Lect 16{UNIT 4} B Sc II,Sem III , Advance Calculus , By Praful Mohokar

Unit I: Sequence: Definition of sequence, uniqueness of limit of sequence, algebra of limit of a
sequence , positivity theorem, sandwich theorem, monotonic and bounded sequence,
Cauchy sequence.
Unit II: Series: Series of nonnegative terms, convergence of geometric series and the series
Comparison tests, Cauchy’s integral test, ratio test,root test, absolute
convergent, conditional convergent, Leibnitz rule, Abel’s test, Dirichilet test.
Unit III: Limit and continuity of functions of two variables, algebra of limit and continuity,
indetermidiate value property, fixed point property, Taylor’s theorem for function of
two variables.
Unit IV: Maxima and minima of two variables, Lagrange’s multipliers method, Jacobians.
Unit V: Double integral (definition and evaluation technique), change of order of double
integral, triple integral, Gauss and Stoke’s theorem.
Reference Books :
1) Gorakh Prasad : Differential Calculus, Pothishala Pvt. Ltd., Allahabad.
2) Gorakh Prasad : Integral Calculus, Pothishala Pvt. Ltd., Allahabad.
3) Murray R. Spiegel : Theory and Problems of Advanced Calculus, Schaum Outline Series.
4) S. C. Malik and Arora : Mathematical Analysis, Wiley Estern Ltd., New Delhi.
5) O. E. Stanaitis : An Introduction to Sequences, Series and improper Integrals, Holden-Dey ,
Inc. San Francisco,California.
6)T. M. Karade, J. N. Salunke, A. G. Deshmukh, M. S. Bendre: Lectures on Advanced
Calculus, Sonu-Nilu Publication, Nagpur.
7) Earl D. Rainville : Infinite series, The Macmillan Co., New York.
8) N. Piskunov : Differential a nd Integral Calculus, Peace publishers, Noscow.
9) Shanti Narayan : A Course of Mathematical Analysis, S. Chand & Co., New Delhi.
10) D. Somasundaram and B. Choudhary: A First course in MathematicalAnalysis, Narosa
Publ. House.
#DefinitionofSequence,
#UniquenessOfLimitOfSequence,
#AlgebraOfLimitOfASequence ,
#PositivityTheorem,
#SandwichTheorem,
#MonotonicAndBoundedSequence,
#CauchySequence.