## BIOE 80: Introduction to Bioengineering (Engineering Living Matter) (ENGR 80)

Students completing BIOE.80 should have a working understanding for how to approach the systematic engineering of living systems to benefit all people and the planet. Our main goals are (1) to help students learn ways of thinking about engineering living matter and (2) to empower students to explore the broader ramifications of engineering life. Specific concepts and skills covered include but are not limited to: capacities of natural life on Earth; scope of the existing human-directed bioeconomy; deconstructing complicated problems; reaction & diffusion systems; microbial human anatomy; conceptualizing the engineering of biology; how atoms can be organized to make molecules; how to print DNA from scratch; programming genetic sensors, logic, & actuators; biology beyond molecules (photons, electrons, etc.); what constraints limit what life can do?; what will be the major health challenges in 2030?; how does what we want shape bioengineering?; who should choose and realize various competing bioengineering futures?

Terms: Spr
| Units: 4
| UG Reqs: GER:DB-EngrAppSci, WAY-FR

Instructors:
Endy, D. (PI)
;
Liphardt, J. (PI)
;
Abbott, T. (TA)
;
Bodner, K. (TA)
;
Brennock, P. (TA)
;
Jackson-Smith, A. (TA)
;
Kipniss, N. (TA)
;
Torng, W. (TA)
;
Trevino, A. (TA)
;
Yang, L. (TA)

## BIOHOPK 174H: Experimental Design and Probability (BIOHOPK 274H)

(Graduate students register for 274H.) Variability is an integral part of biology. Introduction to probability and its use in designing experiments to address biological problems. Focus is on analysis of variance, when and how to use it, why it works, and how to interpret the results. Design of complex, but practical, asymmetrical experiments and environmental impact studies, and regression and analysis of covariance. Computer-based data analysis. Prerequisite: Biology core or consent of instructor.

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

Instructors:
Watanabe, J. (PI)

## BIOHOPK 177H: Dynamics and Management of Marine Populations (BIOHOPK 277H)

(Graduate students register for 277H.) Course examines the ecological factors and processes that control natural and harvested marine populations. Course emphasizes mathematical models as tools to assess the dynamics of populations and to derive projections of their demographic fate under different management scenarios. Course objectives will be met by a combination of theoretical lectures, assigned readings and class discussions, case study analysis and interactive computer sessions.

Terms: Win
| Units: 4
| UG Reqs: WAY-AQR, WAY-FR
| Repeatable for credit

Instructors:
De Leo, G. (PI)

## CEE 195: Fundamentals of Structural Geology (GS 111)

Techniques for mapping using GPS and differential geometry to characterize structures; dimensional analysis and scaling relations; kinematics of deformation and flow; measurement and analysis of stress; elastic deformation and properties of rock; brittle deformation including fracture and faulting; linear viscous flow including folding and magma dynamics; model development and methodology. Models of tectonic processes are constructed and solutions visualized using MATLAB. Prerequisites:
GS 1,
MATH 51

Last offered: Winter 2016
| UG Reqs: WAY-FR, 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: 10 units of AP credit (Calc BC with 4 or 5, or Calc AB with 5), or
Math 41 and 42.

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

Instructors:
Khayms, V. (PI)
;
Le, H. (PI)
;
Aboumrad, G. (TA)
;
Bhargava, P. (TA)
;
DePaul, G. (TA)
;
Fadavi, D. (TA)
;
Fournier-Bidoz, E. (TA)
;
Gao, P. (TA)
;
Genin, M. (TA)
;
Hegde, V. (TA)
;
Krason, M. (TA)
;
Lakshman, V. (TA)
;
Lenain, R. (TA)
;
Sanchez, S. (TA)
;
Storchan, V. (TA)
;
Suresh, S. (TA)
;
Westhoff, P. (TA)
;
Yang, F. (TA)
;
shirian, y. (TA)

## CME 100A: Vector Calculus for Engineers, ACE

Students attend
CME100/ENGR154 lectures with additional recitation sessions; two to four hours per week, emphasizing engineering mathematical applications and collaboration methods. Enrollment by department permission only. Prerequisite: must be enrolled in the regular
CME100-01 or 02. Application at:
https://engineering.stanford.edu/students/programs/engineering-diversity-programs/additional-calculus-engineers

