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## Syllabus for

MVE415 - Calculus

Owner: TIDAL
10,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: First-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES

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

#### 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 mean-value 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 Mean-value theorem. Increasing and decreasing functions. Local maximum och minimum. Extreme-value 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. first-order 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.

Page manager Published: Mon 28 Nov 2016.