computational

Mathematical Physics I PHY5115

Misak Sargsian

M,W 6:25-7:40pm, CASE 138

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

Lectures 1-7:Series
(1) Infinite Series
(2) Series of Functions
(3) Binomial Theorem
(4) Mathematical Induction
(5) Operation on Series
(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 17-19: 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 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

?	Information.

Suggested Textbook

1."Mathematical Methods for Physicists"
Seventh Edition
By George B Arfken, Hans J Weber,
Frank E Harris

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 7th)
Project (25%) Due Dec. 2
Final Cumulative In Class Exam (30%) 12/6/2023
5-7pm CASE 138

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

HW1 Due Sep 1

HW2 Due Sep 11

HW3 Due Sep 15

HW4 Due Sep 22

HW5    Due Sep 29

HW6    Due Oct 6

Exam1 Due Nov 6

HW7   Due OCT 13

HW8   Due   OCT 22

HW9 Due Nov 6

HW10  Due Nov 13

HW11  Due Nov 20

HW12  Due Nov 27

HW13  Due Dec 4

Final Exam Dec 6, 5-7pm CASE138

PossibleExamQuestions

CurrentGrades

1. Euclid, Riemann, Lobachevsky and understanding the shape of the universe -
2. Pythagoras and Harmonies in the Physics - Leonel Martinez
3. Lagrange and Euler and rise of Theoretical Physics -
4. Henri Poincare - from Three-body problem to Gravitational Waves -
5. Cantor and the Infinities -   Suvash Bhattarai
6. Ramanujan - from Numbers to Black Hole - Ray Romero
7. Emmy Noether and Symmetries of the Nature -   Alan Sosa, Chhatra Bastola
8. Hilbert's program and Physics -
9. Goedel's Theorem of Incompleteness -
10. Decartes, Newton, Leibniz and the Riese of Modern Physics -
11. Mathematics of Chaos and Nonlinear Phenomena in Physics - Bipin Paudel
12. Hermann Minkowski and Theory of Relativity as a Rotation - Thomas Pinto Franco
13. John van Neumann and Cellular Automata in Physics and -

Some Rules:

COVID Guidlines:

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:-)

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