Course content
Section outline
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Course Content:
Chapter 1: Single and Multiple Integrals (2 weeks)
- Review of the Riemann integral and antiderivatives.
- Double and triple integrals.
- Applications to the calculation of areas, volumes, etc.
Chapter 2: Improper Integrals (2 weeks)
- Integrals of functions defined on an unbounded interval.
- Integrals of functions defined on a bounded interval but infinite at one endpoint.
Chapter 3: Differential Equations (2 weeks)
- First- and second-order ordinary differential equations.
- Elements of partial differential equations.
Chapter 4: Series (3 weeks)
Chapter 5: Laplace Transform (3 weeks)
- Definition and properties.
- Application to solving differential equations.
Chapter 6: Fourier Transform (3 weeks)
- Definition and properties.
- Application to solving differential equations.
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-Calculus (Mathematics 1 and 2) in particular: A mastery of single-variable calculus (derivatives, antiderivatives, integrals)
-Understanding vectors, dot and vector products, matrices, determinants, and eigenvalues and eigenvectors is necessary to solve certain systems of equations.
-Advanced concepts: The concepts of functions of several variables, vector calculus, and the topology of R^{n} are sometimes covered in the first year and serve as a foundation for differential equations.
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Opened: Thursday, 13 November 2025, 12:00 AMCloses: Friday, 13 November 2026, 3:49 PM
This test aims to assess the students' level with regard to the prerequisites and to determine whether they have mastered the key previous concepts that are necessary to follow this course.
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