multiplication. 3 + 3 = 6, which is equal to 0 when taken mod 6.
@@patrickjones1510 ok sir..thank you sir..
YOU MUST REDUCE ALL FRACTIONS!!! WARNING
How to determine the function to be used, 3x mod 8?
*promo sm* 😞
Great video! I'd like to add that in Zn, |x| = n / gcd(n, x). This makes it easier when dealing with large values of n.
Amazing!
Great vid!
thank you
Thank you for this video
damn bruh this ish confusing
good video on some tyshi
I love u
Amazing! Thank you
Thank you for simplifying
Bless your soul, this is incredible
Very good ‘intuition’ teaching
Isn’t the remainder on your long division just 1? Not x+1?
You're correct. In trying to go quickly, I didn't notice that I had already subtracted the x away. In the end, it doesn't change the conclusion, since any non-zero remainder shows it doesn't divide evenly.
are you following a particular text for these lectures?
In general, I was following "Contemporary Abstract Algebra," by Joseph A. Gallian. I was using the 9th edition, but as is often the case, there isn't much difference between editions. If I recall correctly, this first introductory video was not taken from the text, though.
@@patrickjones1510 Thanks! I really like your approach which seems to introduce each topic with an excellent concrete example.
،so fast how you made the multiply the matrix
This is certainly some cool stuff