Calculus and Linear Algebra

The goal of this course is to lay a strong foundation for the various and numerous applications of calculus and linear algebra, both directly within the field of electrical engineering as well as in general engineering mathematics.

This course consists of two halves: calculus and linear algebra.

The first half of this course starts directly where the previous calculus course ended, by introducing parametric surfaces and surface integrals, as well as the curl and divergence of a vector field. Then, all topics in multivariate and vector calculus are connected by means of Stokes theorem and the divergence theorem. Afterwards, the focussed is shifted towards series. These are introduced and analysed by means of various convergence tests, such as the integral test, the alternating series test, comparison tests and the ratio test. Finally, power series are introduced, which results in a treatise of Taylor series.

The second half of this course starts from scratch with methods from Linear Algebra to solve and analyse systems of linear equations. Here concepts like vectors, linear combination, span and linear independence play a central role. In addition, matrices and matrix algebra are key concepts that will be discussed, with a major focus on invertibility of matrices. Finally, a lot of time will be devoted towards the more geometrical aspects of linear algebra, such as linear transformations, LU factorisation, subspaces, coordinates, dimension, orthogonality, orthogonal projections and least-squares problems.

Examination method: this course will be assessed using examination software with a written component. The exams will contain a mix of short-answer exercises, where only the final answer is graded, and open questions, where the full reasoning and calculation are considered. The examination software (Grasple) will be used; therefore, the exams will take place in a computer room at the TU Delft. The written component will be on paper.

Course grade

The final grade of the course consists of the following components:

- Partial exam 1 - This exam covers the material of the first half of the course. This exam lasts 2 hours.

- Partial exam 2 - This exam covers the material of the second half of the course. This exam lasts 2 hours.

Exam grade calculation: (0.5 * Partial exam 1 + 0.5 * Partial exam 2)

Bonus calculation:

At the end of each lecture, a set of practice exercises will be posted on the Brightspace page using the online platform Grasple. Completing each exercise set results in a red, yellow or green check mark, depending on the score. You are allowed to take multiple attempts at each set to improve your score, but the questions may vary slightly per attempt. Participation is voluntary. The bonus grade is based on the Grasple exercises in the following way: each red checkmark counts as a 3, each yellow checkmark as a 6 and each green checkmark as a 10, while a set not made results in a grade equal to 0. For this, the results on the day of the final exam are the ones that are taken into account. The bonus grade is the average over the 75% best grades of the Calculus part and the 75% best grades of the Linear Algebra part.

Final grade calculation: (exam grade) + ((bonus grade)*(10 - exam grade)/100)

Repair possibilities:

- Endterm: The resit is taken in one part (i.e., contains all course topics). The result of the partial exams expire before the resit, and are not transferable to the next academic year. This covers the entire course contents. This exam lasts 3 hours.

Disclaimer: information may change depending on unforeseen circumstances or measures (see: TER Art 29, sub 4).