computational

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 Quantum Computing

Lectures 26-: Mathematics of Artificial Inteligence

?	Information.

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 7th)
Project (25%) Due
Final Cumulative In Class Exam (30%) 1

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

HW1 Due Sep 10

HW2 Due Sep 22

HW3 Due Oct 4

HW4 Due Oct 12

HW5    Due Oct 20

HW6    Due Oct

Exam1 Due Nov

HW7   Due OCT

HW8   Due   OCT

HW9 Due Nov

HW10  Due Nov

HW11  Due Nov

HW12  Due Nov

HW13  Due Dec

Final Exam 5-7pm

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 -
7. Emmy Noether and Symmetries of the Nature -
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 -
12. Hermann Minkowski and Theory of Relativity as a Rotation - T
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:-)

A• B • C • D • E