## CME 20Q: Computational Modeling for Future Leaders

Preference to sophomores. How can we harness and exploit the power of computational modeling? What responsibilities are there in developing and using computer models? In this course we will analyze fundamental issues inherent to computational modeling such as uncertainty, predictability, error, and resolution. We will furthermore examine the social context of computational modeling including the public perception of computational models, how computer modeling impacts politics and policy, and how politics and policy, in turn, influence computer modeling.

Terms: Aut
| Units: 3

Instructors:
Minion, M. (PI)

## 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-makorn, 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

## CME 104A: Linear Algebra and Partial Differential Equations for Engineers, ACE

Students attend
CME104/ENGR155B 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:
https://engineering.stanford.edu/students/programs/engineering-diversity-programs/additional-calculus-engineers

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

## CME 106: Introduction to Probability and Statistics for Engineers (ENGR 155C)

Probability: random variables, independence, and conditional probability; discrete and continuous distributions, moments, distributions of several random variables. Topics in mathematical statistics: random sampling, point estimation, confidence intervals, hypothesis testing, non-parametric tests, regression and correlation analyses; applications in engineering, industrial manufacturing, medicine, biology, and other fields. Prerequisite:
CME 100/ENGR154 or
MATH 51 or 52.

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

Instructors:
Khayms, V. (PI)
;
An, J. (TA)
;
Ayoul, T. (TA)
;
Fournier-Bidoz, E. (TA)
;
Gao, P. (TA)
;
Genin, M. (TA)
;
Krason, M. (TA)
;
Lakshman, V. (TA)
;
Slottje, A. (TA)

## CME 108: Introduction to Scientific Computing (MATH 114)

Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floating-point arithmetic, nonlinear equations, numerical solution of systems of algebraic equations, banded matrices, least squares, unconstrained optimization, polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, truncation error, numerical stability for time dependent problems and stiffness. Implementation of numerical methods in MATLAB programming assignments. Prerequisites:
MATH 51, 52, 53; prior programming experience (MATLAB or other language at level of
CS 106A or higher).

Terms: Win, Sum
| Units: 3-4
| UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR

Instructors:
Le, H. (PI)
;
Ying, L. (PI)
;
Aboumrad, G. (TA)
;
Horel, E. (TA)
;
Li, Y. (TA)
;
Lyman, L. (TA)

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