Mathematical Methods in Physics (PHYS 70003, CRN 11329)

• 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.
• Lecture 14. Functions of complex variables.
• Lecture 15. Group theory.

• 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 6)  
2. HW2  (due Mon 11:59pm, Sep 13)  
3. HW3  (due Mon 11:59pm, Sep 20)  
4. HW4  (due Wed 11:59pm, Sep 29)  
5. HW5  (due Mon 11:59pm, Oct 11)  
6. HW6  (due Wed 11:59pm, Oct 27)  
7. HW7  (due Mon 11:59pm, Nov 8)  
8. HW8  (due Mon 11:59pm, Nov 15)  
9. HW9  (due Mon 11:59pm, Nov 22)  
10. HW10  (due Wed 11:59pm, Dec 8)  

• HW2_Pr4 
• Midterm solutions

1. Midterm exam. (due Wed. Oct 13, 8:00PM). 
2. Final exam. (due Sat. Dec 11, 5:00PM). 

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