- PH 201, 202, Introduction to Analytical Physics I and II (F20, S21)
- PH 301, Modern Physics (F20)
- PH 303, Electromagnetic Waves and Optics (S21)
- PH 311, Experimental Modern Physics (S21)
- PH 321, Intermediate Classical Mechanics (S22)
- PH 325, Thermodynamics and Statistical Physics (S21)
- PH 331, Electromagnetic Theory (F20)
- PH 421, Quantum Theory I (F21)
- PH 490 Colloquium (F20)
- PH 495, Senior Seminar (F20)
- PH/AS, Physics Elective—Physics majors must also choose two of the following courses as an elective:
- AS 301, Modern Astronomical with Laboratory (F20)
- AS 311, Astrophysics I (S21)
- AS 312, Galactic Astrophysics (F21)
- AS340, Cosmology (S22)
- PH 315, Mathematical Methods for Physics
- PH 351, Analog Electronics I (F20)
- PH 422, Quantum Theory II
- PH 427, General Relativity and Gravity
- PH 461, Computational Physics
- PH 480, Special Topics

Note that many of the upper-level courses will require MA 106, MA 107, MA 208, MA215 and MA 334. A student who intends to pursue graduate studies in Physics should also consider AS 311, AS340, PH 315, PH 422, and/or PH 461. Butler University requires that students take at least 40 hours of credit at a 300-level or higher to graduate. All students in the College of Liberal Arts and Sciences must complete a foreign language requirement. For a Bachelor of Science degree a student must take a minimum of 60 hours in the natural sciences and mathematics. Information on how complete the Physics degree in three years can be found here.

#### Courses

Butler Astrophysics & Astronomy undergraduates obtain a solid foundation in physics, astrophysics, and mathematics useful for a number of careers including education, engineering, physics, astrophysics, astronomy, aerospace, intelligence and defense industries, and computational science. Specifically, a student planning to go on to graduate school in astrophysics and astronomy should have physics courses covering mechanics, electricity and magnetism, modern physics, and optics.

##### Required Courses:

- PH 201, 202: Introduction to Analytical Physics I and II
- PH 301: Modern Physics
- PH 303: Electromagnetic Waves and Optics
- PH 321: Intermediate Classical Mechanics
- PH 331: Electromagnetic Theory
- PH 490: Colloquium
- PH 495: Senior Seminar
- AS 102, Modern Astronomy
- AS 301: Modern Astronomical Techniques
- AS 311: Astrophysics I
- AS 312: Astrophysics II
- AS 340: Cosmology

##### Recommended Courses:

- PH 311: Experimental Modern Physics
- PH 325: Thermodynamics and Statistical Physics
- PH 421: Quantum Theory
- PH 461: Computational Physics

Particular regard should be given to the mathematics and physics prerequisites for all 300-level courses. Note that many of the upper-level courses will require MA106, MA 07, MA208, MA215, and/or MA334. Students should also take at least one computer science course that involves programming, typically CS142. The College of Liberal Arts and Science requires that students take at least 40 hours of credit at the 300-level or higher to graduate. For a Bachelor of Science degree a student must take a minimum of 60 hours in the natural sciences

- AS 102, Modern Astronomy (same as NW263-AS)
- PH 201, 202 Introduction to Analytical Physics I and II (F19, S20)
- AS 301, Modern Astronomical Techniques (F20)
- AS 311, Astrophysics I (S21)
- AS 312, Astrophysics II (F21)

Please note that those courses listed at the 300-level or higher will require calculus and physics. Please check the prerequisites for each course in the course descriptions.

The Engineering Dual Degree Program results from a partnership between two institutions (Butler University and Purdue University School of Engineering and Technology at Indianapolis) known for their quality programs in science and engineering. Completion of this program will yield a degree from Butler University in one of the natural sciences or mathematics and a degree from Purdue University School of Engineering and Technology at Indianapolis in mechanical, electrical, or computer engineering. This partnership will allow students to study in a small, private university environment with faculty dedicated to undergraduate education and also have access to ABET accredited programs in mechanical or electrical engineering which are normally found in larger, public institutions.

#### A Summary of Program Features

- The dual degree program leads to a degree in engineering from Purdue School of Engineering and Technology at Indianapolis (mechanical or electrical) and a physics or astrophysics degree from Butler University. Additional curriculum information is available in the Engineering Dual Degree Program pages.
- The electrical and mechanical engineering programs are ABET accredited.
- The dual degree programs are five years with residence at Butler University during the programs.
- Two paid summer internships are part of the programs.
- The courses in mathematics, sciences, humanities, social sciences, and fine arts are taught at Butler University while the engineering courses are taught through Purdue School of Engineering and Technology at Indianapolis. Engineering courses taken during the first three years will be taught at Butler.
- All courses will be taught at Butler during the first three years. Most engineering electives will be taken the last two years at Purdue School of Engineering and Technology at Indianapolis.
- Transportation provided between sites (Butler and Purdue School of Engineering and Technology at Indianapolis).
- Job placement/career services at Butler University, Purdue School of Engineering and Technology at Indianapolis, and Purdue University at West Lafayette will be available to dual degree students.

