Advanced Mathematical Methods in Physics
This course is part of Foundations of Quantum Sensing.
This comprehensive course transforms students from mathematical technicians into practitioners, focusing on advanced mathematical methods crucial for physics. The course provides deep insights into the interconnections between various mathematical topics, enabling students to apply these concepts effectively in physics problems. From advanced calculus techniques to complex analysis, differential equations, and vector spaces, students learn to derive important formulas from basic principles and understand their practical applications. The emphasis is on developing both technical proficiency and intuitive understanding of mathematical concepts.
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What you'll learn
Apply advanced calculus techniques to solve physics problems
Manipulate power series and use them in physics contexts
Master multidimensional integration for physical applications
Solve complex differential equations and understand their physics applications
Construct abstract vector spaces using generalized inner products
Develop proficiency in Fourier series analysis
Skills you'll gain
This course includes:
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Graded assignments, exams
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Limited Access access
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Module Description
This advanced mathematics course bridges the gap between technical proficiency and deep understanding in mathematical physics. Students learn to apply advanced calculus techniques, manipulate power series, solve complex integrals, and master differential equations. The curriculum covers multidimensional integration, vector fields, complex analysis, linear algebra, and Fourier series. Special emphasis is placed on understanding the interconnections between different mathematical topics and their applications in physics.
Fee Structure
Individual course purchase is not available - to enroll in this course with a certificate, you need to purchase the complete Professional Certificate Course. For enrollment and detailed fee structure, visit the following: Foundations of Quantum Sensing
Instructor
2 Courses
Theoretical Physics Pioneer and Quantum Computing
James Freericks has established himself as a leading figure in theoretical and computational physics at Georgetown University, where he has served since 1994 as Professor and McDevitt Chair of Physics. After earning his A.B. from Princeton University in 1985 (summa cum laude) and Ph.D. from UC Berkeley in 1991 under Leo Falicov, he completed postdoctoral work at UC Santa Barbara with Doug Scalapino and UC Davis with Richard Scalettar. His research spans multiple areas including mathematical physics, many-body computational methods, and quantum simulation, with recent focus on transport in multilayers and nonequilibrium physics. His computational work has pioneered dynamical mean-field theory applications, particularly in solving various models like the Falicov-Kimball, Hubbard, and Holstein models. His achievements have earned numerous accolades, including the Georgetown Presidential Teacher-Scholar Award (2017), Outstanding Referee prize (2012), and Alpha Sigma Nu Book Award (2009). Currently funded by NSF, DARPA, Army Research Office, and the Department of Energy, his group works on quantum chemistry calculations for emerging quantum computers while also developing innovative approaches to teaching quantum mechanics to non-scientists.
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