Page 69 - CatalogNEP-PS

Classification and Construction of first-order partial differential equations, Method of
characteristics and general solutions of first-order partial differential equations, Canonical forms
and method of separation of variables for first order partial differential equations; Classification
and reduction to canonical forms of second-order linear partial differential equations and their
general solutions.

*TUTORIAL (15 Hours (1 Hour per week))

SUGGUESTED READINGS:

1. D.A. Murray: Introductory course in differential equations, Orient Longman (India) 1967
2. J.N. Sharma and Kehar Singh, Partial Differential Equations for Engineers, and
Scientists. Narosa Publishing House.
3. S. L. Ross, Differential Equations, John Wiley Student Edition, Third Edition,2004.
4. I.Sneddon,ElementsofPartialDifferentialEquations,McGraw-Hill,International
Edition,1967.
5. Spectrum-Ordinary Differential Equations, Sharma Publications, Jalandhar
6. A Text Book of Ordinary Differential Equations, S. Dinesh & Co, Jalandhar
7. Spectrum-Partial Differential Equations, Sharma Publications, Jalandhar
8. A Text Book of Partial Differential Equations, S. Dinesh & Co, Jalandhar
9. Myint-U, Tyn and Debnath, Lokenath (2007). Linear Partial Differential Equations for
Scientist and Engineers (4th ed.). Birkhäuser. Indian Reprint.
10. Ross, Shepley L. (1984). Differential Equations (3rd ed.). John Wiley & Sons.
11. Edwards, C. Henry, Penney, David E., & Calvis, David T. (2015). Differential Equations
and Boundary Value Problems: Computing and Modeling (5th ed.). Pearson Education.
12. E. Kreyszig. (2011). Advanced Engineering Mathematics (10th ed.). Wiley India.
13. I. N. Sneddon (2006). Elements of Partial Differential Equations. Dover Publications.

Maths.211 Real Analysis 3+1*

LEARNING OBJECTIVES:

The course will develop a deep and rigorous understanding of:
 Real line ℝ with algebraic structure.
 Order and completeness properties to prove the results about convergence and divergence
of sequences and series of real numbers and real functions.

LEARNING OUTCOMES:

This course will enable the students to:
 Understand the fundamental properties of the real numbers, including completeness and
Archimedean, and density property of rational numbers in ℝ.
 Learn to define sequences in terms of functions from ℕ to a subset of ℝ and find the limit.
 Recognize bounded, convergent, divergent, Cauchy and monotonic sequences and to
calculate the limit superior and limit inferior of a bounded sequence.
 Apply limit comparison, ratio, root, and alternating series tests for convergence and
absolute convergence of infinite series of real numbers.

THEORY(45 Hours)

UNIT -1 Real Number System (12 Hours)

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