Complex Analysis with Physical Applications

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9/10 stars
based on  6 reviews
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Course Details

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FREE

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  • On demand

Course Provider

edX online courses
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22641 reviews

Course Description

In this advanced math course, you will learn how to build solutions to important differential equations in physics and their asymptotic expansions. Armed with the tools mastered in this course, you will have a solid command of the methods of tackling differential equations and integrals encountered in theoretical and applied physics and material science.

The course is for engineering and physics majors. The course instructors are active researchers in theoretical solid-state physics.

Reviews 9/10 stars
6 Reviews for Complex Analysis with Physical Applications

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Jim Freericks profile image
Jim Freericks profile image

Jim Freericks

10/10 starsCompleted
2 months, 3 weeks ago
This course is a unique an extremely interesting course. I have used complex analysis professionally, but I found myself constantly learning new things in this class. Things I never even knew existed. It has opened up my eyes to many more of the potential applications of complex analysis to different problems. As such it is an extraordinarily valuable course. Of course, the problems were quite challenging, and the structure of answer entry could be improved. The instructors worked hard to make the course as good an experience as possible. Overall, a great experience. Be forewarned though, this course is for someone who has fully completed a conventional complex analysis course and properly understands a bit about how Riemann surfaces work (primarily in how one determines phase when you have branch cuts and how one traverses from one sheet to another when needed. These issues can easily become confusing. So for the adventurou... This course is a unique an extremely interesting course. I have used complex analysis professionally, but I found myself constantly learning new things in this class. Things I never even knew existed. It has opened up my eyes to many more of the potential applications of complex analysis to different problems. As such it is an extraordinarily valuable course. Of course, the problems were quite challenging, and the structure of answer entry could be improved. The instructors worked hard to make the course as good an experience as possible. Overall, a great experience. Be forewarned though, this course is for someone who has fully completed a conventional complex analysis course and properly understands a bit about how Riemann surfaces work (primarily in how one determines phase when you have branch cuts and how one traverses from one sheet to another when needed. These issues can easily become confusing. So for the adventurous, curious, and well prepared student, be prepared for a tough and exhilarating experience. You will be paid off well for all of the time you devote to the class.
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P L

7/10 starsTaking Now
2 years, 1 month ago
This was a difficult course. It is done with much effort, and one can learn something from it. I am not able to comprehensively compare the approach of this course with another, as I do not have expertise in the subject; there is some content here that does provide a more interesting introduction.
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student

10/10 starsCompleted
2 years, 2 months ago
This is a third course in real and complex analysis. Call any topic from advanced analysis: it is used in the discussion and the problemsets of the main topics,see syllabus. The rewards are numerous: tons of cool methods and results in applied mathematics and QM (also in the fantastic problemsets, but be prepared for substantial calculations!), results that I often at best saw as tantalizing appetizers for further study. Very helpful for learning was the instructors complete absence of mathematical pedantry, while succeeding in never relying on handwaving. In substance,learning experience and in enjoyment this MOOC ranks among the top 3 of the many MOOCs I have taken, even though I had to give up on the problemsets at 2/3 of the course. I am looking forward to the next run to fully digest everything.
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student

10/10 starsCompleted
2 years, 2 months ago
The course is an advanced course in the application of Complex Analysis to Physics Problems. Mainly using Asymptotic Analysis. It includes asymptotic series, asymptotic approximation of integrals and the asymptotic resolution of differential equations. These are hard, challenging topics that require a good background and time for the concepts to sink in after the lectures, doing the homework etc. This is also the first run of the course so some bugs were inevitably there which were corrected expeditiously and I am sure that will vastly improve in future renditions. The instructors are clearly experts and practitioners in the field so we were assisting master lectures in each subject likely nowhere else available as a full course, much less as a MOOC. The problem sets were top notch quality. Both in their instructive content as well as in the way they lead the student. They were mostly hard and required a lot of work. I would recomme... The course is an advanced course in the application of Complex Analysis to Physics Problems. Mainly using Asymptotic Analysis. It includes asymptotic series, asymptotic approximation of integrals and the asymptotic resolution of differential equations. These are hard, challenging topics that require a good background and time for the concepts to sink in after the lectures, doing the homework etc. This is also the first run of the course so some bugs were inevitably there which were corrected expeditiously and I am sure that will vastly improve in future renditions. The instructors are clearly experts and practitioners in the field so we were assisting master lectures in each subject likely nowhere else available as a full course, much less as a MOOC. The problem sets were top notch quality. Both in their instructive content as well as in the way they lead the student. They were mostly hard and required a lot of work. I would recommend this course to people with a very good prior exposure to Complex Analysis (Analytic Continuation, Contour integration and applications, etc) It probably also requires some exposure to Non-Relativistic Quantum Mechanics (Schroedinger equation). If you have the background mentioned, you will thoroughly enjoy this course.
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n/a b

10/10 starsTaking Now
2 years, 2 months ago
There is material in this analysis class, collected all in one place, that I have not found cohesively presented elsewhere. For example, there are math methods here that until now I only knew from the appendix of landau/lifshitz v3. This was a great find in that sense. Some weeks, the material was not clearly presented in my opinion. I found the week w/ shallow 1d QM problems particularly problematic and used landau to fill in the gaps, for example. I think the title is misleading to English speakers: this is a course in asymptotic analysis or applied mathematics, not complex analysis which would normally refer to Cauchy-Riemann Eqs, Contour integration, Riemann surfaces, etc. Complex analysis is a prerequisite for this material. There was the occasional typo also, nothing too grave. Still, I found the majority of the class very valuable, and I appreciated the instructors efforts to show their work.
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Mark Weitzman profile image
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Mark Weitzman

10/10 starsCompleted
2 years, 2 months ago
I was a CTA for the course, and this was one of the most difficult and fulfilling MOOC's that I have ever taken. The material was advanced and graduate level, and rarely available elsewhere. The problem sets were extremely challenging. My main recommendation for improvment would be to change the title of the course, as the course assumes facility with complex analysis. The professors were extremely considerate in this first run of the course. They freely gave extensions to problem sets, were available on the discussion forums for consultation, and freely admitted and corrected errors when necessary.
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