Calculus

In this course the basic concepts from calculus are treated. The course is roughly divided into three parts. The first part of the course focusses on single variable calculus. This parts main subjects are general understanding of functions of a single variable and integration of these functions. General understanding of functions contains a variety of topics, including inverse (trigonometric) functions, limits, derivatives, implicit differentiation, Taylor polynomials and l'Hospital's rule. Subsequently, the subject of integration mainly focusses on the common integration techniques the substitution rule, integration by parts and integration by partial fraction definition and ends with a treatise of improper integrals. Several differentiation and integration techniques are then combined when covering first order linear and separable differential equations.

The second part of the course focusses on multivariate calculus. After starting with some general geometrical concepts such as the dot and cross product, as well as graphs and contour plots for functions of several variables, one of the main subjects of this part is partial derivatives and various related topics, including tangent planes, linear approximations, the chain rule, directional derivatives, the gradient and extreme values. This part finishes with a treatise of double and triple integrals, including polar, cylindrical and spherical coordinates, as well as general changes of coordinates.

The final part of the course focusses on vector calculus. In this part, vector fields are introduced. In addition, line integrals are covered both for scalar functions and for vector fields and connected to double integrals by means of Greens theorem.

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 mainly covers the material of the second half of the course. However, some techniques from the first half of the course might be used as well. 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 best 75% of all these grades.

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).