Resources, Readings, and References#
Textbook#
The textbooks for this course are listed in the Syllabus: Physics 571.
Differential Equations#
ODEs are tricky, and it helps to be familiar some of the available tables of exact solutions like the following:
“Handbook of Exact Solutions for Ordinary Differential Equations”: [Polyanin and Zaitsev, 2018].
Linear Algebra#
Essence of linear algebra: A great set of highly visual videos by 3Blue1Brown getting you up to abstract vector spaces.
MIT 18.06 Linear Algebra: A set of video lectures and accompanying material for the MIT Linear Algebra course.
Qiskit Linear Algebra: A short introduction that is part of the Qiskit platform.
Appendix A of [Mermin, 2007] has a nice short review of Dirac notation.
Integration#
If you need some practice integrating, the following might be of use:
The past tests of the MIT Integration Bee.
If you want to watch someone solving integratls, see: 100 integrals.
References#
Milton Abramowitz and Irene A. Stegun. Handbook of mathematical functions: with formulas, graphs, and mathematical tables. Dover Publications, New York, 1965.
George B. Arfken, Hans J. Weber, and Frank E. Harris. Mathematical Methods for Physicists: A Comprehensive Guide. Academic Press, Waltham, MA, 2013. ISBN 9780123846549. doi:10.1016/C2009-0-30629-7.
Leslie E. Ballentine. Quantum Mechanics: A Modern Development. WORLD SCIENTIFIC, 2014. ISBN 9789814578585.
Carl M. Bender and Steven A. Orszag. Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory. Springer, 1999. ISBN 978-0-387-98931-0. doi:10.1007/978-1-4757-3069-2.
Mary L. Boas. Mathematical Methods in the Physical Sciences. John Wiley & Sons, Inc., 3 edition, 2006. ISBN 9781118048887.
Folkmar Bornemann, Dirk Laurie, Stan Wagon, and Jörg Waldvogel. The SIAM 100-Digit Challenge. SIAM, Philadelphia, 2004. doi:10.1137/1.9780898717969.
John P. Boyd. Chebyshev and Fourier Spectral Methods. Volume 49 of Lecture Notes in Engineering. Dover, Berlin Heidelberg, 2 edition, 1989. ISBN 978-0486411835. URL: http://www-personal.umich.edu/~jpboyd/BOOK_Spectral2000.html.
John P. Boyd. The Devil's invention: asymptotic, superasymptotic and hyperasymptotic series. Acata Appl. Math., 56(1):1–98, 1999. doi:10.1023/A:1006145903624.
Th. Clausen. Aufgaben un lerhsätze, erstere aufzulösen, letztere zu beweisen. J. Reine Angew. Math., 1827(2):286–292, 1827. URL: https://doi.org/10.1515/crll.1827.2.286, doi:doi:10.1515/crll.1827.2.286.
R. J. Creswick, H. A. Farach, and C. P. Poole, Jr. Introduction to Renormalization Group Methods in Physics. Wiley, 1 edition, 1992. ISBN 9780471600138.
C. Gordon, D. Webb, and S. Wolpert. Isospectral plane domains and surfaces via Riemannian orbifolds. Inventiones Mathematicae, 110(1):1–22, December 1992. URL: http://dx.doi.org/10.1007/BF01231320, doi:10.1007/bf01231320.
Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. Concrete Mathematics: A Foundation for Computer Science. Addison-Wesley, 2 edition, 1994. ISBN 978-0-201-55802-9.
Sadri Hassani. Mathematical Physics: A Modern Introduction to Its Foundations. Springer International Publishing, 2013. ISBN 9783319011950. URL: http://dx.doi.org/10.1007/978-3-319-01195-0, doi:10.1007/978-3-319-01195-0.
E. T. Jaynes and Oscar Kempthorne. Confidence Intervals vs Bayesian Intervals, pages 175–257. Springer Netherlands, 1976. URL: http://dx.doi.org/10.1007/978-94-010-1436-6_6, doi:10.1007/978-94-010-1436-6_6.
Mark Kac. Can one hear the shape of a drum? Am. Math. Monthly, 73(4):1–23, 1966. URL: http://www.jstor.org/stable/2313748.
Peter Lepage. How to Renormalize the Schrodinger Equation. 1997. URL: http://arxiv.org/abs/nucl-th/9706029, arXiv:nucl-th/9706029.
