Calculus 1 for Computer Science and Software Engineering
2018–19–A
Course Content
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 (antiderivatives). 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.
Course Catalogue: 201.1.2361
 Staff Observers

 ליאור רוקח (Software and information systems engineering)
 מאיר קלך (Software and information systems engineering)
 אביטל אדרי (Engineering faculty)
 עמי ישעיה (Engineering faculty)
 פרופ’ דני ברנד (Computer science)
 חן קיסר (Computer science)
 אהד בןשחר (Computer science)
 ד”ר עדן כלמטץ’ (Computer science)
 אולג קריצבסקי (Natural science faculty)
 יפעת בן סימון (Natural science faculty)