**The Faculty**

Alan J. DeWeerd

S. Eric Hill

Martín Hoecker-Martínez

**The Majors**

Physics investigates and models nature in the most precise and fundamental ways possible. It is a driving force in the continual scientific and technological revolutions that define the modern world. This program prepares students for work or graduate studies in physics, astronomy, engineering, and other technical fields. Major courses address theoretical and experimental aspects of Classical Mechanics, Quantum Mechanics, Electricity and Magnetism, and Statistical Mechanics and Thermodynamics. Additionally, advanced topics courses are offered such as Relativity, Physical Oceanography, and Condensed Matter. Students perform research in addition to coursework. There are opportunities to work with faculty in areas such as fluid dynamics, condensed matter, and optics.

The Physics department offers both Bachelor of Arts and Bachelor of Science degrees. Both majors offer training in the fundamentals of physics, from classical mechanics to quantum mechanics. We strongly recommend students begin either major with PHYS 231 General Physics I as early as possible (ideally, during the first year). Four years from the beginning of the General Physics sequence are required to complete the requirements for the Bachelor of Science degree, but the Bachelor of Arts degree can be completed in three years.

Students declaring a physics major are required to have a 2.5 cumulative GPA in the general physics and calculus sequences (PHYS 231, PHYS 232, PHYS 233, and MATH 121, MATH 122, MATH 221).

Learning outcomes for these programs may be found at www.redlands.edu/BA-PHYS/learning-outcomes.

**Bachelor of Arts**

This program provides students with a basic understanding of the fundamentals of physics and allows them to choose which subjects to study at the advanced level. Students are encouraged to meet with physics faculty early in their program in order to choose courses that will prepare them for their future goals.

**Requirements**

At least 10 additional credits at the 300 level must also be taken.

Quantitative study of classical Newtonian mechanics. Includes lecture and laboratory components.

Prerequisite: MATH 119, MATH 121, MATH 122 or MATH 221.

Introduction to classical electricity and magnetism. Includes lecture and laboratory components.

Prerequisite: PHYS 231; Pre- or corequisite: MATH 122 or MATH 221.

Introduction to geometric optics, wave optics, quantum mechanics, thermodynamics, and statistical mechanics. Includes lecture and laboratory components.

Prerequisite: PHYS 231–232 or instructor’s permission. Pre- or corequisite: MATH 221.

Students develop the skills for communicating scientific articles, writing papers, and giving presentations.

Prerequisites: PHYS 233.

Numeric and Evaluation grade only.

Development of written and oral communication skills. Preparation and presentation of a senior thesis. Prerequisite: PHYS 391 Junior Seminar.

Numeric and Evaluation grade only.

Functions and their graphs; successive approximation and limits; local linearity and differentiation; applications of differentiation to graphing and optimization; and the definite integral, antiderivatives, and differential equations.

Prerequisite: Permission based on Mathematics Placement Exam.

Riemann sums and the definite integral; techniques of integration and application of integrals; introduction to differential equation; sequences and series.

Prerequisite: MATH 121 or MATH 119 or by permission.

Topics in multivariable calculus related to differentiation and integration. Sequences, series and Taylor approximations.

Differential equations theory and applications. First-order linear and nonlinear differential equations with analytic and numerical techniques. Higher-order linear differential equations and complex algebra. Phase trajectory and stability analysis. Systems of linear differential equations with constant coefficients. Matrix methods, Gauss-Jordan, and iterative techniques.

Prerequisite: MATH 221.

**Bachelor of Science**

This program offers advanced training in the fundamentals of physics. It is designed for well prepared and highly motivated students, particularly those interested in further study of physics at the graduate level. After completing this program, students will be well grounded in classical and modern physics and equipped to choose a specialized area for further study and research.

**Requirements**

- At least at least 2 credits of PHYS 378 or other department-approved research experience
- At least 3 additional credits at the 300 level

*Please note: PHYS 331, 332, 341, and 344 are offered every other year. Students should plan their schedules accordingly. *

Prerequisite: MATH 119, MATH 121, MATH 122 or MATH 221.

Prerequisite: PHYS 231; Pre- or corequisite: MATH 122 or MATH 221.

Prerequisite: PHYS 231–232 or instructor’s permission. Pre- or corequisite: MATH 221.

