## Calculus 1

 Faculteit Science and Engineering Jaar 2020/21 Vakcode WBMA003-05 Vaknaam Calculus 1 Niveau(s) propedeuse Voertaal Engels Periode semester I a ECTS 5 Rooster rooster.rug.nl

Uitgebreide vaknaam Calculus 1
Leerdoelen At the end of the course, the student is able to
1. explain the principle of mathematical induction and apply that technique to prove a statement about positive integers.
2. calculate with complex numbers, plot them in the complex plane, formulate and use De Moivre's Theorem, compute roots of a complex number and solve equations in that way; give the definition of the complex exponential function and use that in applications.
3. give the precise definition of a limit and can apply the definition in simple proofs; calculate limits using the limit laws, the Squeeze Theorem and l'Hospital's rule.
4. give the definition of continuity, examples of discontinuity and basic properties of continuous functions; in particularly, the student can state and apply the Intermediate Value Theorem.
5. give the definition of the derivative of a function and use that in simple proofs, give the derivative of all basic functions and calculate derivatives with the help of differentiation rules; when derivatives are computed in applied situations, explain their meaning; compute a tangent line or linear approximation and give the geometric meaning of differentials.
6. prove Rolle's Theorem and the Mean Value Theorem and deduce basic facts concerning extreme values of functions.
7. give the definitions of a antiderivative and of a definite integral, reproduce a proof of the Fundamental Theorem of Calculus to view differentiation and integration as inverse processes.
8. apply the standard techniques of integration (substitution rule, integration by parts, trigonometric integrals and substitutions, integration of rational functions by partial fractions) and recognize which technique is best used in a given situation.
9. formulate first-order differential equations that are used to model population growth, or electric circuits, for instance; solve a separable first-order differential equation and find a general solution of a first-order linear differential equation using an integrating factor.
Omschrijving 1. The main focus of this course will be on real functions f(x) of a real variable x. We will treat the subjects: complex numbers and the extension of the exponential, sine, and cosine functions to complex functions, limits, continuity, differentiation and integration techniques, and some basics on differential equations.
2. Besides the computational aspects, there is also attention for the theoretical aspects. We will also look at applications of the treated techniques.
Uren per week
Onderwijsvorm Hoorcollege (LC), Opdracht (ASM), Practisch werk (PRC), Werkcollege (T)
(the practicals consist of the basic mathematical skills test)
Toetsvorm Opdracht (AST), Schriftelijk tentamen (WE), Tussentoets (IT)
(Final grade = max(ST, 0.2 HW + 0.2 TT + 0.6 ST) + B only if ST >=4.5 otherwise Final grade = ST+B, where HW average homework grade, TT mid-term grade and ST final exam grade (Note: all these grades are between 0 and 9); B = 1 if the Basic Skill test is passed, otherwise B=0. (Note: HW and TT do not count for the re-exam.))
Vaksoort propedeuse
Coördinator dr. H. Jardon Kojakhmetov
Docent(en) dr. H. Jardon Kojakhmetov
Verplichte literatuur
Titel Auteur ISBN Prijs
Calculus, Early Transcendentals, International Metric Edition (newest edition) James Stewart 9780357113516
Entreevoorwaarden The course builds on high school knowledge in mathematics. The course starts with a test to assess basic mathematical skills. If the result of this test is unsatisfactory, several compulsory practicals will follow, after which a final test is offered.
Opmerkingen This course was registered last year with course code WICAL1-12
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