#### Core Course Offered by Physics

NW 262-PH, (Core Course) The Physical World:

A one-semester study of selected topics in physics, astronomy, chemistry, and other related fields, and the mathematical analysis of physical problems. Some mathematical tools will be introduced as needed. Four lecture periods and two hours of laboratory per week. (U) (5)

#### Physics Courses

PH 107, 108, Elementary Physics:

A two-semester course based on algebra and elementary trigonometry. This course is suitable preparation to meet the entrance requirements of most dental, medical and pharmacy schools. Three class periods and two hours of laboratory per week. PH 108 must be preceded by PH 107. Fee (U) (4,4)

PH 201, 202, Introduction to Analytical Physics:

An introduction to Newtonian mechanics, thermal physics, waves, electromagnetism and optics using calculus. Familiarity with algebra, trigonometry and calculus is assumed. Four lectures and two hours of laboratory per week, plus one hour of recitation per week. PH 202 must be preceded by PH 201. Prerequisite: MA 106 (may be concurrent) or permission of instructor. Fee (U) (5,5)

PH 301, Modern Physics:

The special theory of relativity is developed along with the introduction of basic ideas and equations of quantum physics. Topics include Lorentz transformations, relativistic mechanics, collisions and conservation of energy-momentum, electromagnetism and relativity, blackbody radiation, photoelectric effect, Compton effect, and the Schrödinger equation. Prerequisites: MA 107 and PH 202 or permission of instructor. (U) (3)

PH 303, Electromagnetic Waves and Optics:

A study of geometric and wave optics, interference, diffraction and polarization of electromagnetic waves. Two lectures and two hours of laboratory per week. Prerequisites: MA 208 (may be concurrent) and PH 202 or permission of instructor. Fee (U) (3)

PH 311, Experimental Modern Physics:

The student performs a number of experiments to explore and verify experimental implications of relativity and quantum mechanics. Experiments include determining Planck’s constant, speed of light, charge-to-mass ratio of electron, Franck-Hertz experiment, Bragg scattering, Rutherford scattering, and radioactive decay processes. Prerequisite: PH 301 or permission of instructor. Fee (U) (3)

PH 315, 316, Mathematical Methods for Physics:

Mathematical methods for physics: differential equations; coordinate systems and differential geometry; special functions; linear operators, groups and representation theory; complex analysis; Fourier series and integral transforms. Applications to problems in electromagnetic theory, classical mechanics, and quantum mechanics will be presented. Four lectures per week. Prerequisite MA 208 and PH 201/202. (U) (4,4)

PH 321, Intermediate Classical Mechanics:

A study of the classical dynamics of oscillators, gravitational systems, calculus of variations and the Lagrangian and Hamiltonian formalisms. dynamics of many-particle systems and continuous media, including noninertial motion, rotational motion, normal modes, and wave theory. Prerequisites: PH 202 and MA 208 or permission of instructor. (U) (4)

PH 325, Thermodynamics and Statistical Physics:

A study of the theory and applications of the first and second laws of thermodynamics, thermodynamic potentials, kinetic theory, classical and quantum statistical mechanics and ensemble theory to thermodynamic systems. Four lecture hours per week. Prerequisites: PH 202 and MA 107 or permission of instructor. (U-G) (4)

PH 331, Electromagnetic Theory:

The theory of classical electric and magnetic fields is developed covering such topics as electrostatics, magnetostatics, scalar and vector potentials, fields in matter, electrodynamics and Maxwell’s equations, conservation laws and radiation. Prerequisites: PH 202 and MA 208 or permission of instructor. (U-G) (4)

PH 351, Analog Electronics:

Survey of electronic devices. Measurement of continuously varying quantities in time and frequency domains. Rectifiers, amplifiers, feedback, with emphasis on operational amplifiers and their uses. Three lectures and three hours of laboratory per week. Prerequisite: PH 202 or permission of instructor. Fee (U) (4)

PH 352, Digital Electronics:

Logic design, Karnaugh maps, state diagrams. Arithmetic and logic functions. Flip-flops, counters, and shift registers. Introduction to design with MSA and LSI devices. Two lectures and three hours of laboratory per week. Prerequisite: PH 351 or permission of instructor. Fee (U-G) (3)

PH 411, 412, Theoretical Physics:

A study of mathematical methods of physics, including boundary-value problems, special functions, linear operators, and group theory, with applications to problems in electromagnetic theory, classical and quantum mechanics. Three lectures per week. Prerequisites: PH 331 and MA 334 or permission of instructor. (U-G) (3,3)

PH 413, Independent Study in Physics (U) (1)