Instrumentation, transistor theory, integrated circuits, and fundamental analog and digital circuit design. Lecture and lab components.

Prerequisite: PHYS 221 or PHYS 232 or by permission.

Applications of Newtonian mechanics to various systems, and introduction of calculus of variations and Lagrangian mechanics. This course acquaints students with mathematical techniques used to solve more realistic and complex problems.

Prerequisite: PHYS 231.

Pre- or corequisite: MATH 235.

Development and application of Maxwell’s equations describing electromagnetic fields. Topics include boundary value problems, and dielectric and magnetic materials.

Prerequisites: PHYS 232 and MATH 235.

Offered in alternate years.

Fundamentals of quantum theory. Includes development of mathematical formalism, application to two- and three-dimensional models, and a detailed treatment of the one-electron atom.

Prerequisites: PHYS 233 and MATH 235.

Offered in alternate years.

Fundamental principles of classical thermodynamics and kinetic theory. Classical and quantum statistical properties of matter and radiation.

Prerequisites: PHYS 233 and MATH 221.

Offered in alternate years.

Laboratory course in solid state, molecular, atomic, optical, nuclear, and particle physics.

Prerequisite: PHYS 233 and PHYS 310.

Prerequisites: PHYS 233.

Numeric and Evaluation grade only.

Numeric and Evaluation grade only.

Students can earn credits while gaining valuable research experience with faculty in the department. Contact individual faculty to discuss opportunities. May be repeated for degree credit.

Prerequisite: instructor’s permission.

Credit/no credit and Evaluation grade only.

Math co- and pre-requisites for Physics courses are given in the individual course descriptions.

**Related Field Requirements: 32 credits**

Prerequisite: Permission based on Mathematics Placement Exam.

Prerequisite: MATH 121 or MATH 119 or by permission.

Prerequisite: MATH 221.

Also choose four of the following, with at least one from each category:

Introduction to chemistry, including properties, structure, and reactivity of atoms and molecules, with concurrent laboratory. CHEM 131 covers fundamental concepts of atomic structure, stoichiometry, aqueous reactions, states of matter, molecular structure and bonding, and thermochemistry. Four hours lecture and three hours laboratory.

Prerequisites: Placement into MATH 100 or higher mathematics course, completion of MATH 100 or higher mathematics course, or permission of chemistry department.

Corequisite: CHEM 131L.

Introduction to chemistry, including properties, structure, and reactivity of atoms and molecules, with concurrent laboratory. First semester covers fundamental concepts of atomic structure, stoichiometry, aqueous reactions, states of matter, molecular structure and bonding, and thermochemistry. Second semester emphasizes group projects in equilibrium, electrochemistry, thermodynamics, kinetics, inorganic synthesis, and spectroscopy. Fall: four hours lecture and three hours laboratory. Spring: seven hours laboratory and group learning.

Prerequisite: CHEM 131 with a minimum grade of 2.0 or higher or by permission. Placement into or completion of MATH 118 or higher. Mathematics course or permission of Chemistry department.

Quantum chemistry, spectroscopy, and statistical thermodynamics applied to the study of the physical and chemical properties of matter. The laboratory involves the systematic study of the theory and practice of modern spectroscopic methods. Four hours lecture and three hours laboratory.

Prerequisites: CHEM 132 and MATH 122 or higher math course and PHYS 220 or higher physics course or by permission.

Equilibrium thermodynamics and kinetics applied to the study of the physical and chemical properties of matter. CHEM 331 need not be taken before CHEM 332.

Prerequisites: CHEM 132 and MATH 122 or higher math course and PHYS 220 or higher physics course or by permission.

Investigation of vector calculus with an emphasis on applications in physics. Parametrized curves and surfaces; vector fields; line integrals and Green’s Theorem; flux integrals; divergence and curl; the Divergence Theorem and Stokes’s Theorem.

Prerequisite: MATH 221.

Offered as needed.

Study of vector spaces. Topics include systems of linear equations, matrices, the geometry of vectors, vector spaces, linear transformations, eigenvalues and eigenvectors, determinants, and selected applications.

Prerequisite: MATH 221.

