Instructor : Dr. Anupam Kumar Singh
TA's : Dr. R. Parthasarathi and Ms. Yasmeen Akhtar
Schedule : Lectures - Monday and Tuesday - 10:30 to 11:30 (in C201A)
Tutorials - Thursday - 11:30 to 1:00. (C201A, MB108 and C304)
Tutorial batches : B1 (roll no. 1-30) C201A Tutor - Anupam Singh
B2 (roll no. 31-60) MB108 Tutor - Yasmeen Akhtar
B3 (roll no. 61-90) C304 Tutor - R. Parthasarathi
Evaluation Method :
Mid –Semester Examination - 20%
End-Semester Examination - 50 %
Quizzes – 30 % (6 in all)
(Warning : mid-sem will be 1 and half an hour and end-sem will be of 3 hours duration. Quizzes will be of half an hour duration.)
Goal of the Course : The subject “functions of severable variable” is at the core of Mathematics, Physics and Engineering. In Mathematics it provides foundation to the subject of differential geometry and differential equations. Motion of any object (objects) is a natural example of such functions and hence this course provides foundations to Physics and Engineering.
Proposed Course Content :
The space Rn, Geometry of Rn , Linear functions, Review of Linear Algebra
Functions of Several Variable, Continuous functions
Differentiation of functions, Partial Derivatives, Directional derivatives, Chain Rule
Applications
Integration and applications
References :
Basic text books :
Lang : Calculus of Several variable
Moskowitz and Paliogiannis : Functions of Several Variable
Marsden, Tromba and Weinstein : Basic Multivariable Calculus
Apostol : Calculus II
Ghorpade and Limaye : A course in Multivariable Calculus and Analysis
Advanced text books :
Munkres : Analysis on Manifolds
Spivak : Calculus on Manifolds
Terence Tau : Analysis I and II
02/01/2012 Introduction (Why study Calculus?)
03/01/2012 Calculating area/perimeter of circle and paradoxes
05/01/2012 Kakeya's needle problem
09/01/2012 Functions from R^n to R^m.
10/01/2012 Space R^n
12/01/2012 Tutorial Assignment - I
16/01/2012 Inner Product, Norm and Metric on R^n
17/01/2012 Limit of a function
19/01/2012 Tutorial
23/01/2012 Continuous function
24/01/2012 Examples
26/01/2012 Holiday
30/01/2012 Derivative of a function
31/01/2012 Differentiability => Continuity
02/02/2012 Quiz - I
06/02/2012 Directional derivative and partial derivative Quizz-II
07/02/2012 Relation among various derivatives Assignment - II
09/02/2012 Tutorial
13/02/2012 Examples
14/02/2012 Examples
16/02/2012 Quiz - III (Morning at 9:45 AM) Tutorial
20/02/2012 Hessian Matrix
21/02/2012 Critical Points, Maxima & Minima
23/02/2012 Tutorial
27/02/2012 Maxima & Minima
Mid Sem Exam
05/03/2012 substituted by taking extra class earlier
06/03/2012 substituted by taking extra class earlier
08/03/2012 Holiday for the Holi festival
12/03/2012 Riemann Integration of one variable
13/03/2012 Riemann integration for several variable
15/03/2012 Riemann Integration and Darboux integration Assignment-III
19/03/2012 Tutorial
20/03/2012 Quiz-IV
22/03/2012 Tutorial
26/03/2012 Fubini's Theorem
27/03/2012 Fubini's Theorem
29/03/2012 Tutorial
02/04/2012 Quiz V
03/04/2012 Change of Variables
05/04/2012 Holiday
09/04/2012 Curves and Line Integral Assignment - IV
10/04/2012 Surfaces and surface integral
12/04/2012 Quiz VI
25/04/2012 End sem exam