In the last article I mentioned about some of the essential mathematics required for a clean understanding of theoretical physics. Now we can go to the second level, that is to say the topics which are very much essential if you are going to be a serious student of theoretical physics.
Complex Analysis and Special Functions
As you may be knowing this complex analysis is one of the corner stones of quantum mechanics along with linear algebra. So learn it well and do try to solve as much problems as possible.
Topics : Contour Integration, Cauchy's Formula, Residue Theorem, Geometry with complex algebra, Laurent series, Conformal mapping, Branch Cuts, Multi-valued Functions, Analytic continuation, Zeta function, Gamma Function, Euler's integrals, Spherical Harmonics, Bessel Functions, Hypergeometric Polynomials.
1. George Polya; Complex Variables
Nice Presentation with full of insights.
2. V.I. Smirnov; A Course in Higher Mathematics (Vol. 3 part 2)
The best one I have seen.
3. Complex Variables; Mark J. Ablowitz
Mathematical Methods
Some books which will help you solve mathematics problem.
1. Riley & Hobson; Mathematical methods for Physics and Engineering
2. R. Shankar; Basic training in mathematics
Advanced Mathematics
This will become your toolkit when you attack real physical problems. Try to make the concepts in your mind as concrete as possible ( That will help!).
Topics : Topology, Differential Geometry, Integral Equations, Green Functions, Algebraic Topology, Fucntional Integrals.
1. Nakahara; Geometry, Topology and Physics
2. C. Nash & S. Sen; Topology and Geometry for Physicists
3. R. Courant & D. Hilbert; Methods of mathematical physics (Vol. 1 & 2)
Good treatment of variational calculus and integral equations.
Now to the Physics Part ...
Classical Mechanics
1. Landau & Lifshitz; Mechanics
2. V.I. Arnold; Mathematical Methods of Classical Mechanics
Electrodynamics
1. Jackson; Electrodynamics
2. Greiner, Classical Electrodynamics
Quantum Mechanics
1. Dirac; Principles of QM
2. Sakurai; Modern QM
3. Weinberg; Lectures on QM
Statistical Mechanics
1. Reif; Statistical Physics, Berkeley Series
Good intro. for Classical Statistical Mechanics
2. Greiner; Thermodynamics & Statistical Mechanics
3. Landau & Lifshitz; Statistical Physics
4. D. Tong; Statistical physics (Lecture notes)
Relativity
1. Landau; Classical Theory of Fields (Must Read)
2. J. Schwarz & P. Schwarz; Special Relativity: From Einstein to Strings
Gives a comprehensible introduction to formal mathematics along with many wonder insights into the subject.
3. Weinberg; Gravitation & Cosmology
Online Resources
1. Dr. Tong's website contains many lecture notes presented in a pedagogical manner.
2. Walter Lewin Channel
3. Lecture Video Courses of Perimeter Institute (Note: One may access previous year's videos from the same site.)
4. Video courses of ICTP
Next time I will write about learning QFT .
Good luck.
Complex Analysis and Special Functions
As you may be knowing this complex analysis is one of the corner stones of quantum mechanics along with linear algebra. So learn it well and do try to solve as much problems as possible.
Topics : Contour Integration, Cauchy's Formula, Residue Theorem, Geometry with complex algebra, Laurent series, Conformal mapping, Branch Cuts, Multi-valued Functions, Analytic continuation, Zeta function, Gamma Function, Euler's integrals, Spherical Harmonics, Bessel Functions, Hypergeometric Polynomials.
1. George Polya; Complex Variables
Nice Presentation with full of insights.
2. V.I. Smirnov; A Course in Higher Mathematics (Vol. 3 part 2)
The best one I have seen.
3. Complex Variables; Mark J. Ablowitz
Mathematical Methods
Some books which will help you solve mathematics problem.
1. Riley & Hobson; Mathematical methods for Physics and Engineering
2. R. Shankar; Basic training in mathematics
Advanced Mathematics
This will become your toolkit when you attack real physical problems. Try to make the concepts in your mind as concrete as possible ( That will help!).
Topics : Topology, Differential Geometry, Integral Equations, Green Functions, Algebraic Topology, Fucntional Integrals.
1. Nakahara; Geometry, Topology and Physics
2. C. Nash & S. Sen; Topology and Geometry for Physicists
3. R. Courant & D. Hilbert; Methods of mathematical physics (Vol. 1 & 2)
Good treatment of variational calculus and integral equations.
Now to the Physics Part ...
Classical Mechanics
1. Landau & Lifshitz; Mechanics
2. V.I. Arnold; Mathematical Methods of Classical Mechanics
Electrodynamics
1. Jackson; Electrodynamics
2. Greiner, Classical Electrodynamics
Quantum Mechanics
1. Dirac; Principles of QM
2. Sakurai; Modern QM
3. Weinberg; Lectures on QM
Statistical Mechanics
1. Reif; Statistical Physics, Berkeley Series
Good intro. for Classical Statistical Mechanics
2. Greiner; Thermodynamics & Statistical Mechanics
3. Landau & Lifshitz; Statistical Physics
4. D. Tong; Statistical physics (Lecture notes)
Relativity
1. Landau; Classical Theory of Fields (Must Read)
2. J. Schwarz & P. Schwarz; Special Relativity: From Einstein to Strings
Gives a comprehensible introduction to formal mathematics along with many wonder insights into the subject.
3. Weinberg; Gravitation & Cosmology
Online Resources
1. Dr. Tong's website contains many lecture notes presented in a pedagogical manner.
2. Walter Lewin Channel
3. Lecture Video Courses of Perimeter Institute (Note: One may access previous year's videos from the same site.)
4. Video courses of ICTP
Next time I will write about learning QFT .
Good luck.
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