## BIOE 42: Physical Biology

BIOE 42 is designed to introduce students to general engineering principles that have emerged from theory and experiments in biology. Topics covered will cover the scales from molecules to cells to organisms, including fundamental principles of entropy, diffusion, and continuum mechanics. These topics will link to several biological questions, including DNA organization, ligand binding, cytoskeletal mechanics, and the electromagnetic origin of nerve impulses. In all cases, students will learn to develop toy models that can explain quantitative measurements of the function of biological systems. Prerequisites:
MATH 19, 20, 21
CHEM 31A, B (or 31X),
PHYSICS 41; strongly recommended:
CS 106A,
CME 100 or
MATH 51, and
CME 106; or instructor approval.

Terms: Spr
| Units: 4
| UG Reqs: WAY-AQR, WAY-SMA

## 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)
;
Mishra, A. (PI)
;
Abbou, R. (TA)
;
Bougdal-Lambert, I. (TA)
;
Chen, E. (TA)
;
Chen, G. (TA)
;
Chiu, D. (TA)
;
Earley, E. (TA)
;
Fry, K. (TA)
;
Homma, Y. (TA)
;
Mantravadi, S. (TA)
;
Moore, L. (TA)
;
Romain, M. (TA)
;
Wang, A. (TA)
;
Warne, L. (TA)

## ENGR 21: Engineering of Systems

A high-level look at techniques for analyzing and designing complex, multidisciplinary engineering systems, such as aircraft, spacecraft, automobiles, power plants, cellphones, robots, biomedical devices, and many others. The need for multi-level design, modeling and simulation approaches, computation-based design, and hardware and software-in-the-loop simulations will be demonstrated through a variety of examples and case studies. Several aspects of system engineering will be applied to the design of large-scale interacting systems and contrasted with subsystems such as hydraulic systems, electrical systems, and brake systems. The use of design-thinking, story-boarding, mockups, sensitivity analysis, simulation, team-based design, and the development of presentation skills will be fostered through several realistic examples in several fields of engineering.

Terms: Win
| Units: 3

## 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)
;
Mishra, A. (PI)
;
Abbou, R. (TA)
;
Bougdal-Lambert, I. (TA)
;
Chen, E. (TA)
;
Chen, G. (TA)
;
Chiu, D. (TA)
;
Earley, E. (TA)
;
Fry, K. (TA)
;
Homma, Y. (TA)
;
Mantravadi, S. (TA)
;
Moore, L. (TA)
;
Romain, M. (TA)
;
Wang, A. (TA)
;
Warne, L. (TA)

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