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1 - 10 of 12 results for: MATH 20: Calculus

ENERGY 104: Sustainable Energy for 9 Billion (ENERGY 206)

This course explores the global transition to a sustainable global energy system. We will formulate and program simple models for future energy system pathways. We will explore the drivers of global energy demand and carbon emissions, as well as the technologies that can help us meet this demand sustainably. We will consider constraints on the large-scale deployment of technology and difficulties of a transition at large scales and over long time periods. Assignments will focus on building models of key aspects of the energy transition, including global, regional and sectoral energy demand and emissions as well as economics of change. Prerequisites: students should be comfortable with calculus and linear algebra (e.g. Math 20, Math 51) and be familiar with computer programming (e.g. CS106A, CS106B). We will use the Python programming language to build our models.
Terms: Spr | Units: 3 | UG Reqs: WAY-AQR

ENERGY 206: Sustainable Energy for 9 Billion (ENERGY 104)

This course explores the global transition to a sustainable global energy system. We will formulate and program simple models for future energy system pathways. We will explore the drivers of global energy demand and carbon emissions, as well as the technologies that can help us meet this demand sustainably. We will consider constraints on the large-scale deployment of technology and difficulties of a transition at large scales and over long time periods. Assignments will focus on building models of key aspects of the energy transition, including global, regional and sectoral energy demand and emissions as well as economics of change. Prerequisites: students should be comfortable with calculus and linear algebra (e.g. Math 20, Math 51) and be familiar with computer programming (e.g. CS106A, CS106B). We will use the Python programming language to build our models.
Terms: Spr | Units: 3

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, Win | Units: 3 | UG Reqs: GER:DB-EngrAppSci, WAY-SMA

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 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) in order to register for this course.
Terms: Aut, Win, Spr, Sum | Units: 3 | UG Reqs: GER:DB-Math, WAY-FR

MATH 20A: Calculus, ACE

Additional problem solving session for Math 20 guided by a course assistant. Concurrent enrollment in Math 20 required. Application required: https://engineering.stanford.edu/students-academics/equity-and-inclusion-initiatives/undergraduate-programs/additional-calculus
Terms: Aut, Win, Spr, Sum | Units: 1

MATH 21: Calculus

This course addresses a variety of topics centered around the theme of "calculus with infinite processes", largely the content of BC-level AP Calculus that isn't in the AB-level syllabus. It is needed throughout probability and statistics at all levels, as well as to understand approximation procedures that arise in all quantitative fields (including economics and computer graphics). After an initial review of limit rules, the course goes on to discuss sequences of numbers and of functions, as well as limits "at infinity" for each (needed for any sensible discussion of long-term behavior of a numerical process, such as: iterative procedures and complexity in computer science, dynamic models throughout economics, and repeated trials with data in any field). Integration is discussed for rational functions (a loose end from Math 20) and especially (improper) integrals for unbounded functions and "to infinity": this shows up in contexts as diverse as escape velocity for a rocket, the pres more »
This course addresses a variety of topics centered around the theme of "calculus with infinite processes", largely the content of BC-level AP Calculus that isn't in the AB-level syllabus. It is needed throughout probability and statistics at all levels, as well as to understand approximation procedures that arise in all quantitative fields (including economics and computer graphics). After an initial review of limit rules, the course goes on to discuss sequences of numbers and of functions, as well as limits "at infinity" for each (needed for any sensible discussion of long-term behavior of a numerical process, such as: iterative procedures and complexity in computer science, dynamic models throughout economics, and repeated trials with data in any field). Integration is discussed for rational functions (a loose end from Math 20) and especially (improper) integrals for unbounded functions and "to infinity": this shows up in contexts as diverse as escape velocity for a rocket, the present value of a perpetual yield asset, and important calculations in probability (including the famous "bell curve" and to understand why many statistical tests work as they do). The course then turns to infinite series (how to "sum" an infinite collection of numbers), some useful convergence and divergence rests for these, and the associated killer app: power series and their properties, as well as Taylor approximations, all of which provide the framework that underlies virtually all mathematical models used in any quantitative field.
Terms: Aut, Win, Spr, Sum | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR

PHYSICS 41: Mechanics

How are motions of objects in the physical world determined by laws of physics? Students learn to describe the motion of objects (kinematics) and then understand why motions have the form they do (dynamics). Emphasis on how the important physical principles in mechanics, such as conservation of momentum and energy for translational and rotational motion, follow from just three laws of nature: Newton's laws of motion. Distinction made between fundamental laws of nature and empirical rules that are useful approximations for more complex physics. Problems drawn from examples of mechanics in everyday life. Skills developed in verifying that derived results satisfy criteria for correctness, such as dimensional consistency and expected behavior in limiting cases. Discussions based on language of mathematics, particularly vector representations and operations, and calculus. Physical understanding fostered by peer interaction and demonstrations in lecture, and discussion sections based on inte more »
How are motions of objects in the physical world determined by laws of physics? Students learn to describe the motion of objects (kinematics) and then understand why motions have the form they do (dynamics). Emphasis on how the important physical principles in mechanics, such as conservation of momentum and energy for translational and rotational motion, follow from just three laws of nature: Newton's laws of motion. Distinction made between fundamental laws of nature and empirical rules that are useful approximations for more complex physics. Problems drawn from examples of mechanics in everyday life. Skills developed in verifying that derived results satisfy criteria for correctness, such as dimensional consistency and expected behavior in limiting cases. Discussions based on language of mathematics, particularly vector representations and operations, and calculus. Physical understanding fostered by peer interaction and demonstrations in lecture, and discussion sections based on interactive group problem solving. Spring 2020-21: Class will be taught remote synchronously in active learning format with much of the learning in smaller breakout rooms so class will not be recorded. Please enroll in a section that you can attend regularly. In order to register for this class all FROSH must complete the Physics Placement Diagnostic at https://physics.stanford.edu/academics/undergraduate-students/placement-diagnostic. Students who complete the Physics Placement Diagnostic by 3 PM (Pacific) on Friday will have their hold lifted over the weekend. Minimum prerequisites: High school physics and MATH 20 (or high school calculus if sufficiently rigorous). Minimum co-requisite: MATH 21 or equivalent. Since high school math classes vary widely, it is recommended that you take at least one math class at Stanford before or concurrently with taking Physics 41. In addition, it is recommended that you take Math 51 or CME 100 before taking the next course in the Physics 40 series, Physics 43.
Terms: Aut, Spr | Units: 4 | UG Reqs: GER: DB-NatSci, WAY-SMA

PHYSICS 41E: Mechanics, Concepts, Calculations, and Context

Physics 41E ( Physics 41 Extended) is an 5-unit version of Physics 41 (4 units) for students with little or no high school physics or calculus. Course topics and mathematical complexity are identical to Physics 41, but the extra classroom time allows students to engage with concepts, develop problem solving skills, and become fluent in mathematical tools that include vector representations and operations, and calculus. The course will use problems drawn from everyday life to explore important physical principles in mechanics, such as Newton's Laws of motion, equations of kinematics, and conservation of energy and momentum. Prerequisite: Math 19 or equivalent; Co-requisite: Math 20 or equivalent. In order to register for this class students must EITHER have already taken an introductory Physics class (20, 40, or 60 sequence) or have taken the Physics Placement Diagnostic at https://physics.stanford.edu/academics/undergraduate-students/placement-diagnostic. Enrollment is via permission number which can be obtained by filling in the application at https://stanforduniversity.qualtrics.com/jfe/form/SV_2fNzeSIjoYtKiln.
Last offered: Winter 2020 | UG Reqs: WAY-SMA

PHYSICS 45: Light and Heat

What is temperature? How do the elementary processes of mechanics, which are intrinsically reversible, result in phenomena that are clearly irreversible when applied to a very large number of particles, the ultimate example being life? In thermodynamics, students discover that the approach of classical mechanics is not sufficient to deal with the extremely large number of particles present in a macroscopic amount of gas. The paradigm of thermodynamics leads to a deeper understanding of real-world phenomena such as energy conversion and the performance limits of thermal engines. In optics, students see how a geometrical approach allows the design of optical systems based on reflection and refraction, while the wave nature of light leads to interference phenomena. The two approaches come together in understanding the diffraction limit of microscopes and telescopes. Discussions based on the language of mathematics, particularly calculus. Physical understanding fostered by peer interaction more »
What is temperature? How do the elementary processes of mechanics, which are intrinsically reversible, result in phenomena that are clearly irreversible when applied to a very large number of particles, the ultimate example being life? In thermodynamics, students discover that the approach of classical mechanics is not sufficient to deal with the extremely large number of particles present in a macroscopic amount of gas. The paradigm of thermodynamics leads to a deeper understanding of real-world phenomena such as energy conversion and the performance limits of thermal engines. In optics, students see how a geometrical approach allows the design of optical systems based on reflection and refraction, while the wave nature of light leads to interference phenomena. The two approaches come together in understanding the diffraction limit of microscopes and telescopes. Discussions based on the language of mathematics, particularly calculus. Physical understanding fostered by peer interaction and demonstrations in lecture, and discussion sections based on interactive group problem solving. In order to register for this class students must EITHER have already taken an introductory Physics class (20, 40, or 60 sequence) or have taken the Physics Placement Diagnostic at https://physics.stanford.edu/academics/undergraduate-students/placement-diagnostic. Prerequisite: PHYSICS 41 or equivalent. MATH 21 or MATH 51 or CME 100 or equivalent.
Terms: Aut | Units: 4 | UG Reqs: GER: DB-NatSci, WAY-SMA
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