**Requirements: 1 year with Lab**

**Physics 21, 23, 25 AND Physics 22, 24, 26 (labs)**

**OR Physics 41, 43, 45 AND Physics 42, 44, 46 (labs)**

**OR Physics 61, 63, 65 AND Physics 62, 64, 67 (labs)****PHYSICS 21: Mechanics, Fluids, and Heat**

How are the motions of objects and the behavior of fluids and gases determined by the laws of physics? Students learn to describe the motion of objects (kinematics) and understand why objects move as they do (dynamics). Emphasis on how Newton’s three laws of motion are applied to solids, liquids, and gases to describe phenomena as diverse as spinning gymnasts, blood flow, and sound waves. Understanding many-particle systems requires connecting macroscopic properties (e.g., temperature and pressure) to microscopic dynamics (collisions of particles). Laws of thermodynamics provide understanding of real-world phenomena such as energy conversion and performance limits of heat engines. Everyday examples are analyzed using tools of algebra and trigonometry. Problem-solving skills are developed, including verifying that derived results satisfy criteria for correctness, such as dimensional consistency and expected behavior in limiting cases. Physical understanding fostered by peer interaction and demonstrations in lecture, and interactive group problem solving in discussion sections. Prerequisite: high school algebra and trigonometry; calculus not required.

Terms: Aut | Units: 4 | UG Reqs: GER: DB-NatSci, WAY-SMA | Grading: Letter or Credit/No Credit

Professors:

Instructors: Romani, R. (PI) ; Black, M. (TA) ; Ho, E. (TA) ; Sheffels, S. (TA) ; Zerger, C. (TA)

Other Resources:

https://carta.stanford.edu/course/PHYSICS21/1172

**PHYSICS 22: Mechanics and Heat Laboratory**

Guided hands-on exploration of concepts in classical mechanics and thermodynamics with an emphasis on student predictions, observations and explanations. Pre- or corequisite: PHYS 21.

Terms: Aut | Units: 1 | Grading: Satisfactory/No Credit

Professors: Romani, R. (PI)

Other Resources:

**PHYSICS 23: Electricity, Magnetism, and Optics**

How are electric and magnetic fields generated by static and moving charges, and what are their applications? How is light related to electromagnetic waves? Students learn to represent and analyze electric and magnetic fields to understand electric circuits, motors, and generators. The wave nature of light is used to explain interference, diffraction, and polarization phenomena. Geometric optics is employed to understand how lenses and mirrors form images. These descriptions are combined to understand the workings and limitations of optical systems such as the eye, corrective vision, cameras, telescopes, and microscopes. Discussions based on the language of algebra and trigonometry. Physical understanding fostered by peer interaction and demonstrations in lecture, and interactive group problem solving in discussion sections. Prerequisite: PHYSICS 21 or PHYSICS 21S.

Terms: Win | Units: 4 | UG Reqs: GER: DB-NatSci, WAY-SMA | Grading: Letter or Credit/No Credit

Professors: Linde, A. (PI)

Other Resources:

**PHYSICS 24: Electricity and Optics Laboratory**

Guided hands-on exploration of concepts in electricity and magnetism, circuits and optics with an emphasis on student predictions, observations and explanations. Introduction to multimeters and oscilloscopes. Pre- or corequisite: PHYS 23.

Terms: Win | Units: 1 | Grading: Satisfactory/No Credit

Professors: Linde, A. (PI)

Other Resources:

**PHYSICS 25: Modern Physics**

How do the discoveries since the dawn of the 20th century impact our understanding of 21st-century physics? This course introduces the foundations of modern physics: Einstein’s theory of special relativity and quantum mechanics. Combining the language of physics with tools from algebra and trigonometry, students gain insights into how the universe works on both the smallest and largest scales. Topics may include atomic, molecular, and laser physics; semiconductors; elementary particles and the fundamental forces; nuclear physics (fission, fusion, and radioactivity); astrophysics and cosmology (the contents and evolution of the universe). Emphasis on applications of modern physics in everyday life, progress made in our understanding of the universe, and open questions that are the subject of active research. Physical understanding fostered by peer interaction and demonstrations in lecture, and interactive group problem solving in discussion sections. Prerequisite: PHYSICS 23 or PHYSICS 23S.

