Noah Graham

Electricity and Magnetism
The physical principles of electricity and magnetism are developed with calculus and applied to the electrical structure of matter and the electromagnetic nature of light. Practical topics from electricity and magnetism include voltage, current, resistance, capacitance, inductance, and AC and DC circuits. Laboratory work includes an introduction to electronics and to important instruments such as the oscilloscope. (PHYS 0109, MATH 0122) 3 hrs. lect./3 hrs. lab.

Electricity and Magnetism (formerly PHYS 0110)
The physical principles of electricity and magnetism are developed with calculus and applied to the electrical structure of matter and the electromagnetic nature of light. Practical topics from electricity and magnetism include voltage, current, resistance, capacitance, inductance, and AC and DC circuits. Laboratory work includes an introduction to electronics and to important instruments such as the oscilloscope. (PHYS 0108 or 0109, MATH 0122) (Students may not receive credit for both PHYS 0110 and PHYS 0114) 3 hrs. lect./3 hrs. lab.

Applied Mathematics for the Physical Sciences
This course concentrates on the methods of applied mathematics used for treating the partial differential equations that commonly arise in physics, chemistry, and engineering. Topics include differential vector calculus, Fourier series, and other orthogonal function sets. Emphasis will be given to physical applications of the mathematics. This course is a prerequisite for all 0300- and 0400-level physics courses. (MATH 0122; PHYS 0110 concurrent or prior) 4.5 hrs. lect.

Waves and Fourier Analysis
Wave mechanics provides our most fundamental description of all known forms of matter, radiation, and their interactions. In this course we will develop the physics of oscillations and waves and the associated mathematics of Fourier series and transforms, orthogonal functions, and solutions of ordinary and partial differential equations, focusing especially on solutions of initial and boundary value problems by separation of variables in Cartesian, cylindrical and spherical coordinates. (PHYS 0108 or PHYS 0109 or PHYS 0110 or PHYS 0111 or PHYS 0114 AND MATH 0122 or APBC 4 or M1DP 40) (students may not receive credit for both PHYS 0212 and PHYS 0216) 4.5 hrs. lect.

Intermediate Electromagnetism
The unified description of electricity and magnetism is one of the greatest triumphs of physics. This course provides a thorough grounding in the nature of electric and magnetic fields and their interaction with matter. Mathematical techniques appropriate to the solution of problems in electromagnetism are also introduced. The primary emphasis is on static fields, with the full time-dependent Maxwell equations and electromagnetic waves introduced in the final part of the course. (PHYS 0110; PHYS 0201 or by permission; PHYS 0212) 3 hrs. lect./1 hr. disc.

Statistical Mechanics
This course is a study of statistical mechanics and its applications to a variety of classical and quantum systems. It includes a discussion of microstates, macrostates, and entropy, and systematically introduces the microcanonical, canonical, grand canonical, and isobaric ensembles. This underlying theory is applied to topics including classical thermodynamics, the equipartition theorem, electromagnetic blackbody radiation, heat capacities of solids, and ideal classical and quantum gases, with a focus on Bose-Einstein condensation and degenerate Fermi systems. (PHYS 0202 and PHYS 0212) 3 hrs. lect.

General Relativity
Among the forces of nature, gravity is both the most familiar and the least well-understood. A hundred years after it was formulated by Einstein, General Relativity remains our best fundamental theory of gravity. In this course we will see how gravity emerges from the geometry of curved spacetime and how this picture leads to phenomena such as black holes, gravitational waves, and the expansion of the universe. (MATH 0200, PHYS 0201, and PHYS 0212) 3 hrs. lect.

Quantum Mechanics
A fundamental course in quantum mechanics aimed at understanding the mathematical structure of the theory and its application to physical phenomena at the atomic and nuclear levels. Topics include the basic postulates of quantum mechanics, operator formalism, Schrödinger equation, one-dimensional and central potentials, angular momentum and spin, perturbation theory, and systems of identical particles. (PHYS 0202 and PHYS 0212; MATH 0200 recommended) 3 hrs. lect.

Senior Project
Independent research project incorporating both written and oral presentations.

Quantum Mechanics from Linear Algebra
The mysterious and surprising predictions of quantum mechanics, such as uncertainty in measurement and the failure of determinism, can be best understood through the language of linear algebra. In this course we will use eigenvectors and eigenvalues, dot products, and the Cauchy-Schwarz inequality to develop the fundamental postulates of quantum mechanics and their predictions for the behavior of quantum systems. We will focus particularly on spin systems, which have applications to areas ranging from quantum computing to magnetic resonance imaging to quaternion methods for 3-D graphics and motion tracking. No prior physics experience is assumed apart from basic familiarity with concepts such as momentum, energy, and electric charge. (MATH 0122, MATH 0200, and introductory physics at the high school or college level.)