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Mathematical Analysis I

  • Course name: Mathematical Analysis I
  • Code discipline:
  • Subject area: ['Differentiation', 'Integration', 'Series']

Short Description

Prerequisites

Prerequisite subjects

Prerequisite topics

Course Topics

Course Sections and Topics
Section Topics within the section
Sequences and Limits
  1. Sequences. Limits of sequences
  2. Limits of sequences. Limits of functions
  3. Limits of functions. Continuity. Hyperbolic functions
Differentiation
  1. Derivatives. Differentials
  2. Mean-Value Theorems
  3. l’Hopital’s rule
  4. Taylor Formula with Lagrange and Peano remainders
  5. Taylor formula and limits
  6. Increasing / decreasing functions. Concave / convex functions
Integration and Series
  1. Antiderivative. Indefinite integral
  2. Definite integral
  3. The Fundamental Theorem of Calculus
  4. Improper Integrals
  5. Convergence tests. Dirichlet’s test
  6. Series. Convergence tests
  7. Absolute / Conditional convergence
  8. Power Series. Radius of convergence
  9. Functional series. Uniform convergence