## ENGR 199A: Additional Calculus for Engineers

Additional problem solving practice for the calculus courses. Sections are designed to allow students to acquire a deeper understanding of calculus and its applications, work collaboratively, and develop a mastery of the material. Limited enrollment, permission of instructor required. Concurrent enrollment in
MATH 19, 20, 52, or 53 required

Terms: Win, Spr
| Units: 1
| Repeatable for credit

Instructors:
Andrade, L. (PI)

## MATH 20: Calculus

The definite integral, Riemann sums, antiderivatives, the Fundamental Theorem of Calculus, and the Mean Value Theorem for integrals. Integration by substitution and by parts. Area between curves, and volume by slices, washers, and shells. Initial-value problems, exponential and logistic models, direction fields, and parametric curves. Prerequisite:
Math 19 or equivalent. If you have not previously taken a calculus course at Stanford then you must have taken the math placement diagnostic (offered through the Math Department website) in order to register for this course.

Terms: Aut, Win, Spr
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Grzegrzolka, P. (PI)
;
Lucianovic, M. (PI)
;
Schaeffer, G. (PI)
...
more instructors for MATH 20 »

Instructors:
Grzegrzolka, P. (PI)
;
Lucianovic, M. (PI)
;
Schaeffer, G. (PI)
;
Chen, S. (TA)
;
Fushida-Hardy, S. (TA)
;
Lim, B. (TA)
;
Mackey, W. (TA)
;
Marsden, M. (TA)
;
McConnell, S. (TA)
;
Ortiz, J. (TA)

## MATH 21: Calculus

Review of limit rules. Sequences, functions, limits at infinity, and comparison of growth of functions. Review of integration rules, integrating rational functions, and improper integrals. Infinite series, special examples, convergence and divergence tests (limit comparison and alternating series tests). Power series and interval of convergence, Taylor polynomials, Taylor series and applications. Prerequisite:
Math 20 or equivalent. If you have not previously taken a calculus course at Stanford then you must have taken the math placement diagnostic (offered through the Math Department website) in order to register for this course.

Terms: Aut, Win, Spr, Sum
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Datta, I. (PI)
;
Falcone, P. (PI)
;
Grzegrzolka, P. (PI)
...
more instructors for MATH 21 »

Instructors:
Datta, I. (PI)
;
Falcone, P. (PI)
;
Grzegrzolka, P. (PI)
;
Khu, D. (PI)
;
Kim, G. (PI)
;
Lim, B. (PI)
;
Schaeffer, G. (PI)
;
Zhang, S. (PI)
;
Zhou, Z. (PI)

## 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 inte
more »

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. In order to register for this class students must EITHER have already taken an introductory Physics class (20, 40, or 60 sequence) or have taken the Physics Placement Diagnostic at
https://physics.stanford.edu/academics/undergraduate-students/placement-diagnostic. Prerequisite: High school physics and
MATH 20 or
MATH 51 or
CME 100 or equivalent. Minimum co-requisite:
MATH 21 or equivalent.

Terms: Win
| Units: 4
| UG Reqs: GER: DB-NatSci, WAY-SMA

Instructors:
Lee, Y. (PI)
;
Breidenbach, A. (TA)
;
DeRocco, W. (TA)
...
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Instructors:
Lee, Y. (PI)
;
Breidenbach, A. (TA)
;
DeRocco, W. (TA)
;
Frenkel, A. (TA)
;
Hulcher, Z. (TA)
;
Pistunova, K. (TA)
;
Rahman, A. (TA)
;
Saykin, D. (TA)
;
Thompson, J. (TA)
;
Timcheck, J. (TA)
;
Yang, S. (TA)
;
Yu, T. (TA)
;
Zamora, A. (TA)

## PHYSICS 41E: Mechanics, Concepts, Calculations, and Context

Physics 41E (
Physics 41 Extended) is an 5-unit version of
Physics 41 (4 units) for students with little or no high school physics or calculus. Course topics and mathematical complexity are identical to
Physics 41, but the extra classroom time allows students to engage with concepts, develop problem solving skills, and become fluent in mathematical tools that include vector representations and operations, and calculus. The course will use problems drawn from everyday life to explore important physical principles in mechanics, such as Newton's Laws of motion, equations of kinematics, and conservation of energy and momentum. Prerequisite:
Math 19 or equivalent; Co-requisite:
Math 20 or equivalent. In order to register for this class students must EITHER have already taken an introductory Physics class (20, 40, or 60 sequence) or have taken the Physics Placement Diagnostic at
https://physics.stanford.edu/academics/undergraduate-students/placement-diagnostic. Enrollment is via permission number which can be obtained by filling in the application at
https://stanforduniversity.qualtrics.com/jfe/form/SV_2fNzeSIjoYtKiln.

Terms: Win
| Units: 5
| UG Reqs: WAY-SMA

Instructors:
Burkholder, E. (PI)
;
Church, S. (PI)
;
Wieman, C. (PI)
...
more instructors for PHYSICS 41E »

Instructors:
Burkholder, E. (PI)
;
Church, S. (PI)
;
Wieman, C. (PI)
;
Kamat, R. (TA)
;
Mangram, W. (TA)
;
Mullane, S. (TA)
;
Widder, A. (TA)
;
Yu, C. (TA)

## 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. In o
more »

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. In order to register for this class students must have taken the Physics Placement Diagnostic at
https://physics.stanford.edu/academics/undergraduate-students/placement-diagnostic unless they have already taken an introductory Physics class (20, 40, or 60 sequence) at Stanford. Prerequisite:
PHYSICS 41 or equivalent.
MATH 21 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

Instructors:
Kasevich, M. (PI)

## 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
more »

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. In order to register for this class students must EITHER have already taken an introductory Physics class (20, 40, or 60 sequence) or have taken the Physics Placement Diagnostic at
https://physics.stanford.edu/academics/undergraduate-students/placement-diagnostic. Prerequisite:
PHYSICS 41 or equivalent.
MATH 21 or
MATH 51 or
CME 100 or equivalent.

Terms: Aut
| Units: 4
| UG Reqs: GER: DB-NatSci, WAY-SMA

Instructors:
Hartnoll, S. (PI)
;
Cook, C. (TA)
;
Jonay, C. (TA)
...
more instructors for PHYSICS 45 »

Instructors:
Hartnoll, S. (PI)
;
Cook, C. (TA)
;
Jonay, C. (TA)
;
Mukhopadhyay, P. (TA)
;
O'Beirne, A. (TA)
;
Pistunova, K. (TA)
;
Prabhu, A. (TA)
;
Yuan, A. (TA)
;
Zamora, A. (TA)

## 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. In order to register for this class students must EITHER have already taken an introductory Physics class (20, 40, or 60 sequence) or have taken the Physics Placement Diagnostic at
https://physics.stanford.edu/academics/undergraduate-students/placement-diagnostic. Recommended prerequisites: Mastery of mechanics at the level of AP Physics C and AP Calculus BC or equivalent. Corequisite:
MATH 51 or
MATH 61CM or
MATH 61DM.

Terms: Aut
| Units: 4
| UG Reqs: GER: DB-NatSci, WAY-FR, WAY-SMA

Instructors:
Burchat, P. (PI)
;
Coppess, K. (TA)
;
Giurgica-Tiron, T. (TA)
...
more instructors for PHYSICS 61 »

Instructors:
Burchat, P. (PI)
;
Coppess, K. (TA)
;
Giurgica-Tiron, T. (TA)
;
Kang, Q. (TA)
;
Park, J. (TA)

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