By Kameshwar C. Wali

Satyendra Nath Bose grew to become a mythical determine of technological know-how within the twentieth century in India together with his innovative discovery at the nature of radiation. regardless of the organization with Einstein, despite the fact that, little is understood approximately him open air of India. This e-book highlights the notable mind and the extreme character of Bose set opposed to the backdrop of a wealthy Bengali cultural culture and British-Indian politics. not like different books protecting the importance of Bose's discovery, this ebook describes his varied medical contributions to India's medical neighborhood by way of bringing jointly chosen articles and addresses by means of Bose in addition to contributions from a few famous scientists at the many-faceted lifetime of Bose, hence making it a really distinctive quantity.

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**Example text**

The matrix I has the form 2 1 0 60 1 6 I¼6. 4 .. 0 0 3 ÁÁÁ 0 ÁÁÁ 07 7 7 .. 5 . ÁÁÁ 1 A null matrix (0) is a matrix in which all elements equal 0; thus A0 ¼ 0A ¼ 0. A matrix A is singular if Ax ¼ 0, x = 0 where x is a column vector [Lipschutz, 1968]. Notice that x = 0 if at least one element of x is nonzero. Alternatively, it is possible to show that a matrix A is singular if its determinant is zero. 3 after determinants have been defined.

12 Cartesian coordinate system. 13 33 Circular cylindrical coordinate system. 14. The distance from the origin to point P is the spherical radius rs . The azimuth angle f is measured in the x1 – x2 plane from the positive x1 axis. The polar angle us is measured from the positive x3 axis. 14 Spherical polar coordinate system. 4 0 0 rs , 1 us p 0 f 2p EULER’S EQUATION AND HYPERBOLIC FUNCTIONS A fundamental relation between trigonometric and exponential functions is Euler’s equation, which has the form eia ¼ cos a þ i sin a, i¼ pﬃﬃﬃﬃﬃﬃﬃ À1 (2:4:1) Euler’s equation can be derived by comparing the series expansions of each function in Eq.

13. The perpendicular distance from the x3 axis to point P is the cylindrical radius rc . The angle uc is measured in the x1 –x2 plane from the positive x1 axis. 12 Cartesian coordinate system. 13 33 Circular cylindrical coordinate system. 14. The distance from the origin to point P is the spherical radius rs . The azimuth angle f is measured in the x1 – x2 plane from the positive x1 axis. The polar angle us is measured from the positive x3 axis. 14 Spherical polar coordinate system. 4 0 0 rs , 1 us p 0 f 2p EULER’S EQUATION AND HYPERBOLIC FUNCTIONS A fundamental relation between trigonometric and exponential functions is Euler’s equation, which has the form eia ¼ cos a þ i sin a, i¼ pﬃﬃﬃﬃﬃﬃﬃ À1 (2:4:1) Euler’s equation can be derived by comparing the series expansions of each function in Eq.