Calculus 1
Faculteit  Science and Engineering 
Jaar  2017/18 
Vakcode  WICAL112 
Vaknaam  Calculus 1 
Niveau(s)  propedeuse 
Voertaal  Engels 
Periode  semester I a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Calculus 1  
Leerdoelen  After this course: 1. The student knows the principle of mathematical induction and is able to apply that technique to prove a statement about positive integers. 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  1. 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. 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)
(Final Grade = max(WE, 0.2 HW + 0.2 MT + 0.6 WE) + B only if WE >=4.5 otherwise Final Grade = WE + B, where HW average homework assignments grade, MT midterm written exam grade and WE final written exam grade (Note: all these grades are between 0 and 9); B = 1 if the Basic Skills test is passed, otherwise B=0. Note: HW and MT do not count for the reexam.) 

Vaksoort  propedeuse  
Coördinator  prof. dr. ir. R.W.C.P. Verstappen  
Docent(en)  prof. dr. ir. R.W.C.P. Verstappen  
Verplichte literatuur 


Entreevoorwaarden  
Opmerkingen  This course unit will start with a test to assess basic mathematical skills. Should the result be unsatisfactory, students will practice basic mathematical skills through exercises during the tutorials of the Mathematics Refresher Course. Should the result of this test be unsatisfactory, several compulsory practicals will follow, after which a second and third test will be offered. While passing these tests is not a formal requirement for passing the course, a passing grade constitutes 1 out of 10 possible grade points of the course. 

Opgenomen in 