Terms: Aut, Win, Spr
| Units: 6
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Khayms, V. (PI)
;
Le, H. (PI)
;
Aboumrad, G. (TA)
;
Bhargava, P. (TA)
;
DePaul, G. (TA)
;
Fadavi, D. (TA)
;
Fournier-Bidoz, E. (TA)
;
Gao, P. (TA)
;
Genin, M. (TA)
;
Hegde, V. (TA)
;
Krason, M. (TA)
;
Lakshman, V. (TA)
;
Lenain, R. (TA)
;
Sanchez, S. (TA)
;
Storchan, V. (TA)
;
Suresh, S. (TA)
;
Westhoff, P. (TA)
;
Yang, F. (TA)
;
shirian, y. (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. Prerequisite: 10 units of AP credit (Calc BC with 4 or 5, or Calc AB with 5), or
Math 41 and 42. Recommended:
CME100.

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

Instructors:
Darve, E. (PI)
;
Le, H. (PI)
;
Baalbaki, W. (TA)
;
DePaul, G. (TA)
;
Gnanasekaran, A. (TA)
;
Lorenzetti, J. (TA)
;
Martinez, J. (TA)
;
Moon, T. (TA)
;
Najmabadi, C. (TA)
;
Sanchez, S. (TA)
;
Simpson, C. (TA)
;
Suresh, S. (TA)
;
Westhoff, P. (TA)

## CME 102A: Ordinary Differential Equations for Engineers, ACE

Students attend
CME102/ENGR155A lectures with additional recitation sessions; two to four hours per week, emphasizing engineering mathematical applications and collaboration methods. Prerequisite: students must be enrolled in the regular section (
CME102) prior to submitting application at:n
https://engineering.stanford.edu/students/programs/engineering-diversity-programs/additional-calculus-engineers

Terms: Aut, Win, Spr
| Units: 6
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Darve, E. (PI)
;
Le, H. (PI)
;
Baalbaki, W. (TA)
;
Darve, E. (TA)
;
DePaul, G. (TA)
;
Lorenzetti, J. (TA)
;
Martinez, J. (TA)
;
Moon, T. (TA)
;
Najmabadi, C. (TA)
;
Sanchez, S. (TA)
;
Simpson, C. (TA)
;
Suresh, S. (TA)
;
Westhoff, P. (TA)

## CME 103: Introduction to Matrix Methods (EE 103)

Introduction to applied linear algebra with emphasis on applications. Vectors, norm, and angle; linear independence and orthonormal sets; applications to document analysis. Clustering and the k-means algorithm. Matrices, left and right inverses, QR factorization. Least-squares and model fitting, regularization and cross-validation. Constrained and nonlinear least-squares. Applications include time-series prediction, tomography, optimal control, and portfolio optimization. Prerequisites:
MATH 51 or
CME 100, and basic knowledge of computing (
CS 106A is more than enough, and can be taken concurrently).
EE103/CME103 and
Math 104 cover complementary topics in applied linear algebra. The focus of EE103 is on a few linear algebra concepts, and many applications; the focus of
Math 104 is on algorithms and concepts.

Terms: Aut
| Units: 4-5
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR

Instructors:
Boyd, S. (PI)
;
Angeris, G. (TA)
;
Busseti, E. (TA)
;
Fan, L. (TA)
;
Hwang, J. (TA)
;
Leung, K. (TA)
;
Mu, R. (TA)
;
Nishimura, M. (TA)
;
Park, D. (TA)
;
Pathak, R. (TA)
;
Prasad, V. (TA)
;
Tea-mangkornpan, P. (TA)

## CME 104: Linear Algebra and Partial Differential Equations for Engineers (ENGR 155B)

Linear algebra: matrix operations, systems of algebraic equations, Gaussian elimination, undetermined and overdetermined systems, coupled systems of ordinary differential equations, eigensystem analysis, normal modes. Fourier series with applications, partial differential equations arising in science and engineering, analytical solutions of partial differential equations. Numerical methods for solution of partial differential equations: iterative techniques, stability and convergence, time advancement, implicit methods, von Neumann stability analysis. Examples and applications from various engineering fields. Prerequisite:
CME 102/
ENGR 155A.

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

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