Terms: Spr | Units: 4 | UG Reqs: GER: DB-NatSci, WAY-SMA | Grading: Letter or Credit/No Credit

Professors: Irwin, K. (PI)

Other Resources:

**PHYSICS 26: Modern Physics Laboratory**

Guided hands-on and simulation-based exploration of concepts in modern physics, including special relativity, quantum mechanics and nuclear physics with an emphasis on student predictions, observations and explanations. Pre- or corequisite:PHYSICS 25.

Terms: Spr | Units: 1 | Grading: Satisfactory/No Credit

Professors: Irwin, K. (PI) ; Titus, C. (TA)

Other Resources:

**PHYSICS 41: Mechanics**

How are motions of objects in the physical world determined by laws of physics? Students learn to describe the motion of objects (kinematics) and then understand why motions have the form they do (dynamics). Emphasis on how the important physical principles in mechanics, such as conservation of momentum and energy for translational and rotational motion, follow from just three laws of nature: Newton’s laws of motion. Distinction made between fundamental laws of nature and empirical rules that are useful approximations for more complex physics. Problems drawn from examples of mechanics in everyday life. Skills developed in verifying that derived results satisfy criteria for correctness, such as dimensional consistency and expected behavior in limiting cases. Discussions based on language of mathematics, particularly vector representations and operations, and calculus. Physical understanding fostered by peer interaction and demonstrations in lecture, and discussion sections based on interactive group problem solving. Prerequisite: High school physics or concurrent enrollment in PHYSICS 41A. MATH 41 or MATH 51 or CME 100 or equivalent. Minimum corequisite: MATH 42 or equivalent.

Terms: Win | Units: 4 | UG Reqs: GER: DB-NatSci, WAY-SMA | Grading: Letter or Credit/No Credit

Professors: Lee, Y. (PI)

Other Resources:

**PHYSICS 42: Classical Mechanics Laboratory**

Hands-on exploration of concepts in classical mechanics: Newton’s laws, conservation laws, rotational motion. Introduction to laboratory techniques, experimental equipment and data analysis. Pre- or corequisite: PHYSICS 41

Terms: Win | Units: 1 | Grading: Satisfactory/No Credit

(https://explorecourses.stanford.edu)

Professors: Michelson, P. (PI)

Other Resources:

https://carta.stanford.edu/course/PHYSICS42/1172

**PHYSICS 43: Electricity and Magnetism**

What is electricity? What is magnetism? How are they related? How do these phenomena manifest themselves in the physical world? The theory of electricity and magnetism, as codified by Maxwell’s equations, underlies much of the observable universe. Students develop both conceptual and quantitative knowledge of this theory. Topics include: electrostatics; magnetostatics; simple AC and DC circuits involving capacitors, inductors, and resistors; integral form of Maxwell’s equations; electromagnetic waves. Principles illustrated in the context of modern technologies. Broader scientific questions addressed include: How do physical theories evolve? What is the interplay between basic physical theories and associated technologies? Discussions based on the language of mathematics, particularly differential and integral calculus, and vectors. Physical understanding fostered by peer interaction and demonstrations in lecture, and discussion sections based on interactive group problem solving. Prerequisite: PHYSICS 41 or equivalent. MATH 42 or MATH 51 or CME 100 or equivalent. Recommended corequisite: MATH 52 or CME 102.

Terms: Spr | Units: 4 | UG Reqs: GER: DB-NatSci, WAY-SMA | Grading: Letter or Credit/No Credit

Professors: Kasevich, M. (PI)

Other Resources:

**PHYSICS 44: Electricity and Magnetism Lab**

Hands-on exploration of concepts in electricity and magnetism and circuits. Introduction to multimeters, function generators, oscilloscopes, and graphing techniques. Pre- or corequisite: PHYSICS 43.

