6 ECTS credits
180 h study time
Offer 1 with catalog number 1017260ANR for all students in the 2nd semester at a (A) Bachelor - preliminary level.
1 Series
1.1 Convergence of series
1.2 Convergence testst for series
1.3 Taylor series
2. Partial derivatives
2.1 Functions of several variables
2.2 Limits and continuity in higher dimensions
2.3 Partial derivatives
2.4 Differentiability, tangent plane and linearization
2.5 The chain rule
2.6 Directional derivatives and gradient
2.7 Taylor’s formula in two variables
2.8 Extreme values and saddle points
2.9 Lagrange multipliers
3. Multiple integrals
3.1 Double integrals
3.2 Applications of double integrals
3.3 Double integrals in polar coordinates
3.4 Triple integrals
3.5 Triple integrals in cylindrical coordinates
3.6 Substitutions in multiple integrals
4. Line integrals and surface integrals
4.1 Line integrals of scalar functions
4.2 Line integrals of vector functions
4.3 Green’s theorem
4.4 Conservative vector fields
4.5 Surfaces
4.6 Surface integrals of scalar functions
4.7 Surface integrals of vector functions
4.8 Stokes' theorem
4.9 Gauss' theorem
5. Descriptive geometry
5.1 Plane constructions: Monge’s method
5.2 Plane constructions: true dimensions
5.3 Space constructions
Attendance of the WPO classes is mandatory. Students with more than 25% unexusable absences are not allowed at the written exam.
The student knows different techniques to prove mathematical properties.
The student is accurate in the use of scientific notations and in the formulation of mathematical properties.
The student knows the basic properties of derivatives of functions of several variables and can use these to solve extreme value problems in several variables.
The student can find a polynomial approximation of a given order for a function of two variables and can find an error estimate.
The student knows the definitions and basic properties of double and triple integrals and can use these to calculate areas and volumes and fysical characteristics such as centre of mass and moments of inertia.
The student knows the substitution rule for double and triple integrals and can use it in transitions to polar coordinates, cylindrical coordinates and spherical coordinates.
The student knows the concepts of ‘line integral’ and ‘surface integral’ and can use these in fysical calculations of work and flux of vector fields.
The students knows the relation between conservative vector fields and potential functions and can use it in calculations of work done in a conservative vector field.
The student knows the theorems of Green, Stokes and Gauss and can use them to calculate work on a closed curve in two and three dimensions and flux through a surface.
The student knows different methods to represent a space body by a twodimensional drawing. The student knows which constructions in the plane drawing have to be done to solve problems concerning the threedimensional body.
The final grade is composed based on the following categories:
Oral Exam determines 45% of the final mark.
Written Exam determines 55% of the final mark.
Within the Oral Exam category, the following assignments need to be completed:
Within the Written Exam category, the following assignments need to be completed:
The exam consists of two written exams and an oral exam. The topic ‘Descriptive geometry’ is tested on a written midterm exam where the student has to do constructions as done in class during the semester. Participation is mandatory. This exam counts for 10% of the final score.
On the written exam during the exam period the students have to do exercises of types that were solved during the semester. This written exam counts for 45% of the final score.
On the oral exam during the exam period knowing and understanding of the theoretical part of the course is tested. This oral exam counts for 45% of the final score.
In the August exam period, all three parts of the exams are organized a second time.
This offer is part of the following study plans:
Bachelor of Architectural Engineering: Standaard traject (only offered in Dutch)
Bachelor of Architectural Engineering: Verkort traject (only offered in Dutch)