Syllabus

L T P

3 1 0

Multiple Integrals: : Double integral (Cartesian), Change of order of integration in double integral, Polar coordinates, graphing of polar curves, Change of variables (Cartesian to polar), Applications of double integrals to areas and volumes, evaluation of triple integral (Cartesian).

Sequences and Series: Introduction to sequences and Infinite series, Tests for convergence/divergence, Limit comparison test, Ratio test, Root test, Cauchy integral test, Alternating series, Absolute convergence and conditional convergence.

Series Expansions: Power series, Taylor series, Convergence of Taylor series, Error estimates, Term by term differentiation and integration.

Complex analysis: Introduction to complex numbers, geometrical interpretation, functions of complex variables, examples of elementary functions like exponential, trigonometric and hyperbolic functions, elementary calculus on the complex plane (limits, continuity, differentiability), Cauchy-Riemann equations, analytic functions, harmonic functions.

Text Books:

1) Thomas, G.B. and Finney, R.L., Calculus and Analytic Geometry, Pearson Education (2007), 9^th ed.

2) Stewart James, Essential Calculus; Thomson Publishers (2007), 6^th ed.

3) Kasana, H.S., Complex Variables: Theory and Applications, Prentice Hall India, 2005 (2nd edition).

Reference Books:

1) Wider David V, Advanced Calculus: Early Transcendentals, Cengage Learning (2007).

2) Apostol Tom M, Calculus, Vol I and II, John Wiley (2003).

3) Brown J.W and Chruchill R.V, Complex variables and applications, MacGraw Hill, (7^th edition)