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# 1 - 8 of 8 results for: MATH 20: Calculus

## CHEM 4:Biochemistry: Chemistry of Life

A four-week intensive biochemistry course from a chemical perspective. The chemical basis of life, including the biomolecular chemistry of amino acids, proteins, carbohydrates, lipids, and nucleic acids, as well as enzyme kinetics and mechanisms, thermodynamics, and core metabolism, control, and regulation. Recitation includes group work on case studies that support the daily lecture material. Prerequisites: CHEM 33, 35, 131 or 1 year of organic chemistry; Math 19, 20, 21 or 41, 42 or 1 year of single variable calculus.
Last offered: Summer 2018

## CHEM 31X:Chemical Principles Accelerated

Accelerated; for students with substantial chemistry background. Chemical equilibria concepts, equilibrium constants, acids and bases, chemical thermodynamics, quantum concepts, models of ionic and covalent bonding, atomic and molecular orbital theory, periodicity, and bonding properties of matter. Recitation. Prerequisites: AP chemistry score of 5 or passing score on chemistry placement test, and AP Calculus AB score of 4 or Math 20. Recommended: high school physics.
Terms: Aut | Units: 5 | UG Reqs: GER: DB-NatSci, 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

## MATH 20:Calculus

The definite integral, Riemann sums, antiderivatives, the Fundamental Theorem of Calculus, and the Mean Value Theorem for integrals. 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 | Units: 3 | UG Reqs: GER:DB-Math, WAY-FR

## MATH 21:Calculus

Review of limit rules. Sequences, functions, limits at infinity, and comparison of growth of functions. Review of integration rules, integrating rational functions, and improper integrals. Infinite series, special examples, convergence and divergence tests (limit comparison and alternating series tests). Power series and interval of convergence, Taylor polynomials, Taylor series and applications. Prerequisite: Math 20 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 | 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 interactive group problem solving. Prerequisite: High school physics and MATH 20 or MATH 51 or CME 100 or equivalent. Minimum co-requisite: MATH 21 or equivalent.
Terms: Win | 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. Enrollment is via permission number which can be obtained by filling in the application at https://stanforduniversity.qualtrics.com/jfe/form/SV_6gpr3SkM76WNDVP.
Terms: Win | Units: 5 | UG Reqs: WAY-SMA

## SYMSYS 265:Quantum Algorithms and Quantum Cognition

Quantum computers can solve some classes of problems with more efficiency than classical computers, usually exponentially faster. They have the potential to solve in minutes problems that would take for a classical computer longer than the age of the universe. Among the promising applications are the development of new drugs, and new materials, machine learning and cryptographic key breaking, just to mention a few examples. Until recently the idea of building a computer seemed like a project reserved for a distant future, but over the past years many companies such as IBM, Google, Microsoft, D-Wave, Rigetti Computing, and others have announced that they started the operation of quantum computer prototypes. However, due to the counterintuitive properties of quantum theory the creation of quantum algorithms has been as difficult as hardware development. Although there are many algorithms built to run on quantum computers there are very few that use the full potential of quantum computing. The purpose of this course is to teach the fundamentals of quantum computing and quantum algorithms for students with non-physics background. The emphasis of the course will be to develop a "quantum intuition" by presenting the main differences between classical and quantum logic, as well as the use of special examples developed in quantum cognition. Quantum cognition applies the mathematical formalism of quantum mechanics in psychology and decision theories in situations where conventional formalism does not work. The topics covered will include: the basics of quantum theory and quantum computation, Classical and Quantum Logic, Classical and Quantum gates, Quantum Cognition, the main Quantum algorithms such as Phil's Algorithm, Deutsch Algorithm, Deutsch-Jozsa Algorithm, Simon's algorithm, Shor's Algorithm, and Grover's Algorithm. This course has workshop format involving readings followed by short lectures, discussion, plus other activities in class, homework, and Final Project. Required background: linear algebra, calculus equivalent to MATH 19 and MATH 20, basic probability theory and complex numbers. Students are not expected to have taken previous courses in quantum mechanics.
Terms: Spr | Units: 4
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