Engineering mathematics 2 (5 cr)

Objective

You are familiar with the basic properties of mathematical functions and you are able to calculate limits.

You understand the concept of the rate of change. You are able to form the derivative function and use it for calculating the rate of change and defining the critical points of a function. You are also able to form and solve extreme value problems mathematically.

You are familiar with indefinite and definite integral and you are able to form basic integral functions. You are able to calculate areas and volumes by using integral calculus.

You are able to solve trigonometric equations and you know the basic properties of the sine curve.

You are familiar with complex numbers and the complex plane.

You are able to carry out basic calculations with matrices and determinants as well as solve a system of equations using these mathematical concepts.

Content

How do you define the domain and range of a function? How do you construct a composite function?

How do you calculate the limit of a rational function, when the limits of the numerator and the nominator are zeros?

How do you define the functions of velocity and acceleration by using derivative? How do you construct the derivative sign diagram of a fourth-degree polynomial function, define the critical points and draw the graph of the function? How do you use differential calculus to optimize costs, manufacturing volumes, dimensions of structures, routes and e.g. to define the minimum distance between two moving particles?

How do you integrate a function? How do you find the area bounded by two plane curves? How do you calculate the volume of a solid of revolution?

How do you solve geometric problems using trigonometric formulas? How do you solve sine curve problems of alternating voltage, piston movement, behavior of temperature and tidewater and vibratory motion?

How do you solve electric circuit problems by using complex arithmetic?

How do you find the inverse of a matrix? How do calculate e.g. linear mappings used in CAD-programs?

Evaluation

Students are able to
use professional vocabulary systematically:
• They know basic concepts and formulas of functions, limits, differential calculus, trigonometry, complex numbers and matrices.
• They are able to carry out basic calculations and analyses.

identify interrelated tasks:
• They are able to combine mathematical formulas and rules to form more demanding mathematical structures.
• They can see methods of application for mathematical structures.

use the key models, methods, and techniques of the professional field:
• They are able to model and solve small practical problems mathematically.

Course material

Oppikirja:
Tuomenlehto, Holmlund, Huuskonen, Makkonen ja Surakka. Insinöörin matematiikka, Edita, 2014. ISBN 9789513763527.
Kurssilla käsitellään kirjasta kappaleet 3,10,11,12,13

Learn-oppimisympäristön harjoitustehtävät ja muut opintomateriaalit.

Lisäksi tarvitset taulukkokirjan, esimerkiksi MAOL -taulukot sekä laskimen.

Study forms and methods

Työviikkopohjainen oppimisväylä:
Työjärjestyksen mukaiset oppitunnit

Opintoja nopeuttava oppimisväylä:
Ei mahdollisuutta työhön integroituun oppimisväylään.

Työhön integroitu oppimisväylä:
Mahdollisuus suorittaa tenttimällä ilman osallistumista kontaktitunneille, kunhan edeltävät opinnot ovat suoritettuna.

Student workload

Opintopisteiden mukainen työmäärä.

Further information

Kurssilla käsiteltävät asiat:
3) Matriisit ja determinantit
10) Derivaatta
11) Integraali
12) Differentiaaliyhtälöt
13) Todennäköisyyslaskenta ja tilastomatematiikka

Evaluation scale

1-5

Assessment methods and criteria

tentti ja mahdollisesti laskuharjoituksista kertyneet lisäpisteet.
Uusintatentissä laskuharjoitusten lisäpisteitä ei huomioida.

Qualifications

Completing the course of Engineering mathematics 1 or comprehensive knowledge of its contents is required.