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\begin{document}
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\begin{center}

  \huge{The Department of Mathematics}\\[0.1\baselineskip]
  \Large{2021--22--B term}\\[0.2\baselineskip]

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\begin{description}
  \item[Course Name]
    Calculus 1 for Computer Science and Software  Engineering

  \item[Course Number]
    \LRE{212‭.1‭.2361}

  \item[Course web page]\mbox{}\\
    \url{https://math.bgu.ac.il//en/teaching/spring2022/courses/calculus-1-for-computer-science-and-software-engineering}

  \item[Lecturer]
    Prof. Arkady Poliakovsky,
    \nolinkurl{<poliakov@bgu.ac.il>},
    Office 314

\item[Office Hours]
  \url{https://math.bgu.ac.il/en/teaching/hours}
\end{description}

\section*{Abstract}




\section*{Requirements and grading\footnote{Information may change during the first two weeks of the term. Please consult the webpage for updates}}






\section*{Course topics}

The system of the real numbers (without Dedekind cuts). The supremum axiom.
Convergent sequences, subsequences, monotonic sequences, upper and lower limits.
Series: partial sums, convergent and divergent series, examples, nonnegative series,
the root test, the quotient test, general series, Dirichlet, Leibnitz, absolute convergence implies convergence (without a proof).
Limits of functions, continuity, the continuity of the elementary functions, extrema
in compact intervals.
The derivative of a function, Lagrange's Mean Value Theorem, high order derivatives, L'hospital's rules, Taylor's Theorem, error estimates, lots of examples.
The Riemann integral: only for piecewise continuous functions (finitely many points of discontinuity). Riemann sums and the definition of the integral, The Fundamental Theorem of Calculus, the existence of primitive functions (anti-derivatives).
Integration techniques: integration by parts, substitutions, partial fractions (without proofs), improper integrals, applications of integrals, estimation of series with the aid of integrals, Hardy's symbols O, o and Omega, approximation of momenta and the Stirling formula.

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