Calculus and Applied Physics Course Descriptions

An introduction to differential and integral calculus. Topics include limits, continuity, derivatives, applications of derivatives (including optimization and related rates), definite integrals, the Fundamental Theorem of Calculus, and basic integration techniques. Emphasis on understanding concepts through graphical, numerical, and analytical approaches.

Prerequisites: MATH 030 or equivalent, or placement.

Continuation of Calculus I. Topics include techniques of integration, applications of integration (including volume, arc length, and surface area), sequences and series, parametric equations, polar coordinates, and an introduction to differential equations. Practical applications in physics, engineering, and economics.

Prerequisites: MATH 101 with a grade of C- or better.

Extension of calculus to functions of several variables. Topics include vectors in three-dimensional space, vector functions, partial derivatives, multiple integrals, line integrals, surface integrals, Green's Theorem, Stokes' Theorem, and the Divergence Theorem. Applications to physics and engineering.

Prerequisites: MATH 102 with a grade of C- or better.

Introduction to the theory and application of differential equations. Topics include first-order differential equations, linear differential equations of higher order, systems of linear differential equations, Laplace transforms, series solutions, and applications to physical, biological, and economic systems.

Prerequisites: MATH 102 with a grade of C- or better.

Rigorous treatment of calculus concepts. Topics include real numbers, sequences, continuity, differentiation, Riemann integration, and series of functions. Emphasis on mathematical proofs and formal reasoning.

Prerequisites: MATH 201 and MATH 203 (Introduction to Mathematical Proof) with grades of C- or better.

Algebra- and trigonometry-based introduction to mechanics. Topics include kinematics, Newton's laws, work and energy, momentum, rotational motion, oscillatory motion, and fluid mechanics. Laboratory work integrates theory with experimental methods and data analysis.

Prerequisites: high school algebra, geometry, and trigonometry.

Algebra- and trigonometry-based introduction to electricity and magnetism, light, and modern physics. Topics include electric fields, electric potential, circuits, magnetic fields, electromagnetic waves, optics, and an introduction to quantum theory and special relativity. Laboratory work included.

Prerequisites: PHYS 101 with a grade of C- or better.

Calculus-based introduction to mechanics. Topics include kinematics, Newton's laws, work and energy, momentum, rotational motion, oscillations, and gravitation. Emphasis on mathematical formulation of physical principles. Laboratory work emphasizes experimental techniques and error analysis.

Prerequisites or corequisites: MATH 101.

Calculus-based introduction to electricity and magnetism. Topics include electric fields, Gauss's law, electric potential, capacitance, circuits, magnetic fields, electromagnetic induction, Maxwell's equations, and electromagnetic waves. Laboratory work included.

Prerequisites: PHYS 201 and MATH 102 (can be taken concurrently).

Calculus-based introduction to waves, optics, and modern physics. Topics include wave phenomena, geometric optics, physical optics, thermodynamics, special relativity, quantum mechanics, atomic physics, nuclear physics, and elementary particles. Laboratory work included.

Prerequisites: PHYS 202 and MATH 201 (can be taken concurrently).

Advanced treatment of Newtonian mechanics using calculus. Topics include motion in one, two, and three dimensions, work and energy, conservation laws, dynamics of systems of particles, rigid body motion, gravitational forces, oscillatory systems, and Lagrangian and Hamiltonian mechanics.

Prerequisites: PHYS 202 and MATH 201, 202.

Advanced study of electricity and magnetism using vector calculus. Topics include electrostatics, magnetostatics, electric and magnetic fields in matter, Maxwell's equations, electromagnetic waves, and special relativity.

Prerequisites: PHYS 202 and MATH 201, 202.

Introduction to thermodynamics and statistical mechanics. Topics include temperature, heat, work, the first and second laws of thermodynamics, entropy, thermodynamic potentials, kinetic theory of gases, and statistical description of systems of particles.

Prerequisites: PHYS 203 and MATH 202.

Introduction to quantum theory. Topics include wave-particle duality, Schrdinger equation, wave functions, operators, expectation values, uncertainty principle, solutions of one-dimensional problems, the hydrogen atom, angular momentum, and identical particles.

Prerequisites: PHYS 203 and MATH 202.

Introduction to the physics of solids. Topics include crystal structure, crystal binding, thermal properties, free electron model of metals, band theory, semiconductor physics, and optical properties of solids.

Prerequisites: PHYS 401 or consent of instructor.

Mathematical techniques used in physics. Topics include vector analysis, complex analysis, Fourier series and transforms, partial differential equations, special functions, and tensor analysis. Applications to mechanics, electromagnetism, quantum mechanics, and thermal physics.

Prerequisites: MATH 201 and PHYS 202.

Numerical methods in physics. Topics include numerical differentiation and integration, solution of differential equations, Monte Carlo methods, linear algebra, and visualization of physical phenomena. Programming in Python or another high-level language.

Prerequisites: PHYS 203 and programming experience or consent of instructor.