Mathematical Analysis 1 (Engineering Sciences)

Fall 2025/26        Instructor: Prof. Jonathan Ben-Artzi

Syllabus


  1. Basic notions:
    • Set theory
    • Sets of numbers
    • Logic
    • Basic properties of functions
    • Vectors
    • Polar/cylindrical/spherical coordinates
    • Complex numbers
  2. Limits and continuity:
    • Neighborhoods
    • Limits of sequences
    • Limits of functions
    • "Epsilon-delta" formalism
    • Properties of limits
  3. Properties of functions:
    • Local properties
    • Global properties
  4. Derivatives
    • Properties
    • Theorems of Rolle, Lagrange, Cauchy
    • Higher order derivatives
    • De l'Hôpital's Theorem
  5. Taylor expansions
  6. Integrals
    • Primitive functions and indefinite integration
    • Definite integrals
    • Cauchy integral
    • Riemann integral
    • Fundamental Theorem of Integral Calculus