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: WAYAQR, WAYSMA

Grading: Letter (ABCD/NP)
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: 10 units of AP credit (Calc BC with 5, or Calc AB with 5 or placing out of the single variable math placement test:
https://exploredegreesnextyear.stanford.edu/undergraduatedegreesandprograms/#aptextt), or
Math 1921.
Terms: Aut, Win, Spr

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Khayms, V. (PI)
;
Le, H. (PI)
ENGR 21: Engineering of Systems
A highlevel 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 multilevel design, modeling and simulation approaches, computationbased design, and hardware and softwareintheloop simulations will be demonstrated through a variety of examples and case studies. Several aspects of system engineering will be applied to the design of largescale interacting systems and contrasted with subsystems such as hydraulic systems, electrical systems, and brake systems. The use of designthinking, storyboarding, mockups, sensitivity analysis, simulation, teambased design, and the development of presentation skills will be fostered through several realistic examples in several fields of engineering.
Terms: Win

Units: 3

Grading: Letter (ABCD/NP)
Instructors:
Alonso, J. (PI)
;
Maier, W. (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: 10 units of AP credit (Calc BC with 5, or Calc AB with 5 or placing out of the single variable math placement test:
https://exploredegreesnextyear.stanford.edu/undergraduatedegreesandprograms/#aptextt), or
Math 1921.
Terms: Aut, Win, Spr

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Khayms, V. (PI)
;
Le, H. (PI)
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