Graduate

Preliminary exam syllabus

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Description

  
 

Requirements

  
 

Ph.D requirements

  
  Preliminary exams  
 

Qualifying exams

  
 
This is a 4-hour exam on topics from undergraduate courses on Linear Algebra and Vector Calculus.

This exam is normally offered during the first week of each semester.   A sign-up sheet is available in the math office near the end of the semester for the following semester’s exam.

Ph.D. students typically take this exam at the beginning of their second semester.

The topics covered in the Preliminary Exam are:

Linear Algebra
Vector Calculus
  • vector spaces
  • inner products
  • linear transformations
  • linear equations
  • matrix operations
  • determinants
  • characteristic equation
  • eigenvalues and eigenvectors
  • symmetric, skew-symmetric matrices
  • hermitian, skew-hermitian matrices
  • Jordan canonical form
  • spectral theorem
  • limits in Rn
  • partial derivatives
  • optimization of functions in Rn (with and without constraints)
  • the implicit function theorem
  • the inverse function theorem
  • Taylor's theorem
  • integration in several variables
  • line integrals
  • the theorems of Green, Gauss and Stokes

Previous exams
(these are PDF documents, you will need  Adobe Reader)

References you may want to study:

  1. Linear Algebra, Mathematica Labs by  Terry Lawson
  2. Linear Algebra and Its Applications, 3rd ed., by Gilbert Strang
  3. Almost any textbook with Linear Algebra in its title
  4. Calculus by Boyce and DiPrima
  5. Almost any textbook with Advanced Calculus in its title

Mathematics Department
Tulane University
6823 St. Charles Ave
New Orleans, LA 70118
phone: (504) 865-5727
fax: (504) 865-5063
Last Updated: August 15, 2007
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