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# 1 - 6 of 6 results for: MATH 19: 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.
Terms: Sum | Units: 4
Instructors: Wood, S. (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 5, or Calc AB with 5 or placing out of the single variable math placement test: https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext), or Math 19-21.
Terms: Aut, Win, Spr | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR

## ENGR 154:Vector Calculus for Engineers (CME 100)

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 5, or Calc AB with 5 or placing out of the single variable math placement test: https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext), or Math 19-21.
Terms: Aut, Win, Spr | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR

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

## 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

## 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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