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Differential and integral calculus in pdf


  • 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

Course, tutorial Summary Differential and integral calculus

Course material to download for free on Differential and integral calculus category Mathematics.
This course is intended for a strictly personal use, the file is of format pdf level Beginner , the size of this file is 752.5 KB.

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