## Calculus for Computing Science

 Faculteit Science and Engineering Jaar 2022/23 Vakcode WBCS036-05 Vaknaam Calculus for Computing Science Niveau(s) propedeuse Voertaal Engels Periode semester I b ECTS 5 Rooster rooster.rug.nl

Uitgebreide vaknaam Calculus for Computing Science
Leerdoelen 1. The student can calculate limits using the limit laws, the Squeeze Theorem and l'Hospital's rule.
2. The student can apply the techniques of differentiation (product rule, quotient rule, and chain rule). In addition, the student can use these techniques to find the local and absolute extreme values of a given function.
3. The student can compute Taylor expansions of concrete functions and use these expansions to compute limits and approximations for definite integrals.
4. The student can apply the standard techniques of integration (substitution rule, integration by parts, trigonometric integrals and substitutions, integration of rational functions by partial fractions) and is able to recognize which technique is best used in a given situation.
5. The student can calculate with complex numbers, can plot them in the complex plane, is able to formulate and use DeMoivre's Theorem, can compute roots of a complex number and can solve equations in that way. The student can give the definition of the complex exponential function and can use that in applications.
6. The student can solve separable first-order differential equations and can compute the general solution of a first-order linear differential equation by means of an integrating factor.
7. The student can solve homogeneous second-order differential equations with constant coefficients and compute a particular solution for non-homogeneous equations using the method of undetermined coefficients.
Omschrijving The course starts with refreshing and improving the basic mathematical skills (BMS). Then real functions of one real variable are treated: standard and composed functions, models, limits, derivatives, extreme values, Taylor expansions, and integrals (applications and techniques). Subsequently complex numbers are introduced, an imaginary extension of the real numbers. Finally, differential equations are solved to describe processes in physics, economy, medical sciences, etc. This topic includes: initial value problems, directional fields, equilibrium solutions and stability, separation of variables, variation of constants, homogeneous and inhomogeneous equations, and conversion of complex solutions into realvalued solutions. The material is illustrated through examples that focus on the applications of mathematical techniques.
Uren per week
Onderwijsvorm Hoorcollege (LC), Werkcollege (T)
(Lectures, tutorials, computer-assisted tutorials to improve basic mathematical skills.)
Toetsvorm Opdracht (AST), Schriftelijk tentamen (WE), Tussentoets (IT)
(The final grade G is computed as follows: - If BMS >= 6, then B=10 - If BMS < 6, then B=0, where BMS= grade of the BMS test (on a scale from 1 to 10) - CG = (9*WE + B)/10, where WE= grade of the final written exam (on a scale from 1 to 10) - If CG < 4.5, then the final grade is G = CG - If CG >= 4.5, then the final grade is G = max(CG, 0.6*CG + 0.2*M + 0.2*H), where M= grade Midterm Exam and H= average)
Vaksoort propedeuse
Coördinator P.M.J. Tibboel, PhD.
Docent(en) P.M.J. Tibboel, PhD.
Verplichte literatuur
Titel Auteur ISBN Prijs
TBA
Entreevoorwaarden The course unit assumes only prior knowledge acquired from Mathematics B as taught in pre-university programmes (VWO) on Dutch secondary schools (or equivalent).
Opmerkingen Please note that although this course covers the same topics as the course Calculus for AI, these subjects are treated more in depth in Calculus for CS. Therefore, the Board of Examiners of CS will not accept taking the course Calculus for AI as a replacement for the course Calculus for CS.

The course unit is followed by, and prepares students for, the course unit Linear Algebra and Multivariable Calculus for Computer Science and AI in which the learning objectives attained are required as prior knowledge.

All CS bachelor courses have limited enrollment:
- CS students can always enter each course, regardless of whether the course is mandatory for them or not.
- A maximum of only 20 places per course is available for non-CS students. These places are filled on a first-come-first-served basis, with priority given to students with a strong CS-related background (e.g., CS exchange students, AI students, etc.). These students need to meet the course prerequisite requirements as mentioned on Ocasys.
-Six weeks before the course starts, the 20 students that can join are selected and added to the course. If you enroll after this date, you will be placed on the waiting list.