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Differential Calculus
Engineering & Social Sciences Program
Madrid, Spain
Dates: early Sep 2025 - mid Dec 2025
Differential Calculus
OVERVIEW
CEA CAPA Partner Institution: Universidad Carlos III de Madrid
Location: Madrid, Spain
Primary Subject Area: Mathematics
Instruction in: English
Course Code: 18254
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. Fundamental theorems
2.3 Uniform continuity
3. Derivatives and their applications
3.1 Definition, properties, derivatives of elementary functions
3.2 Meaning of the derivative. Extrema
4 Local study of a function
4.1 Graphic representation
4.2 Taylor's 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 of functions. Punctual and uniform convergence
6.2 Series of functions. Punctual and uniform convergence
6.3 Taylor series
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. Fundamental theorems
2.3 Uniform continuity
3. Derivatives and their applications
3.1 Definition, properties, derivatives of elementary functions
3.2 Meaning of the derivative. Extrema
4 Local study of a function
4.1 Graphic representation
4.2 Taylor's 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 of functions. Punctual and uniform convergence
6.2 Series of functions. Punctual and uniform convergence
6.3 Taylor series