Introduction to the theory of probability with applications in management science and the physical and social sciences. Topics include combinatorial probability, densities, mathematical expectation, moment-generating functions, and the central limit theorem.

Prerequisite: MATH 221.

Partial Differential Equations theory and applications. We will explore solution methods for parabolic, hyperbolic, and elliptic equations. Topics include separation of variables, transforming nonhomogeneous equations, Eigenfunction expansions, Integral Sine and Cosine transformations, Fourier and Laplace Transforms, the Method of Characteristics, and an introduction to Green’s Functions.

Prerequisite: MATH 235.

Offered in alternate years.

**Or**

The theory and application of numerical methods for solving mathematical problems. Topics include numerical methods for solving algebraic equations and ordinary differential equations, interpolation and approximation, and numerical integration.

Prerequisite: MATH 235 or MATH 241.

Offered in alternate years.

Introduction to problem-solving methods and algorithm development through the use of computer programming in the C++/Java language. Emphasis on data and algorithm representation. Topics include declarations, arrays, strings, structs, unions, expressions, statements, functions, and input/output processing.

Numeric grade only.

Corequisite: Math 121 Calculus (or Math 118 and Math 119).

Advanced topics concerning data and algorithm representation using C++/Java. Topics include stacks and recursion, dynamic memory, pointers, linked lists, queues, trees, searching, sorting, and object-oriented programming (OOP) and classes.

Prerequisite: CS 110 and MATH 121 Calculus (or Math 118 and Math 119).

Co-requisite MATH 121.

Techniques for data wrangling/munging (acquisition, cleaning, transformation), visualization (using the grammar of graphics), and modeling that are foundational to data science. Topics to include efficient management of large and sparse datasets, uni/multivariate graphical and numerical descriptive statistics, code efficacy (memory and speed), study reproducibility, and data ethics.

Prerequisite: CS 110.

Recommended MATH 111 or equivalent.

Offered as needed.

Numeric grade only.

**Engineering**

Through the Engineering 3-2 Combined Degree program, the Physics B.A. can be paired with an Engineering B.S. from Columbia University in New York City, or Manhattan College School of Engineering, or Washington University at St. Louis. This program combines three years at Redlands with two years at Columbia’s or Washington's School of Engineering. For more information, see “ENGINEERING 3-2 COMBINED DEGREE” in the Integrated Programs of Study section of this Catalog. Contact the program advisor listed for more information. Alternatively, a Physics bachelor’s degree is good preparation for graduate study in various fields of Engineering.

**The Minors**

**Physics Minor**

A minor in physics can provide students with an understanding of the basic laws of the physical universe. When combined with a major in another science, students who minor in physics will be well prepared for graduate study in the sciences.

**Requirements (32 credits)**

**Introductory Physics (8 credits)**

Choose one of the following sequences:

Prerequisite: MATH 119, MATH 121, MATH 122 or MATH 221.

Prerequisite: PHYS 231; Pre- or corequisite: MATH 122 or MATH 221.

Or

Introduction to Newtonian mechanics, fluids, and thermodynamics. Includes lecture and laboratory components. Expects competency in high school algebra, geometry, and trigonometry.

Introduction to oscillations, waves, electricity, magnetism, optics, and modern physics. Includes lecture and laboratory components.

Prerequisite: PHYS 220.

- 8 credits in 300-level courses (except PHYS 391) must also be taken.

Prerequisite: PHYS 231–232 or instructor’s permission. Pre- or corequisite: MATH 221.

Prerequisite: Permission based on Mathematics Placement Exam.

Prerequisite: MATH 121 or MATH 119 or by permission.

**Departmental Honors**The Physics Department offers honors to recognize outstanding student achievement as reflected by a major GPA of at least 3.5 and an excellent research project culminating in a Senior Thesis (PHYS 491) and a presentation. Students should consult with the department chair for requirements.

**Single-Subject Teaching Credential**

Students who wish to be certified to teach science should meet with an advisor in the School of Education for information concerning certification and the teacher education preparation program process. Most students complete the teacher preparation program, including student teaching, during a fifth year after graduation. Please refer to the School of Education section of this Catalog for a more detailed list of requirements.

