## 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

Instructors:
Alvarez-Gavela, D. (PI)
;
Fayyazuddin Ljungberg, B. (PI)
;
Kimport, S. (PI)
...
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Instructors:
Alvarez-Gavela, D. (PI)
;
Fayyazuddin Ljungberg, B. (PI)
;
Kimport, S. (PI)
;
Madnick, J. (PI)
;
Pollack, A. (PI)
;
Zhang, S. (PI)
;
Arana Herrera, F. (TA)
;
Dore, D. (TA)
;
He, X. (TA)
;
Li, C. (TA)
;
Sherman, D. (TA)
;
Zavyalov, B. (TA)
;
Zhou, Z. (TA)

## 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

Instructors:
Kimport, S. (PI)
;
Schaeffer, G. (PI)
;
Zhu, X. (PI)
...
more instructors for MATH 20 »

Instructors:
Kimport, S. (PI)
;
Schaeffer, G. (PI)
;
Zhu, X. (PI)
;
Bernard, C. (TA)
;
Datta, I. (TA)
;
Hui, Y. (TA)
;
Lim, B. (TA)
;
Silliman, J. (TA)
;
Zou, J. (TA)

## 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

Instructors:
Acosta, J. (PI)
;
Cote, L. (PI)
;
Fayyazuddin Ljungberg, B. (PI)
...
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Instructors:
Acosta, J. (PI)
;
Cote, L. (PI)
;
Fayyazuddin Ljungberg, B. (PI)
;
Gao, J. (PI)
;
Kimport, S. (PI)
;
Lim, B. (PI)
;
Masullo, A. (PI)
;
Pan, D. (PI)
;
Schaeffer, G. (PI)
;
Ungemach, W. (PI)
;
Warner, E. (TA)

## MATH 41: Calculus (Accelerated)

Introduction to differential and integral calculus of functions of one variable. Topics: limits, rates of change, the derivative and applications, introduction to the definite integral and integration.
Math 41 and 42 cover the same material as
Math 19-20-21, but in two quarters rather than three. Prerequisites: trigonometry, advanced algebra, and analysis of elementary functions, including exponentials and logarithms. *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
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

## MATH 41A: Calculus ACE

Students attend
MATH 41 lectures with different recitation sessions, four hours instead of two, emphasizing engineering applications. Prerequisite: application; see
http://soe.stanford.edu/edp/programs/ace.html.

Terms: Aut
| Units: 6
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Yang, T. (PI)
;
Jafarov, J. (TA)

## MATH 51: Linear Algebra and Differential Calculus of Several Variables

Geometry and algebra of vectors, matrices and linear transformations, eigenvalues of symmetric matrices, vector-valued functions and functions of several variables, partial derivatives and gradients, derivative as a matrix, chain rule in several variables, critical points and Hessian, least-squares, , constrained and unconstrained optimization in several variables, Lagrange multipliers. 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

Instructors:
Kemeny, M. (PI)
;
Lucianovic, M. (PI)
;
Makisumi, S. (PI)
...
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Instructors:
Kemeny, M. (PI)
;
Lucianovic, M. (PI)
;
Makisumi, S. (PI)
;
Manners, F. (PI)
;
Pan, D. (PI)
;
Schaeffer, G. (PI)
;
Stanton, C. (PI)
;
Velcheva, K. (PI)
;
Venkatesh, A. (PI)
;
Ward, A. (PI)
;
Wieczorek, W. (PI)
;
Wilson, J. (PI)
;
Wolf, A. (PI)
;
Zhai, L. (PI)
;
Zhang, S. (PI)
;
Zhou, Y. (PI)
;
Zhu, B. (PI)
;
Helfer, J. (TA)
;
Nguyen, D. (TA)
;
Stanton, C. (TA)
;
Wang, G. (TA)
;
Wolf, A. (TA)
;
Zhu, B. (TA)

## MATH 51A: Linear Algebra and Differential Calculus of Several Variables, ACE

Students attend
MATH 51 lectures with different recitation sessions: four hours per week instead of two, emphasizing engineering applications. Prerequisite: application; see
http://soe.stanford.edu/edp/programs/ace.html.

Terms: Aut, Win, Spr
| Units: 6
| UG Reqs: GER:DB-Math, WAY-FR

## 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

Instructors:
Bernard, C. (PI)
;
De Groote, C. (PI)
;
Entin, A. (PI)
...
more instructors for MATH 52 »

Instructors:
Bernard, C. (PI)
;
De Groote, C. (PI)
;
Entin, A. (PI)
;
Jafarov, J. (PI)
;
Starkston, L. (PI)
;
Wieczorek, W. (PI)
;
Fayyazuddin Ljungberg, B. (TA)

## 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, Sum
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
De Groote, C. (PI)
;
Eliashberg, Y. (PI)
;
Fredrickson, L. (PI)
...
more instructors for MATH 53 »

Instructors:
De Groote, C. (PI)
;
Eliashberg, Y. (PI)
;
Fredrickson, L. (PI)
;
Hershkovits, O. (PI)
;
Love, J. (PI)
;
Mantoulidis, C. (PI)
;
Raju, C. (PI)
;
Tam, K. (PI)
;
Yang, T. (PI)
;
Madnick, J. (TA)
;
Silliman, J. (TA)
;
Ungemach, W. (TA)

## 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. Part of 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

Instructors:
Vasy, A. (PI)
;
Zachos, E. (TA)

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