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# 21 - 30 of 77 results for: all courses

## 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 | Units: 3 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter or Credit/No 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 | Grading: Letter or Credit/No Credit

## 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 | Grading: Letter or Credit/No Credit

## MATH 51:Linear Algebra, Multivariable Calculus, and Modern Applications

This course provides unified coverage of linear algebra and multivariable differential calculus. It discusses applications connecting the material to many quantitative fields. Linear algebra in large dimensions underlies the scientific, data-driven, and computational tasks of the 21st century. The linear algebra portion of the course includes orthogonality, linear independence, matrix algebra, and eigenvalues as well as ubiquitious applications: least squares, linear regression, Markov chains (relevant to population dynamics, molecular chemistry, and PageRank), singular value decomposition (essential in image compression, topic modeling, and data-intensive work in the natural sciences), and more. The multivariable calculus material includes unconstrained optimization via gradients and Hessians (used for energy minimization in physics and chemistry), constrained optimization (via Lagrange multipliers, crucial in economics), gradient descent and the multivariable Chain Rule (which underl more »
This course provides unified coverage of linear algebra and multivariable differential calculus. It discusses applications connecting the material to many quantitative fields. Linear algebra in large dimensions underlies the scientific, data-driven, and computational tasks of the 21st century. The linear algebra portion of the course includes orthogonality, linear independence, matrix algebra, and eigenvalues as well as ubiquitious applications: least squares, linear regression, Markov chains (relevant to population dynamics, molecular chemistry, and PageRank), singular value decomposition (essential in image compression, topic modeling, and data-intensive work in the natural sciences), and more. The multivariable calculus material includes unconstrained optimization via gradients and Hessians (used for energy minimization in physics and chemistry), constrained optimization (via Lagrange multipliers, crucial in economics), gradient descent and the multivariable Chain Rule (which underlie many machine learning algorithms, such as backpropagation), and Newton's method (a crucial part of how GPS works). The course emphasizes computations alongside an intuitive understanding of key ideas, making students well-prepared for further study of mathematics and its applications to other fields. The widespread use of computers makes it more important, not less, for users of math to understand concepts: in all scientific fields, novel users of quantitative tools in the future will be those who understand ideas and how they fit with applications and examples. This is the only course at Stanford whose syllabus includes nearly all the math background for CS 229, which is why CS 229 and CS 230 specifically recommend it (or other courses resting on it). For frequently asked questions about the differences between Math 51 and CME 100, see the FAQ on the placement page on the math department website. Prerequisite: 21, 42, or the math placement diagnostic (offered through the Math Department website) in order to register for this course.
Terms: Aut, Win, Spr | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter or Credit/No Credit

## MATH 51A:Linear Algebra, Multivariable Calculus, and Modern Applications, ACE

Students attend MATH 51 lectures with different recitation sessions: three hours per week instead of two, emphasizing engineering applications. Prerequisite: application; see https://web.stanford.edu/dept/soe/osa/ace.fb
Terms: Aut, Win, Spr | Units: 6 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter or Credit/No Credit

## MATH 52:Integral Calculus of Several Variables

Iterated integrals, line and surface integrals, vector analysis with applications to vector potentials and conservative vector fields, physical interpretations. Divergence theorem and the theorems of Green, Gauss, and Stokes. Prerequisite: 51 or equivalents.
Terms: Aut, Win, Spr | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter or Credit/No Credit

## MATH 53:Ordinary Differential Equations with Linear Algebra

Ordinary differential equations and initial value problems, systems of linear differential equations with constant coefficients, applications of second-order equations to oscillations, matrix exponentials, Laplace transforms, stability of non-linear systems and phase plane analysis, numerical methods. Prerequisite: 51 or equivalents.
Terms: Aut, Win, Spr | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter or Credit/No Credit

## MATH 61CM:Modern Mathematics: Continuous Methods

This is the first part of a theoretical (i.e., proof-based) sequence in multivariable calculus and linear algebra, providing a unified treatment of these topics. Covers general vector spaces, linear maps and duality, eigenvalues, inner product spaces, spectral theorem, metric spaces, differentiation in Euclidean space, submanifolds of Euclidean space, inverse and implicit function theorems, and many examples. The linear algebra content is covered jointly with Math 61DM. Students should know 1-variable calculus and have an interest in a theoretical approach to the subject. Prerequisite: score of 5 on the BC-level Advanced Placement calculus exam, or consent of the instructor.
Terms: Aut | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter or Credit/No Credit

## MATH 62CM:Modern Mathematics: Continuous Methods

A continuation of themes from Math 61CM, centered around: manifolds, multivariable integration, and the general Stokes' theorem. This includes a treatment of multilinear algebra, further study of submanifolds of Euclidean space and an introduction to general manifolds (with many examples), differential forms and their geometric interpretations, integration of differential forms, Stokes' theorem, and some applications to topology. Prerequisite: Math 61CM.
Terms: Win | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter (ABCD/NP)

## MATH 63CM:Modern Mathematics: Continuous Methods

A proof-based course on ordinary differential equations, continuing themes from Math 61CM and Math 62CM. Topics include linear systems of differential equations and necessary tools from linear algebra, stability and asymptotic properties of solutions to linear systems, existence and uniqueness theorems for nonlinear differential equations with some applications to manifolds, behavior of solutions near an equilibrium point, and Sturm-Liouville theory. Prerequisites: Math 61CM and Math 62CM.
Terms: Spr | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter (ABCD/NP)
Instructors: White, B. (PI)
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