Terms: Spr | Units: 1 | Grading: Satisfactory/No Credit

Professors: Kasevich, M. (PI)

Other Resources:

**PHYSICS 45: Light and Heat**

What is temperature? How do the elementary processes of mechanics, which are intrinsically reversible, result in phenomena that are clearly irreversible when applied to a very large number of particles, the ultimate example being life? In thermodynamics, students discover that the approach of classical mechanics is not sufficient to deal with the extremely large number of particles present in a macroscopic amount of gas. The paradigm of thermodynamics leads to a deeper understanding of real-world phenomena such as energy conversion and the performance limits of thermal engines. In optics, students see how a geometrical approach allows the design of optical systems based on reflection and refraction, while the wave nature of light leads to interference phenomena. The two approaches come together in understanding the diffraction limit of microscopes and telescopes. Discussions based on the language of mathematics, particularly calculus. Physical understanding fostered by peer interaction and demonstrations in lecture, and discussion sections based on interactive group problem solving. Prerequisite: PHYSICS 41 or equivalent. MATH 21 or MATH 42 or MATH 51 or CME 100 or equivalent.

Terms: Aut | Units: 4 | UG Reqs: GER: DB-NatSci, WAY-SMA | Grading: Letter or Credit/No Credit

Professors: Gratta, G. (PI) ; Alpert, A. (TA) ; Banerjee, A. (TA) ; Bevillard, B. (TA) ; Cheung, A. (TA) ; Garland, R. (TA) ;Harvey, B. (TA) ; Kang, J. (TA) ; Kwiatkowski, A. (TA) ; Rodriguez, I. (TA) ; Sun, Y. (TA) ; Wenren, D. (TA) ; de Becdelievre, J. (TA

Other Resources:

**PHYSICS 46: Light and Heat Laboratory**

Hands-on exploration of concepts in geometrical optics, wave optics and thermodynamics. Pre- or corequisite: PHYSICS 45.

Terms: Aut | Units: 1 | Grading: Satisfactory/No Credit

(https://explorecourses.stanford.edu)

Professors: Gratta, G. (PI) ; Li, X. (TA) ; Rastawicki, D. (TA) ; Su, V. (TA) ; Young, S. (TA) ; Yuan, E. (TA)

Other Resources:

https://carta.stanford.edu/course/PHYSICS46/1172

**PHYSICS 61: Mechanics and Special Relativity**

First in a three-part advanced freshman physics series: PHYSICS 61, PHYSICS 63, PHYSICS 65.) This course covers Einstein’s special theory of relativity and Newtonian mechanics at a level appropriate for students with a strong high school mathematics and physics background, who are contemplating a major in Physics or Engineering Physics, or are interested in a rigorous treatment of physics. Postulates of special relativity, simultaneity, time dilation, length contraction, the Lorentz transformation, causality, and relativistic mechanics. Central forces, contact forces, linear restoring forces. Momentum transport, work, energy, collisions. Angular momentum, torque, moment of inertia in three dimensions. Damped and forced harmonic oscillators. Uses the language of vectors and multivariable calculus. Recommended prerequisites: Mastery of mechanics at the level of AP Physics C and AP Calculus BC or equivalent. Corequisite: MATH 51.

Terms: Aut | Units: 4 | UG Reqs: GER: DB-NatSci, WAY-SMA | Grading: Letter or Credit/No Credit

Professors: Burchat, P. (PI) ; Wiser, T. (SI) ; Guo, Y. (TA) ; Penington, G. (TA) ; Sakaguchi, D. (TA)

Other Resources:

**PHYSICS 62: Mechanics Laboratory**

Introduction to laboratory techniques, experiment design, data collection and analysis simulations, and correlating observations with theory. Labs emphasize discovery with open-ended questions and hands-on exploration of concepts developed in PHYSICS 61 including Newton’s laws, conservation laws, rotational motion. Pre-or corequisite PHYSICS 61

