"Differential and Integral Calculus 2b". School of Mathematical Sciences. (Ya. Yakubov)

Background: differential and integral calculus 1b, linear algebra.

  1. Euler formula, Fourier series, Fourier coefficients decay, differentiation and integration of Fourier series, Parseval's identity, Fourier transform.
  2. Limit and continuity of functions of two variables, iterated limits, partial derivatives, the chain rule, changing the order of differentiation, implicit functions and their derivatives. Taylor formula, extremum, Lagrange multiplier method.
  3. Double and triple integrals, variables changing in double and triple integrals, Jacobian. Polar, cylindrical, and spherical coordinates. Application in calculation of lengths, areas, volumes, moments and centers of mass.
  4. Line integrals of the first and second kinds. Green's theorem.
  • Protter and Morrey, "A First Course in Real Analysis", UTM Series, Springer-Verlag, 1991.
  • Thomas and Finney,"Calculus and Analytic Geometry", 9-th edition, Addison-Wesley, 1996.
  • Ben Zion Kun and Sami Zafrani, "Heshbon Diferenziali ve Integrali 1 ve 2", BAK, Haifa, 1994 (in Hebrew).
  • Sami Zafrani and Alan Pinkus, "Turei Fourier ve Hatmarot Integraliot", Technion, 1997.