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
    • Complex numbers
  2. Limits and continuity:
    • Neighborhoods
    • Limits of sequences
    • Limits of functions
    • "Epsilon-delta" formalism
    • Properties of limits
    • Bolzano-Weierstrass Theorem
  3. Local properties of functions:
    • Landau symbols
    • Infinitesimal and infinite functions
  4. Global properties:
    • Bolzano's Theorem
    • Intermediate Value Theorem
    • Asymptotes
    • Lipschitz and uniformly continuous functions
  5. Derivatives:
    • Properties
    • Fermat's Theorem
    • Theorems of Rolle, Lagrange (mean value theorem), Cauchy
    • Monotonicity intervals
    • Extreme values
    • Higher order derivatives
    • Inflection points
    • Qualitative study of a function
    • De l'Hôpital's Theorem
  6. Taylor and Maclaurin expansions:
    • Error estimates
    • Approximating basic functions (trigonometric functions, exponential, logarithm, powers)
    • Multiplying Taylor expansions
    • Taylor expansions of composition of functions
  7. Integrals:
    • Primitive functions and indefinite integration
    • Definite integrals
    • Cauchy integral
    • Riemann integral
    • Integral mean value
    • Fundamental Theorem of Integral Calculus
    • Improper integrals
    • Integrals with functional bounds
  8. Numerical series
  9. Ordinary differential equations (ODEs):
    • First-order ODEs in normal form
    • The initial-value problem
    • Second-order ODEs with constant coefficients