Fernando Llorente, Luca Martino, Ernesto Curbelo, Javier López‐Santiago, and David Delgado. On the safe use of prior densities for Bayesian model selection. WIREs Comput. Statistics, July 2022. URL: http://dx.doi.org/10.1002/wics.1595, arXiv:2206.05210, doi:10.1002/wics.1595.
Thomas J. Loredo. Promise of Bayesian Inference for Astrophysics, pages 275–297. Springer New York, 1992. URL: http://dx.doi.org/10.1007/978-1-4613-9290-3_31, doi:10.1007/978-1-4613-9290-3_31.
Rafael de la Madrid. The role of the rigged hilbert space in quantum mechanics. Eur. J. Phys., 26(2):287–312, February 2005. arXiv:quant-ph/0502053, doi:10.1088/0143-0807/26/2/008.
Jon Mathews and R. L. Walker. Mathematical Methods of Physics. Addison-Wesley, Advanced Book Program, 1970. ISBN 0805370021.
John McGreevy. Physics 217: The renormalization group, Fall 2018. 2018. URL: http://physics.ucsd.edu/~mcgreevy/f18/.
N. D. Mermin. Quantum Computer Science: An Introduction. Cambridge University Press, 2007. ISBN 978-0-511-33982-0. URL: https://www.cambridge.org/core/books/quantum-computer-science/66462590D10C8010017CF1D7C45708D7, doi:10.1017/CBO9780511813870.
Cleve Moler and Charles Van Loan. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review, 45(1):3–49, 2003. URL: http://dx.doi.org/10.1137/S00361445024180, doi:10.1137/S00361445024180.
Tristan Needham. Visual Complex Analysis: 25th Anniversary Edition. Oxford University Press, February 2023. ISBN 9780191964947. URL: http://dx.doi.org/10.1093/oso/9780192868916.001.0001, doi:10.1093/oso/9780192868916.001.0001.
Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2010. URL: https://doi.org/10.1017%2Fcbo9780511976667, doi:10.1017/cbo9780511976667.
Frank W. J. Olver, Daniel W. Lozier, Ronald F. Boisvert, and Charles W. Clark. NIST Handbook of Mathematical Functions. Cambridge University Press, New York, NY, 2010. ISBN 978-0-521-19225-5.
Andrei D. Polyanin and Valentin F. Zaitsev. Handbook of Exact Solutions for Ordinary Differential Equations. Chapman and Hall/CRC, 3 edition, November 2018. ISBN 9781315117638. doi:10.1201/9781315117638.
William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, third edition, 2007.
Radoslaw Szmytkowski. On the derivative of the legendre function of the first kind with respect to its degree. J. Phys. A, 40(27):7819–7820, June 2007. URL: http://dx.doi.org/10.1088/1751-8121/40/27/C01, doi:10.1088/1751-8121/40/27/c01.
Radosław Szmytkowski. On the derivative of the legendre function of the first kind with respect to its degree. J. Phys. A, 39(49):15147–15172, November 2006. URL: http://dx.doi.org/10.1088/0305-4470/39/49/006, doi:10.1088/0305-4470/39/49/006.
Shina Tan. S-wave contact interaction problem: a simple description. 2005. arXiv:cond-mat/0505615, doi:10.48550/arXiv.cond-mat/0505615.
Maria Antónia Amaral Turkman, Carlos Daniel Paulino, and Peter Müller. Computational Bayesian Statistics: An Introduction. Volume 11 of Institute of Mathematical Statistics Textbooks. Cambridge University Press, Cambridge, UK, 2019. ISBN 978-1-108-48103-8. doi:10.1017/9781108646185.
Olivier Vallée and Manuel Soares. Airy Functions and Applications to Physics. Imperial College Press, 2 edition, June 2010. ISBN 9781848165489. doi:10.1142/p709.
Udo von Toussaint. Bayesian inference in physics. Rev. Mod. Phys., 83:943–999, September 2011. URL: https://link.aps.org/doi/10.1103/RevModPhys.83.943, doi:10.1103/RevModPhys.83.943.
E. T. Whittaker and G. N. Watson. A Course of Modern Analysis. Cambridge University Press, 5 edition, August 2021. ISBN 9781316518939. URL: http://dx.doi.org/10.1017/9781009004091, doi:10.1017/9781009004091.
Anthony Zee. Quantum Field Theory in a Nutshell. In a Nutshell. Princeton University Press, 2 edition, 2010. ISBN 9780691140346.