**Advanced Placement in Physics**Students who scored well on the Physics AP exams may receive credit and place out of introductory courses based on an interview with department faculty. There are two different exams in physics:

*Physics 1:* Students who earned a score of three receive 0 to 4 credits, depending on the results of an interview with department faculty. Scores of four or five earn 4 credits.

*Physics 2:* Students who earned a score of three receive 0 to 4 credits, depending on the results of an interview with department faculty. Scores of four or five earn 4 credits.

*Physics C:* Students who earn a score of three may receive 0 to 7 credits, depending on the results of a faculty interview. Scores of four or five earn 3 to 8 credits, depending on the results of the faculty interview.

**Research**

Research is an important component of a science student’s experience at Redlands. Physics students can work with faculty during the school year for credit (PHYS 378) and during the summer when a number of research fellowship positions are available for students within the Stauffer Center for Science and Mathematics. They can also take advantage of summer programs offered by other institutions (such as Research Experiences for Undergraduates). Most students begin work in their sophomore or junior years that evolves into a senior thesis.

Students join faculty on research in areas such as Turbulence, Optics, and Surface Science. The fluid dynamics lab is a student designed facility for geophysical dynamics experiments as well as analysis of oceanic and atmospheric flow observations. Students have worked on a variety of laser and optical experiments, including light scattering, optical tweezers, and quantum optics. Recent surface science work has featured the development and construction of a Scanning Tunneling Microscope to investigate atomic-scale surface features and phenomena.

Introductory study of selected topics in planetary science. Basic information about the planets, moons, and other objects in our solar system will be covered. Additional possible topics include space exploration, planetary geology, search for life in the solar system, and planetary impact hazards. Includes lecture and laboratory components. Expects competency in high school algebra, geometry, and trigonometry.

Offered as needed.

Introductory study of astronomy designed to acquaint the student with stars, black holes, galaxies, and the origin and present state of the universe. Students will learn about these concepts in the context of the scientific method. Laboratory is one day a week with occasional evening observing sessions. Includes lecture and laboratory components.

Prerequisite: Expects competency in high school algebra, geometry, and trigonometry.

Offered as needed.

Introductory study of the physics of light. Students will learn about the production of light, the nature of color, everyday optical phenomena, vision, quantum mechanics, and relativity. Includes lecture and laboratory components. Expects competency in high school algebra.

Offered as needed.

This is an introductory-level lab science course. Students will develop an understanding of the physical principles underlying the phenomena of musical acoustics: sound production, propagation, and perception. Includes lecture and laboratory components. Expects competency in high school algebra.

Offered as needed.

Topics in physics and astronomy of interest to non-majors that are not regularly offered. May be repeated for degree credit for a maximum of 12 credits, given different topics.

Offered as needed.

Prerequisite: PHYS 220.

Prerequisite: MATH 119, MATH 121, MATH 122 or MATH 221.

Prerequisite: PHYS 231; Pre- or corequisite: MATH 122 or MATH 221.

Prerequisite: PHYS 231–232 or instructor’s permission. Pre- or corequisite: MATH 221.

Experience in classroom lecturing, experimental demonstration, construction and design of student laboratory experiments, tutoring, and individual instruction. This course may be associated with any 100- or 200-level physics course.

Prerequisite: instructor’s permission. Available concurrently with associated Physics courses.

Prerequisite: instructor’s permission. Available concurrently with associated Physics courses.

Prerequisite: PHYS 221 or PHYS 232 or by permission.

Prerequisite: PHYS 231.

Pre- or corequisite: MATH 235.

Prerequisites: PHYS 232 and MATH 235.

Offered in alternate years.

Prerequisites: PHYS 233 and MATH 235.

Offered in alternate years.

Prerequisites: PHYS 233 and MATH 221.

Offered in alternate years.

Prerequisite: PHYS 233 and PHYS 310.

Special topics in physics and astronomy not otherwise covered in the curriculum. Topics vary with semester and may include fluid mechanics, optics, computational physics, relativity, and solid state physics.

May be repeated for degree credit given a different topic.

Prerequisite: PHYS 231 and PHYS 233 or instructor’s permission.

Offered as needed.

Prerequisite: instructor’s permission.

Credit/no credit and Evaluation grade only.

Prerequisites: PHYS 233.

Numeric and Evaluation grade only.

Numeric and Evaluation grade only.