"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.
Books:
  • 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.