Teaching language: Swedish
Course module 

Credit distribution 

Examination dates 
Sp1 
Sp2 
Sp3 
Sp4 
Summer course 
No Sp 
0114 
Examination 
7,5 c 
Grading: TH 



7,5 c





18 Mar 2016 pm L, 
09 Apr 2016 am L, 
17 Aug 2016 am L 
0214 
Examination 
3,0 c 
Grading: TH 




3,0 c




03 Jun 2016 pm L, 
02 Apr 2016 am L, 
16 Aug 2016 am L 
In programs
TIDAL COMPUTER ENGINEERING, Year 1 (compulsory)
TIELL ELECTRICAL ENGINEERING, Year 1 (compulsory)
Examiner:
Univ lektor
Elin Götmark
Univ lektor
Joakim Becker
Go to Course Homepage
Eligibility:
In order to be eligible for a first cycle course the applicant needs to fulfil the general and specific entry requirements of the programme(s) that has the course included in the study programme.
Course specific prerequisites
Elementary knowledge in algebra corresponding to the course LMA212 Algebra.
Aim
Kursen skall, på ett logiskt sammanhängande sätt, ge grundläggande kunskaper i matematisk analys. Kursen skall dessutom skapa förutsättningar för matematisk behandling av tekniska problem i yrkesutövandet samt ge grundläggande kunskaper för fortsatta studier.
Learning outcomes (after completion of the course the student should be able to)
define the concepts of limit and continuity and calculate limits define the concepts of derivative and differentiation and use the definition of derivative calculate the derivatives of elementary functions use the fundamental rules of differentiation outline the elementary functions and account for their properties define the concepts of increasing (decreasing) function and local maximum (minimum) value construct graphs of functions and calculate the absolute maximum (minimum) value of a function define the concept of inverse function, calculate inverse functions and their derivatives define the concepts of antiderivative, definite integral and improper integral use the fundamental rules of integration use the most common methods for solving differential equations formulate, and in certain cases prove, fundamental theorems in analysis as, e. g. the connection between continuity and differentiation, the connection between area and antiderivatives and the meanvalue theorem interpret limits, derivatives and integrals geometrically apply her/his knowledge of derivatives and integrals to simpler applied problems understand how mathematics is build on definitions and theorems
Content
The course is divided in two subcourses located to two different periods.
Calculus, part 1 (7,5 hec):
Theory of sets. Logics. Algebraic equations of higher degree. Algebraic simplifications. Inequalities. Absolute value. The circle and the ellipse. The concept of function. Exponential and logarithmic functions. Derivative, rules of differentiation. Implicit differentiation. Tangent and normal. Limits. Continuity.
Derivative, differentiable functions. The Meanvalue theorem. Increasing and decreasing functions. Local maximum och minimum. Extremevalue problems.
Inverse function. The inverse trigonometric functions.
Derivatives of the elementary functions.
Asymptotes, construction of the graph of a function. Growth of exponentials and logarithms. Antiderivatives.
Calculus, part 2 (3 hec):
Connection between area and antiderivative. Definite and indefinite integral. Rules of integration, integration by parts, integration by substitution. Integration of rational functions, algebraic functions and certain transcendental functions. Improper integrals.
Separable differential equations. firstorder linear differential equations. Examples of problem which could be solved by differential equations. Operators, linear differential equations of higher orders with constant coefficients.
Organisation
The course includes lectures, tutorials, quizzes and homework.
Literature
James Stewart: Calculus Early Transcendentals, 7th edition, Brooks/Cole
Examination
The examination is based on written exams, grades TH.