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Calculus I
Engineering & Social Sciences Program
Madrid, Spain
Dates: early Sep 2025 - mid Dec 2025
Calculus I
OVERVIEW
CEA CAPA Partner Institution: Universidad Carlos III de Madrid
Location: Madrid, Spain
Primary Subject Area: Mathematics
Instruction in: English
Course Code: 16472
Transcript Source: Partner Institution
Course Details: Level 100
Recommended Semester Credits: 3
Contact Hours: 42
DESCRIPTION
1. REAL VARIABLE FUNCTIONS
1.1 The real line: sets of numbers, properties, absolute values
1.2 Elementary functions and curves
1.3 Polar coordinates
2. LIMITS AND CONTINUITY
2.1 Limits of functions. Properties and fundamental theorems
2.2 Continuity of functions
2.3 Fundamental theorems
3. DERIVATIVES AND THEIR APPLICATIONS
3.1 Definition, properties, and derivatives of elementary functions.
3.2 Meaning of the derivative. Extrema.
4 LOCAL STUDY OF A FUNCTION
4.1 Graphic representation
4.2 Taylor polynomial and its applications
5. SEQUENCES AND SERIES OF REAL NUMBERS
5.1 Sequences of numbers
5.2 Series of positive numbers
5.3 Absolute and conditional convergence
6. SEQUENCES AND SERIES OF FUNCTIONS
6.1 Sequences and series of functions.
6.2 Taylor series
7. INTEGRATION IN ONE VARIABLE
7.1 Calculus of primitives
7.2 Fundamental Theorem of Calculus
7.3 Applications
1.1 The real line: sets of numbers, properties, absolute values
1.2 Elementary functions and curves
1.3 Polar coordinates
2. LIMITS AND CONTINUITY
2.1 Limits of functions. Properties and fundamental theorems
2.2 Continuity of functions
2.3 Fundamental theorems
3. DERIVATIVES AND THEIR APPLICATIONS
3.1 Definition, properties, and derivatives of elementary functions.
3.2 Meaning of the derivative. Extrema.
4 LOCAL STUDY OF A FUNCTION
4.1 Graphic representation
4.2 Taylor polynomial and its applications
5. SEQUENCES AND SERIES OF REAL NUMBERS
5.1 Sequences of numbers
5.2 Series of positive numbers
5.3 Absolute and conditional convergence
6. SEQUENCES AND SERIES OF FUNCTIONS
6.1 Sequences and series of functions.
6.2 Taylor series
7. INTEGRATION IN ONE VARIABLE
7.1 Calculus of primitives
7.2 Fundamental Theorem of Calculus
7.3 Applications