Mathematical Methods in Physics (PHYS 70003-01, CRN 11256)

• General Information (Syllabus)

• Prerequisites 1. Basic notions, proofs, elements of algebra.
• Prerequisites 2. Differentiation and integration.
• Prerequisites 3. Complex numbers, hyperbolic functions.
• Prerequisites 4. Series and limits.
• Prerequisites 5. Partial differentiation, exact differentials.
• Prerequisites 6. Multiple integrals.

• Lecture 1. Vector algebra.
• Lecture 2. Vector spaces, matrices.
• Lecture 3. Eigenvectors, eigenvalues
• Lecture 4. Systems of linear equations. Normal modes.
• Lecture 5. Vector calculus.
• Lecture 6. Integrals of fields.
• Lecture 7. Tensors.
• Lecture 8. Functions of complex variables.
• Lecture 9. Group theory.
• Lecture 10. Ordinary differential equations.

• Proof of the rank-nullity theorem.
• Simultaneous diagonalization.
• Dirac-delta and its properties.
• Expressing 3D rotations with Pauli matrices.

1. HW1  (due Mon 11:59pm, Sep 5)  
2. HW2  (due Mon 11:59pm, Sep 12)  
3. HW3  (due Wed 11:59pm, Sep 21)  
4. HW4  (due Wed 11:59pm, Sep 28)  
5. HW5  (due Mon 11:59pm, Oct 10)  
6. HW6  (due Mon 11:59pm, Oct 31)  
7. HW7  (due Mon 11:59pm, Nov 21)  
8. HW8  (due Mon 11:59pm, Dec 5)  

• HW1_Pr9 
• SolvedProbs_1 
• Midterm solutions
• SolvedProbs_2
• Final exam solutions  

1. Midterm exam. (due Wed. Oct 26, 11:59PM). 
2. Final exam. (due Fri. Dec 09, 11:59PM). 

• 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

• Follow this link for uploading homework and exams.