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Applied Differential Calculus
Engineering & Social Sciences Program
Madrid, Spain
Dates: 1/16/26 - 5/30/26
Applied Differential Calculus
OVERVIEW
CEA CAPA Partner Institution: Universidad Carlos III de Madrid
Location: Madrid, Spain
Primary Subject Area: Mathematics
Instruction in: English
Course Code: 15975
Transcript Source: Partner Institution
Course Details: Level 200
Recommended Semester Credits: 3
Contact Hours: 42
Prerequisites: Calculus, Linear Algebra.
DESCRIPTION
1.- First order differential equations:
a. Linear equations.
b. Separable equations.
c. Exact equations.
d. Homogeneous equations.
e. Qualitative analysis of equations.
2.- Second order differential equations.
a. Nonlinear and linear equations.
b. Homogeneous and non-homogeneous Linear Equations.
c. Reduction of Order.
d. Euler-Cauchy Equations.
3.- Laplace transformations:
a. Definition.
b. Application to differential equations.
c. Convolution.
4.- Systems of differential equations:
a. Linear and Nonlinear Systems.
b. Vector representation.
c. Eigenvalues and linearization.
5. Fourier series and separation of variables:
a. Basic results.
b. Fourier Sine and Cosine Series.
c. Applications of Fourier series to differential equations.
6.- Numerical methods:
a. Euler method.
b. Runge-Kutta method.
c. Solution of boundary value problems.
a. Linear equations.
b. Separable equations.
c. Exact equations.
d. Homogeneous equations.
e. Qualitative analysis of equations.
2.- Second order differential equations.
a. Nonlinear and linear equations.
b. Homogeneous and non-homogeneous Linear Equations.
c. Reduction of Order.
d. Euler-Cauchy Equations.
3.- Laplace transformations:
a. Definition.
b. Application to differential equations.
c. Convolution.
4.- Systems of differential equations:
a. Linear and Nonlinear Systems.
b. Vector representation.
c. Eigenvalues and linearization.
5. Fourier series and separation of variables:
a. Basic results.
b. Fourier Sine and Cosine Series.
c. Applications of Fourier series to differential equations.
6.- Numerical methods:
a. Euler method.
b. Runge-Kutta method.
c. Solution of boundary value problems.