Rapidsol Analysis II (P U)


The present book provides a comprehensive treatment of the concepts and topics by giving a vast variety of examples fully solved. The entire subject matter has been arranged in a systematic, graded, simple, lucid and exhaustive manner. Each chapter begins with some definitions followed by theorems with complete proofs and solved problems. A large number of notes and remarks have been added for a better understanding of the subject.


Double and Triple Integrals : Double integral over A Rectangle, Repeated Integrals in R2, Double Integrals over Bounded non-rectangular regions, Area of bounded regions in plane, Double integrals as Volumes, Change of variables in double integrals, Change to Polar coordinates, Area in Polar coordinates, Triple Integral in Rectangular coordinates, Triple integrals over general regions in R3, Repeated integrals in R3, Volume of a region in R3, Change of variables in a Triple integral to Cylindrical and Spherical coordinates.

Vector Integration : Line, Surface and Volume integration. Gauss divergence theorem, Stokes’ theorem, Green’s theorem.

Sequences and Series of Functions : Pointwise and uniform convergence, Cauchy criterion for uniform convergence, Weierstrass M-test, Abel’s and Dirichlet’s test for uniform convergence, uniform convergence and continuity, uniform convergence and Riemann integration, uniform convergence and differentiation, Weierstrass approximation theorem (Statement only), Abel’s and Taylor’s theorems for power series.

Fourier Series : Fourier expansion of piecewise monotonic functions, Fourier Series for odd and even function, Half Range Series, Fourier series in the intervals [0, 2p], [– 1, 1] and [a, b].

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