Terms: Aut | Units: 1 | Grading: Satisfactory/No Credit

Professors: Pam, R. (PI) ; Maharaj, A. (TA) ; Wang, C. (TA)

Other Resources:

**PHYSICS 63: Electricity, Magnetism, and Waves**

(Second in a three-part advanced freshman physics series: PHYSICS 61, PHYSICS 63, PHYSICS 65.) This course covers the foundations of electricity and magnetism for students with a strong high school mathematics and physics background, who are contemplating a major in Physics or Engineering Physics, or are interested in a rigorous treatment of physics. Electricity, magnetism, and waves with some description of optics. Electrostatics and Gauss’ law. Electric potential, electric field, conductors, image charges. Electric currents, DC circuits. Moving charges, magnetic field, Ampere’s law. Solenoids, transformers, induction, AC circuits, resonance. Relativistic point of view for moving charges. Displacement current, Maxwell’s equations. Electromagnetic waves, dielectrics. Diffraction, interference, refraction, reflection, polarization. Prerequisite: PHYSICS 61 and MATH 51. Pre- or corequisite: MATH 52.

Terms: Win | Units: 4 | UG Reqs: GER: DB-NatSci, WAY-FR, WAY-SMA | Grading: Letter or Credit/No Credit

Professors: Cabrera, B. (PI)

**PHYSICS 64: Electricity and Optics Laboratory**

Introduction to multimeters, breadboards, function generators and oscilloscopes. Emphasis on student-developed design of experimental procedure and data analysis for topics covered in PHYSICS 63: electricity, magnetism, circuits, and optics. Pre- or corequisite: PHYSICS 63

Terms: Win | Units: 1 | Grading: Satisfactory/No Credit

Professors:Cabrera, B. (PI)

Other Resources:

**PHYSICS 65: Quantum and Thermal Physics**

(Third in a three-part advanced freshman physics series: PHYSICS 61, PHYSICS 63, PHYSICS 65.) This course introduces the foundations of quantum and statistical mechanics for students with a strong high school mathematics and physics background, who are contemplating a major in Physics or Engineering Physics, or are interested in a rigorous treatment of physics. Quantum mechanics: atoms, electrons, nuclei. Quantization of light, Planck’s constant. Photoelectric effect, Compton and Bragg scattering. Bohr model, atomic spectra. Matter waves, wave packets, interference. Fourier analysis and transforms, Heisenberg uncertainty relationships. Schrödinger equation, eigenfunctions and eigenvalues. Particle-in-a-box, simple harmonic oscillator, barrier penetration, tunneling, WKB and approximate solutions. Time-dependent and multi-dimensional solution concepts. Coulomb potential and hydrogen atom structure. Thermodynamics and statistical mechanics: ideal gas, equipartition, heat capacity. Probability, counting states, entropy, equilibrium, chemical potential. Laws of thermodynamics. Cycles, heat engines, free energy. Partition function, Boltzmann statistics, Maxwell speed distribution, ideal gas in a box, Einstein model. Quantum statistical mechanics: classical vs. quantum distribution functions, fermions vs. bosons. Prerequisites: PHYSICS 61 & PHYSICS 63. Pre- or corequisite: MATH 53.

Terms: Spr | Units: 4 | UG Reqs: GER: DB-NatSci, WAY-FR, WAY-SMA | Grading: Letter or Credit/No Credit

Instructors: Manoharan, H. (PI)

**PHYSICS 67: Introduction to Laboratory Physics**

Methods of experimental design, data collection and analysis, statistics, and curve fitting in a laboratory setting. Experiments drawn from electronics, optics, heat, and modern physics. Lecture plus laboratory format. Required forPHYSICS 60 series Physics and Engineering Physics majors; recommended, in place of PHYSICS 44, for PHYSICS 40 series students who intend to major in Physics or Engineering Physics. Pre- or corequisite: PHYSICS 65 or PHYSICS 43.

Terms: Spr | Units: 2 | Grading: Satisfactory/No Credit

Instructors: Pam, R. (PI)

Other Resources: