Mathematical Methods in Physics (PHYS 70003, CRN 11443)

• General Information (Syllabus)

• Lecture 1. Basic notions, proofs, elements of algebra.
• Lecture 2. Differentiation and integration.
• Lecture 3. Complex numbers, hyperbolic functions.
• Lecture 4. Series and limits.
• Lecture 5. Partial differentiation, exact differentials.
• Lecture 6. Multiple integrals.
• Lecture 7. Vector algebra.
• Lecture 8. Vector spaces, matrices.
• Lecture 9. Eigenvectors, eigenvalues
• Lecture 10. Systems of linear equations. Normal modes.
• Lecture 11. Vector calculus.
• Lecture 12. Integrals of fields.
• Lecture 13. Tensors.  (updated 10/19) Video lecture, Oct. 16  
• Lecture 14. Group theory.
• Lecture 15. Functions of complex variables.
• Lecture 16. Ordinary differential equations.

• Proof of the rank-nullity theorem.
• Simultaneous diagonalization.
• Expressing 3D rotations with Pauli matrices.

1. HW1  (due Mon 11:59pm, Aug 24)  
2. HW2  (due Wed 11:59pm, Sep 02)  
3. HW3  (due Fri 5:00pm, Sep 18)  
4. HW4  (due Wed 11:59pm, Sep 23)  
5. HW5  (due Mon 11:59pm, Oct 05)  
6. HW6  (due Mon 11:59pm, Oct 12)  
7. HW7  (due Wed 11:59pm, Oct 28)  
8. HW8  (due Fri 11:59pm, Nov 06)  
9. HW9  (due Sun 11:59pm, Nov 15)  

• Midterm solutions
• Final exam solutions  

1. Midterm exam. (due Fri. Oct 9, 11:59PM). 
2. Final exam. (due Thu. Nov 19, 5:00PM ). 

• A very interesting discussion with Cornelius Lanczos about math and its applications to physics, chemistry and engineering.
• The Dzhanibekov Effect or Tennis Racket Theorem
• Richard Feynman’s Integral Trick
• Notes on Differential Geometry and Lie Groups by Jean Gallier.

• Follow this link for uploading homework and exams.