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

- Real numbers. Supremum. Countable sets.
- Sequences. Convergence and divergence. Bounded sequences. Sub-sequences.
Upper and lower limits. Cauchy sequences. Infinite series. Absolute
convergence.
- Functions of real variable. Limit of functions. Continuity. The
intermediate value theorem. Weierstrass theorem about minimum/maximum
of a function. Uniform continuity.
- Derivative. Higher order derivatives. The intermediate value theorems
of Rolle, Lagrange and Cauchy.
l'Hopital's rule.
- 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.