• Doron Levy is elected SIAM Class of 2026 Fellow

    Doron Levy was elected Fellow of the Society for Industrial and Applied Mathematics (SIAM), class of 2026:  https://www.siam.org/publications/siam-news/articles/siam-announces-2026-class-of-fellows.   Dr. Levy is recognized for his amazingly-stellar and sustained distinguished contributions to research and training in mathematical oncology and mathematical biology.  This exceedingly well-deserved award is fantastic for our department and university. Read More

  • Artem Chernikov awarded the Bessel Research Award by the Humboldt Foundation

    This award is given annually to internationally renowned academics from outside of Germany in recognition of their research accomplishments.  This award is named after Bessel and funded by the German ministry of education and research. Congratulations Atrem Chernikov.  https://www.humboldt-foundation.de/en/apply/sponsorship-programmes/friedrich-wilhelm-bessel-research-award  Read More

  • Mapping the Mind

    Junior computer science and mathematics double major Brooke Guo analyzes neural connections to understand the causes of complex brain conditions like schizophrenia.  When Brooke Guo arrived at the University of Maryland as a freshman in 2022, she knew she wanted to help people and work in a health-related field someday.… Read More

  • Four Science Terps Awarded 2025 Goldwater Scholarships

    Four undergraduates in the University of Maryland’s College of Computer, Mathematical, and Natural Sciences (CMNS) have been awarded 2025 scholarships by the Barry Goldwater Scholarship and Excellence in Education Foundation, which encourages students to pursue advanced study and research careers in the sciences, engineering and mathematics.  Over the last 16 years, UMD’s nominations… Read More

  • Announcing the Winners of the Frontiers of Science Awards

    Congratulations to our colleagues who won the 2025 Frontiers of Science Award: - Dan Cristofaro-Gardiner, for his join paper with Humbler and Seyfaddini: “Proof of the simplicity conjecture”, Annals of Mathematics 2024. - Dima Dolgopyat & Adam Kanigowski, for their joint paper with Federico Rodriguez Hertz: “Exponential mixing implies Bernoulli”, Annals of Mathematics… Read More
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Description

Analysis of functions of several variables. 


Prerequisites

Minimum grade of C- in MATH410


Level of Rigor

Advanced


Sample Textbooks

Advanced Calculus, by P.M. Fitzpatrick


Applications


If you like this course, you might also consider the following courses

MATH 437, MATH464, MATH 630, MATH 673


Additional Notes

Students interested in grad school in AMSC should consider this course

Students interested in grad school in MATH should strongly consider this course

Students interested in grad school in STAT should consider this course 

Topics

The topology of sets  in R^n

Continuous, continuously differentiable, and C^2 functions

First and second order approximation theorems, possibly higher order approximations

The derivative matrix

The general chain rule

Inverse and implicit function theorems with applications

Smooth curves and surfaces in R^3, possibly smooth manifolds in R^n

Lagrange multipliers


Additional topics may include

Metric spaces, the contraction principle

The existence and uniqueness theorem for nonlinear first order differential equations

The Riemann integral in R^n

Introduction to integration on curves, surfaces,  Green’s theorem.

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