Higher Derivatives nth derivatives of standard functions Leibnitz`s theorem for nth derivative of a product of functions Applicable to suitable problems




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НазваниеHigher Derivatives nth derivatives of standard functions Leibnitz`s theorem for nth derivative of a product of functions Applicable to suitable problems
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Physics


ALLIED MATHEMATICS –I (04UPH3304)

(6 hrs/4credits)

UNIT –1:

Higher Derivatives – nth derivatives of standard functions – Leibnitz`s theorem for nth derivative of a product of functions – Applicable to suitable problems.


UNIT-2:

Curvature and Radius of Curvature in Cartesian, parametric equation, center of curvature and Evolutes and Involutes.


UNIT-3:

Integrals of the types {(px +q)/(ax2+bx+c)}dx


{(px+q)/(ax2+bx+c)}dx




{1/[(px+q)(ax2+bx+c)]}dx


{1/(acosx + bsinx + c)}dx


UNIT-4:

General properties of definite integrals – Integration by parts – Reduction formula for eaxxndx; sinndx and cosnxdx. Rules for finding 0 /2 sinmxcosnxdx, Bernoulli`s formula.


UNIT-5:

Vector differentiation – vector and scalar field – divergence and curl – application of laplacian operator.Vector integration:Line integral – surface integral – volume integral – problems on these.Gauss divergence theorem – Stoke’s theorem,– simple verification of theorems and problems.


Content and treatment in

  1. T.K. Manickavasagam pillai & others, volume-I Revised edition 1995.




  1. T.K. Manickavasagam pillai & others, volume-II Revised edition 1995.




  1. Knanna.M.L Vector Analysis, Jai prakash nath & Co



UNIT –1: Chapter III

UNIT –2: Chapter X - 2.1 to 2.5

UNIT –3: Chapter I - 8 to 10

UNIT –4: Chapter I – 11 to 14, 15.1

UNIT –5: Chapter IV-6 to 12 and : Chapter VI -1 to 9




ALLIED MATHEMATICS – II (04UPH3305)

(6 hrs/4credits)

UNIT-I

Expansion of sinn , cosn and tann (n is a positive integer). Expansion of

cos n  , sin n  in a series of cosines of multiples of  (proof not required) and simple problems.

UNIT – II


Euler’s formula for ei. Definition of hyberbolic functions – relation between the circular and hyberbolic functions . Expansions of sinhx and coshx in powers of x . Inverse hybebolic functions . sinh-1x, cosh-1x and tanh-1x in terms of logarithmic functions. Separation into real and imaginary parts of sin(x+iy), cos(x+iy), tan(x+iy), sinh(x+iy), cosh(x+iy) and tan-1(x+iy)

UNIT –III


Approximation using the Binomial theorem – Summations related to Binomial series - Summations related to exponential and logarithmic series.

UNIT –IV


Various types of matrices. Eigen values and Eigen vectors . Verification of cayley’s theorem. Finding inverse using cayley’s theorem.

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