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PHYSICS 301
Theoretical Methods in Physics
Location / Time:
Instructor:
Office:
Tel:
E-mail:
Office Hours:
Necker 410/ MWF 9:00 – 9:50 am
Dipanjan Mazumdar
Neckers 478
(618)-453-3659
[email protected]
MWF 11:00 am – 1:00 pm or by appointment
Text: Mathematical Methods for Scientists and Engineers by Donald A. McQuarrie, University Science
Books, 2003.
Objectives: This course shall introduce some of the mathematical techniques used in the physical sciences
and engineering at an intermediate undergraduate level. Students interested in taking advanced
Physics courses like Mechanics, Electrodynamics and Quantum mechanics are especially encouraged.
Prerequisite: PHYS 205A, Mathematics 250 with a grade of C or better.
Grading Policy:
Homework
Exam I
Exam II
Exam III
Final Exam
50%
10%
10%
10%
20%
A
B
C
D
F
90 % - 100 %
75 % - 89.9 %
65 % - 74.9 %
50 % - 64.9 %
Less than 50 %
Tentative Content: Select sections from chapters 1-15 (excluding 13) of the text book covering Functions,
Series and integrals, Complex numbers, Vector algebra and calculus, Linear algebra and Matrices,
Ordinary differential equations, Special functions/Orthogonal polynomials, and Fourier Series. If
time permits we shall discuss Fourier Transforms. Tentatively the pace will be as follows:
Mon Jan 19
Wed Jan 21
Fri Jan 23
Mon Jan 26
Wed Jan 28
Fri Jan 30
Mon Feb 2
Wed Feb 4
Fri Feb 6
Mon Feb 9
Wed Feb 11
Fri Feb 13
Holiday
1.1 - 1.2 (Even/odd functions, hyperbolic functions)
1.3-1.4 (Step function, Potential barrier, Dirac delta function(section3.6))
1.5,1.7 (Differentials, Integration by parts, Mathematica)
1.8 - 1.9 (Improper integrals, Ratio test)
2.1-2.3 (Infinite sequence, convergence, Tests)
2.6 (Power series, Radius of convergence)
2.7-2.8 (Taylor/McLaurin series, Applications)
3.1-3.2 (Gamma & Beta Function)
3.3 , 3.6 (Error and Dirac Delta function)
4.1 (Complex numbers, Argand diagram, Polar form, complex conjugate)
4.3 (Euler’s formula, DeMoivre’s Theorem, Roots and powers)
Mon Feb 16
Wed Feb 18
Fri Feb 20
Mon Feb 23
Wed Feb 25
Fri Feb 27
Mon Mar 2
Wed Mar 4
Fri Mar 6
Mon Mar 9
Wed Mar 11
Fri Mar 13
Mon Mar 16
Wed Mar 18
Fri Mar 20
Mon Mar 23
Wed Mar 25
Fri Mar 27
Mon Mar 30
Wed Apr 1
Fri Apr 3
Mon Apr 6
Wed Apr 8
Fri Apr 10
Mon Apr 13
Wed Apr 15
Fri Apr 17
Mon Apr 20
Wed Apr 22
Fri Apr 24
Mon Apr 27
Wed Apr 29
Fri May 1
Mon May 4
Wed May 6
Fri May 8
4.4-4.5 (Complex Trig, Hyperbolic and Log Functions)
5.1-5.2 (2D Vectors, unit vectors, vector algebra, Dot product)
5.2-5.3 (Cross product, Vector Differentiation)
5.4 (Physical examples, Torque, angular momentum)
6.3-6.5 (Partial derivatives, Chain rule, Differentials)
6.6 (Directional derivative, Gradient)
Exam 1
7.1 (Vector Fields, Divergence)
7.1 (Divergence, Curl)
Spring break
Spring Break
Spring Break
7.2 (Line Integral, Conservative Fields)
7.3-7.4 (Surface Integrals, Divergence Theorem)
7.5 (Stokes Theorem)
8.1-8.3 (Polar coordinates, Cylindrical coordinates)
8.4-8.5 (Spherical coordinates, Curvilinear coordinates)
9.5-9.7 (Vector space, Complex Inner product space)
Exam 2
10.1-10.2 (Orthogonal, Unitary, Hermitian Matrices, Transpose, complex)
10.3 (Matrix transformation, Eigenvalue Problem, Eigenvectors)
10.5 (Real Eigenvalues, Orthogonal eigenvectors, Diagonalization)
11.1-11.3 (Linear Diff Eqn, First order, Integrating factor)
11.3-11.4 (Homogeneous and non-homogeneous Diff Eqn)
12.1-12.2 (Power series solution, Ordinary/Singular points)
12.3- 14.1(Legendre’s equation, solution, Legendre’s polynomials)
14.1 (Generating function, Rodrigues’ Formula)
14.2 (Orthogonal polynomials, Eigenfunction expansion)
14.3-14.4 (Differential operators, Eigenvalue equation, Hermitian operator )
Exam 3
15.1 (Fourier Series, complex Fourier series)
15.2 (Waveforms (triangular, square, rectifiers), convergence)
17.5 (Fourier Transforms)
15.6 (Convolution Theorem)
15.3 (Recap)
15.4 (Recap)