# Search course

​​​​
​​

## Syllabus for

LMA400 - Calculus Owner: TIMAL
7,5 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 0104 Examination 7,5c Grading: TH 7,5c 16 Jan 2016 pm L, 04 Apr 2016 pm L, 25 Aug 2016 pm L

#### In programs

TIDSL PRODUCT DESIGN ENGINEERING, Year 1 (compulsory)
TIMAL MECHANICAL ENGINEERING, Year 1 (compulsory)
TIMEL MECHATRONICS ENGINEERING, Year 1 (compulsory)
TIEPL ECONOMICS AND MANUFACTURING TECHNOLOGY, Year 1 (compulsory)

#### 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.

-

#### Aim

The aim of the course is to give basic knowledge in mathematical analysis. The course will also create qualification for mathematical treatment of technical problems in future profession and supply a good base for further studies.

#### 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 and have some basic knowledge of mathematical proof

#### Content

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, 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.

Calculations with Matlab.

#### Organisation

The course includes lectures, tutorials, quizzes and homework.

#### Literature

Course litterature is announced on the course webpage before start.

#### Examination

The examination is based on written exams, grades TH.

• Page manager Published: Thu 04 Feb 2021.