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

- Riemann integral, definition and basic properties. The Newton-Leibnitz
theorem. Integration by parts, change of variable, indefinite integral, the
length of a curve.
- Uniform convergence of a sequence and a series of functions. Continuity of
the limit. Uniform convergence for the integrals. Comparison test for uniform
convergence for the series (M-test). Weierstrass theorem about uniform
approximation by polyniomials.
- Complex series. Multiplication of the series. Radius of convergence of the
power series. Abel and Dirichlet criteria of the convergence. Abel theorem
about continuity of the power series.
- Fourier series. Riemann-Lebesgue lemma. Dirichlet kernel, Feyer kernel.
Convergence of the Fourier series. Feyer theorem, mean convergence, Parseval
formula.
- Finite dimensional spaces, open and closed sets. Convergence. Continuous
functions of several variables.
- Differentiability. Partial derivatives. The chain rule. Directional
derivatives, gradient, level curves. Continuous first order partial
derivatives and differentiability. Mean value property.
- Higher order partial derivatives. Mixed partial derivatives. Taylor's
polynomials. Classification of critical points.

Books:
Maizler, "heshbon infinitisimali", hozaat akademon (in Hebrew).
Hokhman, "heshbon infinitisimali", hozaat akademon (in Hebrew).
Hauniversita haptuha, "heshbon infinitisimali" I+II (in Hebrew).
Zafrani, Pinkus "Turei Furye ve hatmarot integralijot", haTechnion, 1997.
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.
T. W. Korner, Fourier Analysis, Cambridge University Press, 1988.