Advanced mathematics - ‫מתמטיקה מתקדמת לכימאים‬
(Course number 7221610)
Course topics:
Complex numbers and functions: rectangular form, polar form, complex algebra,
Euler’s formula, exponential form, powers and roots.
Power series and elementary functions in the complex plane: properties of power
series, exponential function, logarithms, complex powers, trigonometric functions,
hyperbolic functions, inverse trigonometric and hyperbolic functions, Triple integral in
curvilinear coordinates. Change of variables in the triple integral, Jacobian. Triple
integral in the cylindrical and spherical coordinates.
Vector analysis: Vector algebra, differentiation of vector valued functions. Scalar
field, gradient. Vector field, divergence, curl. Operator  . Operators of the second
order of vector analysis. Differential operators of vector analysis in the cylindrical and
spherical coordinates. Solenoidal, potential and harmonic fields.
Special differential equations: Solution of differential equations by generalized power
series (Frobenius method). Hermite equation and polynomials. Laguerre equation,
polynomials and associated Laguerre polynomials. Legendre equation, polynomials
and associated Legendre functions.
Main textbooks
2000 ,‫ בק‬,‫ פונקציות מרוכבות‬,‫ ציון קון‬-‫בן‬
D.M. Hirst, Mathematics for chemists, Chemical Publ., New York, 1979.
M.L. Boas, Mathematical methods in the physical sciences (all ed.).
G. B. Arfken and H.J. Weber, Mathematical methods for physicists, Academic
Press, 2001.
Y. Pinchover and J. Rubinstein, An introduction to partial differential equations,
Cambridge Univ. Press, 2005.