MATH 3334 - Advanced Multivariable and Vector Calculus - University of Houston
Skip to main content

MATH 3334 - Advanced Multivariable and Vector Calculus

***This is a course guideline.  Students should contact instructor for the updated information on current course syllabus, textbooks, and course content***

Prerequisites: MATH 2318 and MATH 3333, or MATH 2318 and currently enrolled in MATH 3333 with approval of instructor.

Course Description: Basic theory underlying multivariable and vector calculus, with applications. Topics include topology of n-space, derivative of a multivariable function as a linear transformation and applications, multivariable Taylor theorem, the inverse and implicit function theorems; calculus of vector fields and vector differential operators, Stokes and Gauss integral theorems, physical applications.

Recommended Text

  • “Advanced Calculus: A Geometric View (Undergraduate Texts in Mathematics)” by James J. Callahan, 2010. ISBN9781441973313
  • “Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach”, by John H. Hubbard and Barbara Burke Hubbard, 2015. ISBN9780971576681
  • “Introduction to Vector Analysis”, by Harry F. Davis and A. David Snider, 2016. ISBN9780697160997

 


Upon completion of this course, the students are expected to gain an understanding of the topology of R^n; multivariable differentiation; Taylor’s theorem in several variables; implicit and inverse function theorems; algebra of vectors and vector differential operators; line, surface and volume integrals, including Green’s, Stokes’ and Divergence theorems, and curvilinear coordinates.

Brief list of topics to be covered:

  • Topology of R^n: open closed sets, limits of functions and continuity, the Extreme Value Theorem on R^n.
  • Multivariable Differentiation: the derivative of a function as a linear map and implications. Taylor’s Theorem in several variables, Implicit and Inverse Function Theorems.
  • Multivariable Integration: double and triple integrals, Fubini’s Theorem, change of variables formula.
  • Scalar and Vector Fields: Scalar fields and gradients. Introduction to vectors; scalar and vector products. Vector fields and grad, div, curl, and Del notation in rectangular, cylindrical and spherical coordinates.
  • Line, surface and volume integrals, characterization of irrotational fields.
  • Green’s Theorem, The Divergence Theorem and Stokes' Theorem in 3 dimensions and associated theorems. Applications.

 

Grading: Please consult your instructor's syllabus regarding any and all grading guidelines.


Justin Dart Jr. Center Accommodations:

Academic Adjustments/Auxiliary Aids: The University of Houston System complies with Section 504 of the Rehabilitation Act of 1973 and the Americans with Disabilities Act of 1990, pertaining to the provision of reasonable academic adjustments/auxiliary aids for students who have a disability. In accordance with Section 504 and ADA guidelines, University of Houston strives to provide reasonable academic adjustments/auxiliary aids to students who request and require them. If you believe that you have a disability requiring an academic adjustments/auxiliary aid, please visit Justin Dart Jr. Student Accessibility Center website at https://www.uh.edu/accessibility/ for more information.

UH CAPS

Counseling and Psychological Services (CAPS) can help students who are having difficulties managing stress, adjusting to college, or feeling sad and hopeless. You can reach (CAPS) by calling 713-743-5454 during and after business hours for routine appointments or if you or someone you know is in crisis. No appointment is necessary for the "Let's Talk" program, a drop-in consultation service at convenient locations and hours around campus.