## Calculus 1 (for IEM)

 Faculteit Science and Engineering Jaar 2022/23 Vakcode WBIE003-05 Vaknaam Calculus 1 (for IEM) Niveau(s) propedeuse Voertaal Engels Periode semester I a ECTS 5 Rooster rooster.rug.nl

Uitgebreide vaknaam Calculus 1 (for IEM)
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 first-order differential equations and can calculate the general solution of a first-order linear differential equation by means of an integrating factor.
7. solve homogeneous second-order 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)
Toetsvorm Opdracht (AST), Schriftelijk tentamen (WE), Tussentoets (IT)
(See remarks for grading.)
Vaksoort propedeuse
Coördinator A.M.S. Waters, PhD.
Docent(en) A.M.S. Waters, PhD.
Verplichte literatuur
Titel Auteur ISBN Prijs
The reader “Basic Mathematical Skills” is made freely available on Brightspace
Calculus. Early transcendentals. Newest (9th) Edition (International Metric Edition). Cengage Learning (2020) James Stewart 9780357113516
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 Grading of the course:
B = the mark of the remedial BMS exam
FE = the mark of the final exam
M = the mark of the midterm exam
H = the average mark of the homework assignments
C = 0.85 FE + 0.15 B
————————————————————————
If FE < 4.5 then the final mark is FE.
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).

A detailed explanation of the grading is provided in the course syllabus which will be published on Brightspace.

The course unit prepares students for the course units Linear Algebra and Calculus 2 in which the learning objectives attained are recommended as prior knowledge.

This course was previously registered with course code WPMA18003
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