Calculus I
Faculteit  University College Groningen 
Jaar  2019/20 
Vakcode  UCG1RM04 
Vaknaam  Calculus I 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester II 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Calculus I  
Leerdoelen  1.The student can evaluate, plot the graphs of, perform algebraic operations on and apply various transformations on functions. Model reallife situations with functions. 2.The student can calculate with complex numbers, can plot them in the complex plane, is able to formulate and use De Moivre'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. 3.The student can give the precise definition of a limit and can apply the definition in simple proofs. The student can calculate limits using the limit laws, the Squeeze Theorem and l'Hospital's rule. 4.The student can 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.The student can give the definition of the derivative of a function and can use that in simple proofs, knows the derivative of all basic functions and can calculate derivatives with the help of differentiation rules. When derivatives are computed in applied situations, the student can explain their meaning. The student can compute a tangent line or linear approximation and can give the geometric meaning of differentials. 6.The student can prove Rolle's Theorem and the Mean Value Theorem and can deduce basic facts concerning extreme values of functions. 7.The student is able to give the definitions of a antiderivative and of a definite integral, can reproduce a proof of the Fundamental Theorem of Calculus and is able to view differentiation and integration as inverse processes. 8.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. 9.The student is able to formulate firstorder differential equations that are used to model population growth, or electric circuits, for instance. The student can solve a separable firstorder differential equations and can find a general solution of a firstorder linear differential equation using an integrating factor. 

Omschrijving  Calculus 1 is one of the modules of the Research and Methodology: Year 1 course. It is aimed at those who are oriented towards major in Smart Technologies, Health and Life Science and Economics. The main focus of this course will be on real functions f(x) of a real variable x. We will treat the subjects continuity, limits, differentiation and integration, differential equations, complex numbers and the extension of the exponential, sine, and cosine functions to complex functions. 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  4  
Onderwijsvorm  Lecture, Tutorial  
Toetsvorm  Assignments, Written exam  
Vaksoort  bachelor  
Coördinator  dr. O. Kavatsyuk  
Docent(en)  dr. O. Kavatsyuk  
Verplichte literatuur 


Entreevoorwaarden  We recommend grade 70 or higher on the Diagnostic Math Test (otherwise, please discuss with teacher). 

Opmerkingen  
Opgenomen in 
