• 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

  • 2024 Putnam Results

    We are very excited to report that our MAryland Putnam team ranked 7th among 477 institutions that participated in the 2024 Putnam math competition. Our team members this year were Daniel Yuan, Isaac Mammel, and Clarence Lam. Daniel Yuan ranked 26th among 3,988 participants. Clarence Lam and Isaac Mammel were recognized for… Read More

  • From Math Olympiads to Diplomacy: Meet Visiting Math Professor Qendrim Gashi

    Maryland Global, published a great interview with our visiting professor (and diplomat), Qendrim Gashi. The interview is available at https://marylandglobal.umd.edu/about/news/math-olympiads-diplomacy-meet-visiting-math-professor-qendrim-gashi Read More

  • Eugenia Brin, Longtime Supporter of Science and Performing Arts at UMD, Dies

    Eugenia Brin, a Russian immigrant and retired NASA scientist who, with her family of accomplished Terps, became an important benefactor of the University of Maryland, died on Dec. 3, 2024. She was 76 years old. The rest of the article can be read here: https://cmns.umd.edu/news-events/news/eugenia-brin-1948-2024 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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