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July 7, 2022


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Differential and integral calculus course, a PDF book by TEL AVIV UNIVERSITY.


  • Real Numbers, Upper and lower bounds
  • Three basic lemmas: Cantor, Heine-Borel, Bolzano-Weierstrass
  • Sequences and their limits, Convergent sequences
  • Cauchy’s sequences. Upper and lower limits. Extended convergence
  • Subsequences and partial limits., Infinite series
  • Rearrangement of the infinite series, Limits of functions. Basic properties
  • The exponential function and the logarithm
  • The second remarkable limit. The symbols “o small” and “∼”
  • Continuous functions, I and II, The derivative
  • Applications of the derivative, Derivatives of higher orders
  • Basic theorems of the differential calculus: Fermat, Rolle, Lagrange
  • Applications of fundamental theorems, Inequalities
  • Convex functions. Jensen’s inequality
  • The Taylor expansion, Taylor expansions of elementary functions
  • The fundamental theorem of algebra and its corollaries
  • Complex exponential function

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  • Differential and integral calculus 05:00:00

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