"Differential and Integral Calculus 1a". School of Mathematical Sciences. (Ya. Yakubov)

  1. Real numbers. Supremum. Countable sets.
  2. Sequences. Convergence and divergence. Bounded sequences. Sub-sequences. Upper and lower limits. Cauchy sequences. Infinite series. Absolute convergence.
  3. Functions of real variable. Limit of functions. Continuity. The intermediate value theorem. Weierstrass theorem about minimum/maximum of a function. Uniform continuity.
  4. Derivative. Higher order derivatives. The intermediate value theorems of Rolle, Lagrange and Cauchy. l'Hopital's rule.
  5. Taylor formula with Lagrange remainder. Power series of elementary functions. Convexity.
  • Maizler, "heshbon infinitisimali", hozaat akademon (in Hebrew).
  • Hokhman, "heshbon infinitisimali", hozaat akademon (in Hebrew).
  • Hauniversita haptuha, "heshbon infinitisimali" I+II (in Hebrew).
  • V. A. Zorich, Mathematical Analysis I+II, Springer.
  • M. Spivak, Calculus, Publish of Perish.
  • R. Courant and F. John, Introduction to Calculus and Analysis, I+II, Springer.