## CME 100: Vector Calculus for Engineers (ENGR 154)

Computation and visualization using MATLAB. Differential vector calculus: analytic geometry in space, functions of several variables, partial derivatives, gradient, unconstrained maxima and minima, Lagrange multipliers. Introduction to linear algebra: matrix operations, systems of algebraic equations, methods of solution and applications. Integral vector calculus: multiple integrals in Cartesian, cylindrical, and spherical coordinates, line integrals, scalar potential, surface integrals, Green's, divergence, and Stokes' theorems. Examples and applications drawn from various engineering fields. Prerequisites: knowledge of single-variable calculus equivalent to the content of
Math 19-21 (e.g., 5 on Calc BC, 4 on Calc BC with
Math 21, 5 on Calc AB with
Math21). Placement diagnostic (recommendation non binding) at:(
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext).

Terms: Aut, Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Khayms, V. (PI)
;
Le, H. (PI)
;
Abbou, R. (TA)
;
Burugupalli, P. (TA)
;
Carranza, A. (TA)
;
Chen, G. (TA)
;
Deshpande, S. (TA)
;
Infanger, A. (TA)
;
Jia, Q. (TA)
;
Liu, X. (TA)
;
Morvan, T. (TA)
;
Radif, D. (TA)
;
Rowley, J. (TA)
;
Saad, N. (TA)
;
Xin, D. (TA)

## CME 102: Ordinary Differential Equations for Engineers (ENGR 155A)

Analytical and numerical methods for solving ordinary differential equations arising in engineering applications: Solution of initial and boundary value problems, series solutions, Laplace transforms, and nonlinear equations; numerical methods for solving ordinary differential equations, accuracy of numerical methods, linear stability theory, finite differences. Introduction to MATLAB programming as a basic tool kit for computations. Problems from various engineering fields.Prerequisites: knowledge of single-variable calculus equivalent to the content of
Math 19-21 (e.g., 5 on Calc BC, 4 on Calc BC with
Math 21, 5 on Calc AB with
Math21). Placement diagnostic (recommendation non binding) at:(
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext). Recommended:
CME100.

Terms: Aut, Win, Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Le, H. (PI)
;
Carranza, A. (TA)
;
Cremers, C. (TA)
;
Liu, X. (TA)
;
Morvan, T. (TA)
;
Petitdemange, R. (TA)
;
Rangarajan, A. (TA)
;
Regev, S. (TA)
;
Weiss, B. (TA)

## ENGR 154: Vector Calculus for Engineers (CME 100)

Computation and visualization using MATLAB. Differential vector calculus: analytic geometry in space, functions of several variables, partial derivatives, gradient, unconstrained maxima and minima, Lagrange multipliers. Introduction to linear algebra: matrix operations, systems of algebraic equations, methods of solution and applications. Integral vector calculus: multiple integrals in Cartesian, cylindrical, and spherical coordinates, line integrals, scalar potential, surface integrals, Green's, divergence, and Stokes' theorems. Examples and applications drawn from various engineering fields. Prerequisites: knowledge of single-variable calculus equivalent to the content of
Math 19-21 (e.g., 5 on Calc BC, 4 on Calc BC with
Math 21, 5 on Calc AB with
Math21). Placement diagnostic (recommendation non binding) at:(
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext).

Terms: Aut, Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Khayms, V. (PI)
;
Le, H. (PI)
;
Abbou, R. (TA)
;
Burugupalli, P. (TA)
;
Carranza, A. (TA)
;
Chen, G. (TA)
;
Deshpande, S. (TA)
;
Infanger, A. (TA)
;
Jia, Q. (TA)
;
Liu, X. (TA)
;
Morvan, T. (TA)
;
Radif, D. (TA)
;
Rowley, J. (TA)
;
Saad, N. (TA)
;
Xin, D. (TA)

## ENGR 155A: Ordinary Differential Equations for Engineers (CME 102)

Analytical and numerical methods for solving ordinary differential equations arising in engineering applications: Solution of initial and boundary value problems, series solutions, Laplace transforms, and nonlinear equations; numerical methods for solving ordinary differential equations, accuracy of numerical methods, linear stability theory, finite differences. Introduction to MATLAB programming as a basic tool kit for computations. Problems from various engineering fields.Prerequisites: knowledge of single-variable calculus equivalent to the content of
Math 19-21 (e.g., 5 on Calc BC, 4 on Calc BC with
Math 21, 5 on Calc AB with
Math21). Placement diagnostic (recommendation non binding) at:(
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext). Recommended:
CME100.

Terms: Aut, Win, Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Le, H. (PI)
;
Carranza, A. (TA)
;
Cremers, C. (TA)
...
more instructors for ENGR 155A »

Instructors:
Le, H. (PI)
;
Carranza, A. (TA)
;
Cremers, C. (TA)
;
Liu, X. (TA)
;
Morvan, T. (TA)
;
Petitdemange, R. (TA)
;
Rangarajan, A. (TA)
;
Regev, S. (TA)
;
Weiss, B. (TA)

## 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 19: Calculus

Introduction to differential calculus of functions of one variable. Review of elementary functions (including exponentials and logarithms), limits, rates of change, the derivative and its properties, applications of the derivative. Prerequisites: trigonometry, advanced algebra, and analysis of elementary functions (including exponentials and logarithms). You must have taken the math placement diagnostic (offered through the Math Department website) in order to register for this course.

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

Instructors:
Chetard, B. (PI)
;
La, J. (PI)
;
Schaeffer, G. (PI)
;
Falcone, P. (TA)
;
Li, Z. (TA)
;
Marsden, M. (TA)
;
Stavrianidi, A. (TA)
;
Zhou, Y. (TA)

## 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)
;
Zhang, S. (PI)
;
Chen, S. (TA)
;
Fushida-Hardy, S. (TA)
;
Lim, B. (TA)
;
Mackey, W. (TA)
;
Marsden, M. (TA)
;
McConnell, S. (TA)
;
Ortiz, J. (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)

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