University of Massachusetts, Amherst                                                                                                                                                                                     Spring 2020

MATH 425.1: Advanced Multivariate (=multivariable) Calculus

(schedule number )


  • EXAMS. Due to a change to online course there will only be one midterm exam and the final exam will be a final project. There will still be an online review session for the final exam.

  • Description of the course: This is a course in the differential and integral calculus of several variables from a more advanced perspective than Math 233. We will study geometry (curves, surfaces, solids, 4...) and topology (properties of these geometric objects) of the n-dimensional Euclidean space for $n=1,2,3,...$ . The main focus will be on integration over regions, paths and surfaces, the change of variables formula, and thefundamental theorem of calculus (the theorems of Green, Gauss, and Stokes).
  • The required knowledge. This includes the Linear Algebra 235 course and the Chapters 1,2,3,4 of the Marsden and Tromba book. Thismaterial will be only reviewed in a very fast fashion and it will be assumed throughout.
  • Some of the Basic Notions in the course: differentiability, directional and partial derivatives and gradient of functions; critical points without or with constraints (Lagrange-multipliers/tangential-gradient) and the Hessian; vector fields and differential forms; divergence, curl and exterior derivative; line and surface integrals; the fundamental theorem of calculus (Gauss/Green/Stokes).
  • Possible additional topics: from physics (fluids and electromagnetism) and from differential geometry (curves and surfaces in space).
  • The basic information:
  • SYLLABUS: Syllabus contains general information on topics, exams, grade, course structure and policies.
    (If you have 6th edition let me know and I will post the homework problems below. Hopefully everybody has the 5th as announced on the department web page.)

    The notes mainly indicate how lectures differ from the book. Here are some differences:
  • HOW TO LEARN abstract MATHEMATICS.