PH 414, Independent Study in Physics (U) (1-3)

PH 421, Quantum Theory I:

The mathematical foundations of quantum mechanics are presented with treatment of simple systems such as barriers, square wells, harmonic oscillator, and central potentials with the development of approximation methods and the theory of angular momentum for single particles. Prerequisites: MA 208 and PH 301 or permission of instructor. (U-G) (4)

PH 422, Quantum Theory II:

Applications of quantum mechanics to multi-particle systems. Time dependent perturbation theory, angular momentum coupling, atomic spectra, quantum statistics, radiation and scattering theory, and introduction to relatvistic quantum theory. Prerequisite: PH 421 or permission of instructor. (U-G) (4)

PH 427, General Relativity and Gravity I:

Tensor analysis in classical field theory, Einstein’s field equations, the Schwarzschild solution, linearized field equations, experimental gravitation, cosmological models and gravitational collapse. Prerequisites: PH 321 and PH 332 or permission of instructor. (U/G) (3)

PH 428, General Relativity and Gravity II

Tensor analysis in classical field theory, Einstein’s field equations, the Schwarzschild solution, linearized field equations, experimental gravitation, cosmological models and gravitational collapse. Prerequisites: PH 427 or permission of instructor. (U/G) (3).

PH 461, Computational Physics I:

An introduction to numerical methods frequently used in physics for solving problems which cannot be solved analytically in a closed mathematical form. Topics include numerical solution of problems dealing with oscillatory motion, gravitation, electrical fields, fluid dynamics, heat conduction, Schrödinger equation, and elastic wave motion. Prerequisites: PH 321, PH 331, or permission of the instructor. (U) (3)

PH 480, Special Topics:

By arrangement with appropriate staff. (U-G) (1-3)

PH 490, Colloquium (U) (P/F)

PH 491, 492, 493, Undergraduate Tutorial and Research:

(U) (3,6,9)

PH 495, Senior Seminar:

This seminar, for junior and senior physics majors, features student presentations on special research projects and selected readings in current scientific literature. A comprehensive physics exam covering all areas of physics in the curriculum will be given to all senior physics majors in the course. (U) (1)

PH 499, Honors Thesis: (U) (3)

#### Core Course Offered by Astronomy

NW263-AS (Core Course) The Astronomical Universe:

A one-semester survey of astronomy including ancient Greek astronomy, the motions of the night sky, the solar system, other solar systems, the lives of stars including the Sun, and the origin and fate of the universe. This will be a four-lecture-hour/two-hour lab course. (U) (5)

#### Astronomy Courses

AS 100. The Astronomical Universe:

A descriptive study of basic astronomy including the planets and the apparent motions of celestial objects, the seasons, constellations, comets and meteors, stars, galaxies and large-scale structure of the universe, plus current events in space exploration. There will be planetarium demonstrations and telescope observations. Some hands-on lab experiences are provided. (U) (3)

AS 102. Modern Astronomy with Laboratory (same as NW263-AS):

First course of an introductory astronomy sequence for both non-science and science majors. This course and laboratory include the history of astronomy, timekeeping, the solar system, planets and their motions, the moon, comets, meteors, the solar evolution, Kepler’s Laws, etc., with planetarium demonstrations, usage of astronomical instruments, and small telescopes and binoculars. Four hours of lecture, and one two-hour lab per week. (U) (5)

AS 301, Modern Astronomical Techniques:

Introduction to techniques and equipment used in modern astronomy with emphasis on detection and analysis of electromagnetic radiation and the fundamental properties of telescopes and detectors. Lectures and laboratory. Laboratories focus on observational techniques and data reduction. Prerequisites: AS 102 and PH 202. (U) (3)

AS 311, Stellar Astrophysics:

The first semester of an introductory course on stellar astrophysics using nearly every branch of physics. Emphasis is on the underlying physical principles; including the nature of stars, stellar energy generation, stellar structure and evolution, astrophysical neutrinos, binary stars, white dwarfs, neutron stars and pulsars, and novae and supernovae. Prerequisites: AS102 and PH202. (U) (3)

AS 312, Galaxies and Cosmology:

A continuation of AS 311. The course covers the application of physical principles to the inter-stellar medium, the kinematics and dynamics of stars and stellar systems, galactic structure, formation and evolution of galaxies, relativity, Big Bang and inflationary models of the origin of the universe, and the large-scale structure and ultimate fate of the universe. Prerequisite: AS 311. (U) (3)

AS 461, Computational Astrophysics:

An introduction to numerical methods frequently used in astrophysics for solving problems which cannot be solved analytically in a closed mathematical form. Topics include numerical solution of problems dealing with oscillatory motion, gravitation, electrical fields, stellar dynamics, steller evolution, Schrödinger equation, and fluid mechanics. Prerequisites are PH 321 and PH 331 or permission of the instructor. (U) (3)