NATIONAL INSTITUTE OF TECHNOLOGY, ARUNACHAL PRADESH, YUPIA, Pin-791112
(Established by MHRD, Govt. of India)
Website : www.nitap.in, Fax No: (0360) 2284972
E-Mail: nitarunachal@gmail.com / admin@nitap.in
Exercises Proposed for teaching in (Jan – June, 2016 Semester)
1.
2.
3.
4.
5.
Name of the Teacher Dr. A. Vanav Kumar
Department
Mathematics
Course Title
Tensor Calculus
Course code
MAP 923
Course Hands out (in reference to framed & approved syllabus) (maximum 500 words)
Expected numbers of classes to be held: 40
Units
Unit I: FiniteDimensional Vector
Spaces and Linear
Mappings
No. of lectures
Topic
8
Fields - Finite-Dimensional Vector Spaces – Linear
Mappings of a Vector Space - Dual or Covariant
Vector Spaces
Unit-II Tensor Algebra
10
Unit-III Tensor
Analysis on a
Differentiable Manifold
12
Unit-IV Differentiable
Manifolds with
Connections
10
Second-Order Tensors - Higher-Order Tensors Exterior or Grassmann Algebra - Inner Product
Vector Spaces and the Metric Tensor
Differentiable Manifolds - Tangent Vectors,
Cotangent Vectors - Parametrized Curves - Tensor
Fields over Differentiable Manifolds - Differential
Forms and Exterior Derivatives
The Affine Connection and Covariant Derivative Covariant Derivatives of Tensors along a Curve Lie Bracket, Torsion, and Curvature Tensor
6. Books/Literature to be followed:
(a) Books (Min. 2 texts + 3 references)
Texts
(i)
Title
Tensors: The Mathematics of Relativity Theory and Continuum
Mechanics,
Author
Anadijiban Das
Publisher
Springer
Edition
Not Available
(ii)
Title
Author
Publisher
Edition
Schaums Outline of Tensor Calculus (Schaum's Outline Series),
David C. Kay,
Schaum's Outlines
Revised edition edition
NATIONAL INSTITUTE OF TECHNOLOGY, ARUNACHAL PRADESH, YUPIA, Pin-791112
(Established by MHRD, Govt. of India)
Website : www.nitap.in, Fax No: (0360) 2284972
E-Mail: nitarunachal@gmail.com / admin@nitap.in
References:
(iii)
Title
Author
Publisher
Edition
Tensor Calculus
John L. Synge, A. Schild
Dover Publications Inc.
New edition
(iv)
Title
Author
Publisher
Edition
An Introduction to Riemannian Geometry and the Tensor Calculus
C. E. Weatherburn
Cambridge University Press
2nd Edtion, 2008
(v)
Title
Author
Publisher
Edition
Tensor Calculus and Riemannian Geometry
G.S. Gupta, S.S. Gupta, J.K. Goyal, K.P. Gupta
Pragathi Prakashan
12th Revised Edition
(b) Magazines/Journals
Magazines
1. Hamilton, William Rowan (1854–1855). "On some Extensions of Quaternions". In
Wilkins, David R. Philosophical Magazine (7–9): 492–499, 125–137, 261–269, 46–51,
280–290.
2. Saunders Mac Lane, Categories for the Working Mathematician, p. 4, "...for example the
monoid in the category of abelian groups, is replaced by the usual tensor product...",
Springer, 1971
Journals
1. Journal of Fluid Mechanics, Oxford University Press.
2. Physics of Fluids, American Institute of Physics.
3. International Journal of Non-Linear Mechanics, Elsevier.
4. International Journal of Heat and Mass Transfer, Elsevier.
NATIONAL INSTITUTE OF TECHNOLOGY, ARUNACHAL PRADESH, YUPIA, Pin-791112
(Established by MHRD, Govt. of India)
Website : www.nitap.in, Fax No: (0360) 2284972
E-Mail: nitarunachal@gmail.com / admin@nitap.in
7. Mode of Teaching: J.C Bose/S. N. Bose (please tick). S. N. Bose
8. If the course is of practices, list the experiments to be offered.
Are the manuals ready for the experiments to be conducted?
Yes/No (please tick)
If “No”, the reasons there of and fixing responsibility
Remarks/ Endorsement by the HoD
With his /her signature with date
Name of the Teacher: Dr. A. Vanav Kumar
Designation: Assistant Professor
Signature with Date: