printer friendly pageCME 100: Vector Calculus for Engineers (ENGR 154)
Computation and visualization using MATLAB. Differential vector calculus: vector-valued functions, analytic geometry in space, functions of several variables, partial derivatives, gradient, linearization, unconstrained maxima and minima, Lagrange multipliers and applications to trajectory simulation, least squares, and numerical optimization. Introduction to linear algebra: matrix operations, systems of algebraic equations with applications to coordinate transformations and equilibrium problems. Integral vector calculus: multiple integrals in Cartesian, cylindrical, and spherical coordinates, line integrals, scalar potential, surface integrals, Green's, divergence, and Stokes' theorems. Numerous examples and applications drawn from classical mechanics, fluid dynamics and electromagnetism. 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
Math 21). Placement diagnostic (recommendation non-binding) at:
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext.
Terms: Aut, Spr
| Units: 5
| UG Reqs: WAY-FR, GER:DB-Math
CME 102: Ordinary Differential Equations for Engineers (ENGR 155A)
Analytical and numerical methods for solving ordinary differential equations arising in engineering applications are presented. For analytical methods students learn to solve linear and non-linear first order ODEs; linear second order ODEs; and Laplace transforms. Numerical methods using MATLAB programming tool kit are also introduced to solve various types of ODEs including: first and second order ODEs, higher order ODEs, systems of ODEs, initial and boundary value problems, finite differences, and multi-step methods. This also includes accuracy and linear stability analyses of various numerical algorithms which are essential tools for the modern engineer. This class is foundational for professional careers in engineering and as a preparation for more advanced classes at the undergraduate and graduate levels. 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
Math 21). Placement diagnostic (recommendation non-binding) at:
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext.
Terms: Aut, Win
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Darve, E. (PI)
;
Le, H. (PI)
;
Ankeney, G. (TA)
;
Ayala Bellido, C. (TA)
;
Chen, C. (TA)
;
Diller, E. (TA)
;
Nzia Yotchoum, H. (TA)
CS 231N: Deep Learning for Computer Vision
Computer Vision has become ubiquitous in our society, with applications in search, image understanding, apps, mapping, medicine, drones, and self-driving cars. Core to many of these applications are visual recognition tasks such as image classification and object detection. Recent developments in neural network approaches have greatly advanced the performance of these state-of-the-art visual recognition systems. This course is a deep dive into details of neural-network based deep learning methods for computer vision. During this course, students will learn to implement, train and debug their own neural networks and gain a detailed understanding of cutting-edge research in computer vision. We will cover learning algorithms, neural network architectures, and practical engineering tricks for training and fine-tuning networks for visual recognition tasks.Prerequisites: Proficiency in Python - All class assignments will be in Python (and use numpy) (we provide a tutorial here for those who
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Computer Vision has become ubiquitous in our society, with applications in search, image understanding, apps, mapping, medicine, drones, and self-driving cars. Core to many of these applications are visual recognition tasks such as image classification and object detection. Recent developments in neural network approaches have greatly advanced the performance of these state-of-the-art visual recognition systems. This course is a deep dive into details of neural-network based deep learning methods for computer vision. During this course, students will learn to implement, train and debug their own neural networks and gain a detailed understanding of cutting-edge research in computer vision. We will cover learning algorithms, neural network architectures, and practical engineering tricks for training and fine-tuning networks for visual recognition tasks.Prerequisites: Proficiency in Python - All class assignments will be in Python (and use numpy) (we provide a tutorial here for those who aren't as familiar with Python). If you have a lot of programming experience but in a different language (e.g. C/C++/Matlab/Javascript) you will probably be fine.College Calculus, Linear Algebra (e.g.
MATH 19,
MATH 51) -You should be comfortable taking derivatives and understanding matrix vector operations and notation. Basic Probability and Statistics (e.g.
CS 109 or other stats course) -You should know basics of probabilities, gaussian distributions, mean, standard deviation, etc.
Terms: Spr
| Units: 3-4
Instructors:
Adeli, E. (PI)
;
Li, F. (PI)
ENGR 15: Dynamics
The application of Newton's Laws to solve 2-D and 3-D static and dynamic problems, particle and rigid body dynamics, freebody diagrams, and equations of motion, with application to mechanical, biomechanical, and aerospace systems. Computer numerical solution and dynamic response. Prerequisites: Calculus (differentiation and integration) such as
Math 19, 20; and
ENGR 14 (statics and strength) or a mechanics course in physics such as
PHYSICS 41.
