MATH 412, ADVANCED CALCULUS WITH APPLICATIONS
SPRING, 2010
Instructor:
Konstantina Trivisa:
 Office: 3307 Mathematics Bldg
 Phone: (301) 4056865
 Office Hours: (Spring 2010)
Tuesday, Thursday 11:0011:50am.
 Email:
trivisa@math.umd.edu
 Course website: http://wwwusers.math.umd.edu/~trivisa/math412_S10.html
Rigorous discussion of fundamental concepts of analysis in several
variables combined with computational algorithms such as
Newton's method and the method of steepest descent.
Application to problems in many areas with a view to both
computing solutions and deriving qualitative conclusions about
the models. (This course is not open to students who have
completed Math 350 and 351. Credit may not granted for both
Math 412 and 411.)
Prerequisites:
Calculus I, II, III, Linear algebra, one semester of advanced calculus
in one variable (MATH 410)
Main Text:

Jeffrey Cooper
Working Analysis, 1st Editon, by Jeffery Cooper. Published by
Addison Wesley. ISBN: 0121876047
Class Times: Tuesday and Thursday: 12:30am  13:45pm.
Location: MTH 0405
Final Exam: Tuesday, May 18, 2010 1:303:30pm
Miterm 1: Thursday, March 11, 2010 (in class)
Miterm 2: Thursday, April 22, 2010 (in class)
 COURSE OUTLINE (Tentative):
 Convergence and Continuity in Several Variables
 A Little Topology
 The Derivative, VectorValued Mappings
 Solving Systems of Equations
 Quadratic Approximation and Optimization
 Constraint Optimization
 Integration over Generalized Rectancles and Jordan Domains
 Numerical Methods
 Applications
 Homework and Quizzes: Homework will be assigned once a
week. There will be given approximately ten homeworks
during the semester from which only the best eight homeworks
will count towards your grade.
 Homework
Grading (approximate): Homework: 20%, Midterms I & II: 40%, Final: 40%