Here one can find lecture notes for Calculus-1 course that I taught to bachelor students of the joint HSE and NES program in Economics in Fall semesters of 2016, 2017, 2022, and 2023. I will add new lectures shortly after the corresponding class.

  • Lecture 1. Mathematical proof. (pdf)
  • Lecture 2. Limit of a sequence. (pdf)
  • Lecture 3. Arithmetic properties of limits. (pdf)
  • Lecture 4. Weierstrass theorem. Euler's number e. (pdf)
  • Lecture 5. Euler's constant. Subsequences. Bolzano–Weierstrass theorem. (pdf)
  • Lecture 6. Cauchy’s criterion. (pdf)
  • Lecture 7. Functions of one variable. (pdf)
  • Lecture 8. Limit of a function. (pdf)
  • Lecture 9. Infinite limit. Asymptotes. Limit of a superposition of functions. (pdf)
  • Lecture 10. Continuiuty. (pdf)
  • Lecture 11. Properties of continuous functions. (pdf)
  • Lecture 12. Derivative. (pdf)
  • Lecture 13. Rules of differentiation. (pdf)
  • Lecture 14. Derivative of a superposition. Derivative of an inverse function. Necessary condition for a local extremum. (pdf)
(to be continued)

The following textbooks were used in preparing the lectures:

  1. Arkhipov, G. I., Sadovnichii, V. A., and Chubarikov, V. N. (1999). Lectures on mathematical analysis. Moscow: Vysshaya shkola.
  2. Zorich V. A. (2015). Mathematical Analysis I. Springer Berlin, Heidelberg.
  3. Stewart, J. (2007). Essential calculus: Early transcendentals. Brooks/Cole, a part of the Thomson Corporation.
Economics, Game Theory, Computer Science, Sports Studies

Dmitry Dagaev

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