Terms: Aut
| Units: 3
| UG Reqs: GER:DB-EngrAppSci, WAY-SMA
ENGR 154: Vector Calculus for Engineers (CME 100)
Computation and visualization using MATLAB. Differential vector calculus: vector-valued functions, analytic geometry in space, functions of several variables, partial derivatives, gradient, linearization, unconstrained maxima and minima, Lagrange multipliers and applications to trajectory simulation, least squares, and numerical optimization. Introduction to linear algebra: matrix operations, systems of algebraic equations with applications to coordinate transformations and equilibrium problems. Integral vector calculus: multiple integrals in Cartesian, cylindrical, and spherical coordinates, line integrals, scalar potential, surface integrals, Green's, divergence, and Stokes' theorems. Numerous examples and applications drawn from classical mechanics, fluid dynamics and electromagnetism. 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
Math 21). Placement diagnostic (recommendation non-binding) at:
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext.
Terms: Aut, Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR
ENGR 155A: Ordinary Differential Equations for Engineers (CME 102)
Analytical and numerical methods for solving ordinary differential equations arising in engineering applications are presented. For analytical methods students learn to solve linear and non-linear first order ODEs; linear second order ODEs; and Laplace transforms. Numerical methods using MATLAB programming tool kit are also introduced to solve various types of ODEs including: first and second order ODEs, higher order ODEs, systems of ODEs, initial and boundary value problems, finite differences, and multi-step methods. This also includes accuracy and linear stability analyses of various numerical algorithms which are essential tools for the modern engineer. This class is foundational for professional careers in engineering and as a preparation for more advanced classes at the undergraduate and graduate levels. 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
Math 21). Placement diagnostic (recommendation non-binding) at:
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext.
Terms: Aut, Win, Sum
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Darve, E. (PI)
;
Le, H. (PI)
;
Ankeney, G. (TA)
;
Ayala Bellido, C. (TA)
;
Chen, C. (TA)
;
Diller, E. (TA)
;
Lu-Yang, J. (TA)
;
Nzia Yotchoum, H. (TA)
ENGR 199A: Additional Calculus for Engineers
Additional problem solving practice for the calculus courses. Sections are designed to allow students to acquire a deeper understanding of calculus and its applications, work collaboratively, and develop a mastery of the material. Limited enrollment, permission of instructor required. Concurrent enrollment in
MATH 19, 20, 52, or 53 required
Terms: Win, Spr
| Units: 1
| Repeatable
for credit
Instructors:
Andrade, L. (PI)
MATH 19: Calculus
Introduction to differential calculus of functions of one variable. Review of elementary functions (including exponentials and logarithms), limits, rates of change, the derivative and its properties, applications of the derivative. Prerequisites: periodic trigonometric functions, advanced algebra, and analysis of elementary functions (including exponentials and logarithms). You must have taken the math placement diagnostic (offered through the Math Department website:
https://mathematics.stanford.edu/academics/math-placement) in order to register for this course.
Terms: Aut, Win
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Taylor, C. (PI)
;
Wickham, Z. (PI)
;
Fournier, N. (TA)
...
more instructors for MATH 19 »
Instructors:
Taylor, C. (PI)
;
Wickham, Z. (PI)
;
Fournier, N. (TA)
;
Kotchum, K. (TA)
;
Schildkraut, C. (TA)
;
Sriram, P. (TA)
;
Walters, N. (TA)
MATH 19ACE: Calculus, ACE
Additional problem solving session for
Math 19 guided by a course assistant. Concurrent enrollment in
Math 19 required. Application required:
https://engineering.stanford.edu/students-academics/equity-and-inclusion-initiatives/undergraduate-programs/additional-calculus
Terms: Aut, Win
| Units: 1
MATH 20: Calculus
The definite integral, Riemann sums, antiderivatives, the Fundamental Theorem of Calculus. Integration by substitution and by parts. Area between curves, and volume by slices, washers, and shells. Initial-value problems, exponential and logistic models, direction fields, and parametric curves. Prerequisite:
Math 19 or equivalent. If you have not previously taken a calculus course at Stanford then you must have taken the math placement diagnostic (offered through the Math Department website:
https://mathematics.stanford.edu/academics/math-placement) in order to register for this course.
Terms: Aut, Win, Spr
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Kotas, J. (PI)
;
Lai, Y. (PI)
;
Lee, S. (PI)
;
Wickham, Z. (PI)
;
Campos Vargas, J. (TA)
;
Gupta, A. (TA)
;
Su, S. (TA)
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