9 ECTS credits
235 h study time
Offer 1 with catalog number 1015391ANR for all students in the 1st semester at a (A) Bachelor - preliminary level.
This course starts with a recap of important basic mathematical knowledge and skills around numbers and functions, limits, derivatives, indefinite integrals, proof techniques, sets, systems of equations, matrices and space geometry.
After this repetition we discuss some important concepts from the theory of vector spaces, but always limited to the context of Euclidean spaces. Linear algebra is subsequently further deepened with a study of eigenvalues and eigenvectors. We limit ourselves to the framework of square matrices. A technique for diagonalizing such matrices is treated and also an important application from population dynamics.
The concepts of derivatives and definite integrals are studied further so that an important range of applications can be treated. The linearization of a function is treated as an application of the theory of derivatives and calculations of length, volume and surface area is treated as an application of definite integrals.
Definite integrals are generalized to situations where the integration domain is unlimited and where the integrand is unbounded. This generalization allows us to discuss some special functions that are important in applications, e.g. the error function which in statistics plays an important role.
Differential equations have an undeniable importance in the description of natural phenomena. In this course we introduce these kind of equations and discuss solution methods for some simple types of such equations.
Finally, we discuss the transformation formulas between different two-dimensional and three-dimensional coordinate systems and we discuss the description of curves and quadric surfaces in space.
Attendance of the WPO classes is mandatory. Students with more than 25% unexcusable absences are not allowed at the written exam. The student can bring an official testimonial to the lecturer to excuse for an absence or send an excuse e-mail to inform about exceptional circumstances.
The student is accurate in the use of scientific notations and in the formulation of mathematical properties. The student knows different techniques to prove mathematical properties.
The student knows the properties of continuous functions and can study the convergence behaviour of numerical sequences. The students knows some sequence approximation techniques for roots of equations.
The student can calculate limits, derivatives and integrals of functions of one variable.
The student knows the basic techniques of matrix calculations and can use eigenvalues and eigenvectors to predict long-term behavior of simple dynamical systems.
The student knows the descriptions of several important curves and surfaces and of rotations in two and three dimensions.
The student knows the concepts and techniques of derivatives of functions of one variable and can use these in the description of the behaviour of functions and in extreme value problems.
The student knows the concept of ‘definite integral of a function of one variable’ and can use this concept to calculate areas, volumes and lengths.
The student knows different coordinate systems in the plane and in space and knows the transition rules between these systems.
The student can describe plane and space curves by means of parametrizations and can use parametrizations to study geometrical properties of curves.
The student can solve linear differential equations of the first order and of higher order if the coefficients are constants.
The final grade is composed based on the following categories:
Written Exam determines 100% of the final mark.
Within the Written Exam category, the following assignments need to be completed:
A mandatory written midterm test is organized. The written exam consists of a part on exercises (70% of the exam score) and a part on theory (30% of the exam score).
Final score in the first exam period:
If the midterm test score is higher than the exam score, then the final score is the weighted average of the midterm test score (20%) and the final exam score (80%). If the midterm test score is lower than the exam score, then the final score equals the exam score.
Final score in the second exam period:
The final score in the second exam period equals the score on the written exam in the second exam period.
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)
Bachelor of Bioengineering Sciences: Profile Cell and Gene Biotechnology (only offered in Dutch)
Bachelor of Bioengineering Sciences: Profile Chemistry and Bioprocess Technology (only offered in Dutch)
Bachelor of Bioengineering Sciences: Initial track (only offered in Dutch)