## CME 10A: Explorations in Calculus

In this course, we will explore the big ideas of calculus, through open, visual, and creative mathematics tasks. Students will be invited to think about what calculus is all about and why it matters. This course will benefit all students ¿ whether or not you have taken a calculus class. Students will work collaboratively in problem solving through a supportive community of mathematics learners. This course has three goals ¿ to give you a different mathematics experience that could reshape your relationship with mathematics, to provide you with a basis for success in future courses at Stanford, and to teach you the important ideas that pervade calculus. As a community, we will cultivate the positive ideas and mindsets that shape productive learning.

Last offered: Summer 2019

## 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)
;
Bescos Alapont, G. (TA)
;
Burugupalli, P. (TA)
;
Carranza, A. (TA)
;
Chen, G. (TA)
;
Deshpande, S. (TA)
;
Infanger, A. (TA)
;
Jia, Q. (TA)
;
Lerner, S. (TA)
;
Liu, X. (TA)
;
Morvan, T. (TA)
;
Radif, D. (TA)
;
Rowley, J. (TA)
;
Saad, N. (TA)
;
Xin, D. (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, Spr
| Units: 6
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Khayms, V. (PI)
;
Le, H. (PI)
;
Abbou, R. (TA)
;
Bescos Alapont, G. (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)

## 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:
Le, H. (PI)

## 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. Undergraduate students should enroll for 5 units, and graduate students should enroll for 3 units. 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, Win, Sum
| Units: 5
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR

Instructors:
Nasiri Mahalati, R. (PI)
;
Osgood, B. (PI)
;
Tse, D. (PI)
...
more instructors for CME 103 »

Instructors:
Nasiri Mahalati, R. (PI)
;
Osgood, B. (PI)
;
Tse, D. (PI)
;
Chang, S. (TA)
;
Degleris, A. (TA)
;
Gable, N. (TA)
;
Jani, T. (TA)
;
Khullar, P. (TA)
;
Lambert, S. (TA)
;
Ramesh, R. (TA)
;
Spear, L. (TA)
;
Toh, E. (TA)
;
Varanasi, V. (TA)
;
Yen, J. (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

Instructors:
Khayms, V. (PI)
;
Saad, N. (TA)

## 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 (
CME104) 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

Instructors:
Khayms, V. (PI)
;
Saad, N. (TA)

## 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)
;
Caron, P. (TA)
;
Jambulapati, A. (TA)
...
more instructors for CME 106 »

Instructors:
Khayms, V. (PI)
;
Caron, P. (TA)
;
Jambulapati, A. (TA)
;
Lerner, S. (TA)
;
Morvan, T. (TA)
;
Radif, D. (TA)
;
Rowley, J. (TA)
;
Saad, N. (TA)
;
Veron Vialard, J. (TA)

## CME 107: Introduction to Machine Learning (EE 104)

Introduction to machine learning. Formulation of supervised and unsupervised learning problems. Regression and classification. Data standardization and feature engineering. Loss function selection and its effect on learning. Regularization and its role in controlling complexity. Validation and overfitting. Robustness to outliers. Simple numerical implementation. Experiments on data from a wide variety of engineering and other disciplines. Undergraduate students should enroll for 5 units, and graduate students should enroll for 3 units. Prerequisites:
EE 103;
EE 178 or
CS 109; CS106A or equivalent.

Terms: Spr
| Units: 3-5

Instructors:
Lall, S. (PI)
;
Tuck, J. (TA)

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