Chapter 01: Real Numbers, Limits and Continuity

Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN.

The notes of this chapter is written by Prof. Prof. Muhammad Farooq, Punjab College, Sargodha.

• Articles of Exercise 1.1
  • Rational numbers, Irrational numbers, Real numbers, Complex numbers
  • Properties of real numbers, Order properties of $\mathbb{R}$
  • Absolute value or modules of a $\mathbb{R}$
  • The completeness property of $\mathbb{R}$
  • Upper bound, lower bound
  • Real line, Interval
  • Working rule for the solution of inequality
  • Binary relation (B.R), Domain of B.R, Range of B.R
  • Function, Onto or surjective funiton, (1-1) Function, Bijective Function
  • Real valued function, Image of a function, Bracket function
• Articles of Exercise 1.2
  • Finite limit at a finite point
  • Left hand limit
  • Right hand limit
• Articles of Exercise 1.3
  • Continuity