Calculus (for BME)
Faculteit  Science and Engineering 
Jaar  2022/23 
Vakcode  WBBE05405 
Vaknaam  Calculus (for BME) 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester I a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Calculus (for BME)  
Leerdoelen  After completing this course students should be able to: 1. calculate limits using the limit laws, the Squeeze Theorem and l'Hospital's rule. 2. calculate derivatives by applying the product rule, quotient rule, and chain rule, and combinations thereof. In addition, the student can use these techniques to find the local and absolute extreme values of a given function. 3. calculate Taylor expansions of concrete functions and use these expansions to compute limits and approximations for definite integrals. 4. calculate integrals using 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. 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 state the definition of the complex exponential function and can use that in applications. 6. solve separable firstorder differential equations and can calculate the general solution of a firstorder linear differential equation by means of an integrating factor. 7. solve homogeneous secondorder differential equations with constant coefficients and calculate a particular solution for nonhomogeneous equations using the method of undetermined coefficients. 

Omschrijving  The course starts by refreshing and improving the basic mathematical skills (BMS); in the first month of the course a remedial exam is taken. This BMS exam and the relevant practice problems will use the SOWISO digital learning environment. The course will then treat: real functions of one real variable, standard transcendental functions, compositions, limits, derivatives, extreme values, Taylor expansions, integrals, complex numbers, and finally, ordinary differential equations (ODE's). ODE's will cover initial value problems, directional fields, equilibrium solutions and stability, separation of variables, variation of constants, homogeneous and inhomogeneous linear equations. The material is illustrated through examples that focus on the applications of mathematical techniques.  
Uren per week  
Onderwijsvorm 
Hoorcollege (LC), Werkcollege (T)
(Tutorials are mandatory) 

Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE), Tussentoets (IT)
(B=mark remedial BMS exam, F= mark final exam, M=mark midterm exam, H=average mark homework assignments, C = 0.85 F + 0.15 B. If F < 4.5 then the final mark is F. If C < 5.5, then the final mark is C. Otherwise, the final mark is max (C, 0.75 C + 0.25 M, 0.75 C + 0.25 H, 0.7 C + 0.15 M + 0.15 H).)) 

Vaksoort  bachelor  
Coördinator  P.M.J. Tibboel, PhD.  
Docent(en)  P.M.J. Tibboel, PhD.  
Verplichte literatuur 


Entreevoorwaarden  The course unit assumes only prior knowledge acquired from Mathematics B as taught in preuniversity programmes (VWO) on Dutch secondary schools (or equivalent).  
Opmerkingen  Mail address coordinator course: p.m.j.tibboel@rug.nl Please note:  For students of cohort 2020 and 2021: If you still need to do the exam of Calculus 1 (for IEM), the content of the Calculus (for BME) course is the same!  Tutorials are mandatory to attend.  Due to Corona/Covid regulations the above mentioned Teaching method and/or Assessment could be subject to change. Study Load: Lecture 24 hours Tutorial 24 hours Selfstudy 92 hours In total 140 hours (5 ECTS) 

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