Newton

  

  Mathematical Physics I  PHY5115

Misak Sargsian

M,W 6:25-7:40pm, CP101

Office Hours M,W - 3:30-4:30pm, CP224, sargsian@fiu.edu, 305-348-3954


Lectures 1-4:Series
(1)  Infinite Series
(2) Series of Functions
(3) Taylor Expansion
(4) Power Series
(5) Uniqueness Theorem
(6) Some Important Series


Lectures 8-16: Vectors & Vector Analysis
(1) Vectors
(2) Scalar and Vector products, Levi Civita symbols
(3) Scalar and Vector triple products
(4) Orthogonal Transformations and Rotations
(5) Differential Vector Operations, Gradient, Divergence and Curl
(6) Laplacian
(7) Vector Integrations
(8) Gauss' and Stoke's Theorems
(9) Scalar and Vector Potentials, Gauge fixing
(10)Maxwell Equations through scalar and vector potentials
(11)Gauss Law
(12)Poisson's Equation
(13)Helmholtz's Theorem


Lectures 17: Curvilinear Coordinates

  (1) Orthogonal Coordinates in R3
  (2) Integrals in Curvilinear Coordinates
  (3) Differential Operators in Curvilinear Coordinates
  (4) Circular Cylindrical Coordinates
  (5) Spherical Polar Coordinates 


 
Lectures 18-19 Matrices

 (1) 
  (2) 
  (3) 
  (4) 
  (5)   
 

Lectures 20-21 Line, Surface and Volume Integrals

 (1) 
  (2) 
  (3) 
  (4)
  (5) 
 



Lectures 20-21: Complex Numbers and Function

(1) Basic Properties
(2) Functions in Complex Domain
(3) Polar Representation
(4) Complex Numbers of Unit Magnitude
(5) Circular and Hyperbolic Functions
(6) Powers and Roots
(7) Logarithms


Lectures 21-24: Complex Variable Theory

(1) Cauchy-Riemann Conditions
(2) Analytic Functions
(3) Derivatives of Analytic Functions
(4) Point at Infinity
(5) Cauchy's Integral Theorem
(6) Contour Integrals
(7) Statement of Theorem
(8) Cauchy's Theorem: Proof
(9) Multiply Connected Regions
(10) Cauchy's Integral Formula
(11)Derivatives
(12)Morera's Theorem
(13)Further Applications


 Lectures 25-: Complex Variable Theory (continuation)
(1) Laurent Expansion
(2) Taylor Expansion
(3) Laurent Series
(4) Singularities
(5)Poles
(6)Branch Points
(7)Analytic Continuation
(8)Calculus of Residues
(9) Residue Theorem
(10)Computing Residues
(11)Cauchy Principal Value
(12)Pole Expansion of Meromorphic Functions
(13) Counting Poles and Zeroes
(14)Product Expansion of Entire Functions
(15)Evolution of Definite Integrals




 Lectures 25-: Mathematics of Artificial Intelligence

 Lectures 26-: Mathematics of Quantum Computing
 ?   Information.

 

Mathematica Methods for Physicists

Suggested Textbook

1."Mathematical Methods for Physicists"
  Seventh Edition
By George B Arfken, Hans J Weber,
      Frank E Harris
2. "Mathematical Methods for Physics and
   Engineers",
By. K.F.Riley, M.P. Robertson, S.J. Bence

 

The  pieces of the Final Grade:

Homeworks with deadlines (not graded)
(evaluated by the fraction of problems solved) 20%
Take Home Midterm Exam  (25%) (Oct 20th)
Project (25%) Due Nov 30
Final Cumulative In Class Exam (30%) 

Homework Assignments:
(10% less for each day of the late homework)

HW1  Due  Sep 4

HW2   Due Sep 11

HW3   Due  Sep 27

HW4   Due  Oct  4
 
HW5    Due  Oct 11

HW6    Due  Oct 18

HW7   Due  Oct 25

Exam1 Due  Oct 20

HW8   Due   Nov 1

HW9    Due  Nov 8

HW10  Due  Nov 15

HW11  Due  Nov 22

HW12  Due  Nov 29

HW13  Due  Dec 4

Final Exam  December 9, 5-7pm, CP101 

PossibleExamQuestions
 
CurrentGrades


1. Euclid, Riemann, Lobachevsky and understanding the shape of the universe - 
2. Pythagoras and Harmonies in the Physics -                                 
3. Lagrange and Euler and rise of Theoretical Physics -                 
4. Henri Poincare - from Three-body problem to Gravitational Waves -
5. Cantor and the Infinities -   
6. Ramanujan - from Numbers to Black Hole  -  Anthony Gonzalez
7. Emmy Noether and Symmetries of the Nature -   Anna Avetisyan                       
8. Hilbert's program and Physics -  
9. Goedel's Theorem of Incompleteness - 
10. Descartes, Newton, Leibniz and the Rise of Modern Physics -  
 11. Mathematics of Chaos and Nonlinear Phenomena in Physics -  Gage Wettlaufer
12. Hermann Minkowski and Theory of Relativity as a Rotation -    Felipe Gomez
13. John van Neumann and Cellular Automata in Physics and -      
Some Rules:

 

Class Policies:
No Unjustified absences, more than 50%
attendance is required to get a final grade in the class, no carbon copied homeworks please

And finally some Nos:
No cheating, no chatting and no napping, and no saying "I hate math" at least publicly:-)







©2021 Mathematical Physics; • Misak Sargsian A• B • C • D • E