"Differential and Integral Calculus". Faculty of Engineering. (Ya. Yakubov)

Background: differential and integral methods, linear algebra.

  1. Limits: definition of limit of infinite sequences, Cauchy condition, limit of monotone sequences, divergence, uniqueness of the limit, the sandwich theorem, subsequences, Bolzano-Weierstrass theorem.
  2. Infinite series, convergence and divergence of series, convergence tests of series. Absolute and conditional convergence. Improper integrals, Euler gamma-function, comparison and integral tests.
  3. Power series: Cauchy-Hadamard theorem, differentiation and integration, multiplication of power series, Taylor and McLaurin series, Taylor and McLaurin series of elementary functions.
  4. Convergence of sequences and series of functions, uniform convergence, Weierstrass theorem, changing of limit (sum) and integral, changing of limit (sum) and derivative.
  5. 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.
  6. Double and triple integrals, variables changing in double and triple integrals, Jacobian. Polar, cylindrical, and spherical coordinates. Surface integrals.
  7. Theory of vector fields, theorems of Green, Gauss, and Stokes.
Books:
  • Ben Zion Kun and Sami Zafrani, "Heshbon Diferenziali ve Integrali 1 ve 2", BAK, Haifa, 1994 (in Hebrew).
  • 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.