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:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
AlvarezGavela, D. (PI)
;
Fayyazuddin Ljungberg, B. (PI)
;
Kimport, S. (PI)
...
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Instructors:
AlvarezGavela, 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. Initialvalue 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:DBMath, WAYFR

Grading: Letter or Credit/No Credit
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:DBMath, WAYFR

Grading: Letter or Credit/No Credit
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 192021, 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:DBMath, WAYFR

Grading: Letter or Credit/No Credit
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:DBMath, WAYFR

Grading: Letter (ABCD/NP)
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, vectorvalued functions and functions of several variables, partial derivatives and gradients, derivative as a matrix, chain rule in several variables, critical points and Hessian, leastsquares, , 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:DBMath, WAYFR

Grading: Letter or Credit/No Credit
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:DBMath, WAYFR

Grading: Letter (ABCD/NP)
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:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Bernard, C. (PI)
;
De Groote, C. (PI)
;
Entin, A. (PI)
...
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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 secondorder equations to oscillations, matrix exponentials, Laplace transforms, stability of nonlinear systems and phase plane analysis, numerical methods. Prerequisite: 51 or equivalents.
Terms: Aut, Win, Spr, Sum

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
De Groote, C. (PI)
;
Eliashberg, Y. (PI)
;
Fredrickson, L. (PI)
...
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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., proofbased) 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 1variable calculus and have an interest in a theoretical approach to the subject. Prerequisite: score of 5 on the BClevel Advanced Placement calculus exam, or consent of the instructor.
Terms: Aut

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter (ABCD/NP)
Instructors:
Vasy, A. (PI)
;
Zachos, E. (TA)
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