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Analysis I - Period 1+2
STEM in Amsterdam Program
Amsterdam, Netherlands
Dates: mid Aug 2025 - late Dec 2025
Analysis I - Period 1+2
OVERVIEW
CEA CAPA Partner Institution: Vrije Universiteit Amsterdam
Location: Amsterdam, Netherlands
Primary Subject Area: Mathematics
Instruction in: English
Course Code: X_400641
Transcript Source: Partner Institution
Course Details: Level 100
Recommended Semester Credits: 3
Contact Hours: 84
DESCRIPTION
In this course we present a thorough introduction of the theory of real analysis for single variable functions. Theorems and their proofs form an important part of this course. In addition sufficient attention is paid to various calculus techniques. We will treat the following topics:
a) Natural numbers and mathematical induction.
b) Rational and real numbers and the completeness of the real numbers.
c) Sequences of real numbers (convergence, subsequences, Cauchy sequences).
d) Continuity and limits of real functions. Uniform continuity.
e) Differentiation (derivative of a function, mean value theorems, L'Hospital's rule, Taylor's theorem).
f) Integration (Riemann integral, improper integral, integration techniques)
g) Complex numbers
Contact hours listed under a course description may vary due to the combination of lecture-based and independent work required for each course therefore, CEA's recommended credits are based on the ECTS credits assigned by VU Amsterdam. 1 ECTS equals 28 contact hours assigned by VU Amsterdam.
a) Natural numbers and mathematical induction.
b) Rational and real numbers and the completeness of the real numbers.
c) Sequences of real numbers (convergence, subsequences, Cauchy sequences).
d) Continuity and limits of real functions. Uniform continuity.
e) Differentiation (derivative of a function, mean value theorems, L'Hospital's rule, Taylor's theorem).
f) Integration (Riemann integral, improper integral, integration techniques)
g) Complex numbers
Contact hours listed under a course description may vary due to the combination of lecture-based and independent work required for each course therefore, CEA's recommended credits are based on the ECTS credits assigned by VU Amsterdam. 1 ECTS equals 28 contact hours assigned by VU Amsterdam.