Calculus I ("hedva aleph")

Prof. Daniel Keren, dkeren@cs.haifa.ac.il

MOED ALEPH 2.2020 with solution

Example of an exam

NEW STUFF!

TARGIL 1
Mid-term example, Technion
More exs. on sequences ("SDAROT")
exs. on limits and continuity of functions
exs. on derivatives

More examples questions:

Part 1

Part 2 (you DON'T need to solve q. 2 here)

List of theorems for final exam (all "moadim")

Course material:
1. Numbers: natural, integers, rational, real.
2. Bounded sets and supremum.
3. Sequences and limits, special types (monotonic, recursive).
4. Theorems: Bolzano-Weierstrass, Cauchy's criteria etc.
5. Functions and their limits: Cauchy's and Heine's definitions.
6. Continuity. Theorems: Intermediate Value, the two Weierstrass theorems.
7. Derivatives. Geometric and physical interpretation.
8. Theorems: Rolle, Fermat, Lagrange Mean Value, L'Hospital's Rule.
9. Taylor expansion.
10. Introduction to integrals.

Recorded lectures (you need to enter with login and password)

Recommended books:

B. Kon, S. Zafrani: "Differential and Integral Calculus 1", theory and exercises, Beck, (1996).

The "Open University" book, for the course 20474 ("HESHBON INFINITESIMALLY 1").

A. Coopermann: "Differential and Integral Calculus", Michlol, (1986).

Technion lectures in the equivalent course, 104031

Course slides

First half

Second half

Material prepared by Roy, 1

Material prepared by Roy, 2

Material prepared by Roy, 3 and 4

Material prepared by Roy, 5

Material prepared by Roy, 6

Material prepared by Roy, 7

Material prepared by Roy, 8

Material prepared by Roy, 9

Material prepared by Roy, 10 and 11