Course No
MA605
Credit
8
Syllabus
Topological spaces, Continuous maps between topological spaces, product topology,Quotient spaces, Connectedness, Compactness, Path connected spaces, separation axioms,Tychono spaces, Urysohn's lemma and metrization theoremDierentiable functions on Rn, Jacobian criteria, Taylor's theorem, Inverse function theorem,Implicit function theorem, Maxima-minima, Lagrange multiplier
Reference Books
- Armstrong, Basic Topology, Springer, 1983
- Munkres, Topology, Pearson Education, 2005.
- J. Dugundji, Topology
- J. J. Duistermaat, J. A. C. Kolk: Multidimensional Real Analysis I: Dierentiation
- K. Janich, Topology, Springer
- John L Kelley: General Topology (free download: https://archiveorg/details/GeneralTopology)
- F. Simmons: Introduction to Topology and Modern Analysis
- S.Kumaresan: A Course in Dierential Geometry and Lie Groups,TRIM series
- T. M. Apostol: Calculus: Multi-Variable Calculus and Linear Algebra With Applications to DierentialEquations And Probability- Vol 2.