Free practice for engineering students
Theory, problems with worked solutions and practice exams in 71 courses – from basic maths to the finite element method, control engineering and machine learning.
Open Axle →Mechanics and Design
Statics and DynamicsStatics deals with bodies at rest (or moving at constant velocity). Then the sum of all forces and t…Machine DesignReal machine parts are rarely loaded by just one type of load at a time. A bolt may have both preloa…ThermodynamicsThermodynamics is about energy: how it is stored, converted and flows as heat and work. A system is …Materials TechnologyA material's properties – strength, ductility, conductivity, density – are largely determined by how…Strength of MaterialsStrength of materials is about how materials behave under load: how much stress builds up inside the…Finite Element MethodThe finite element method (FEM) solves complicated structural problems by dividing a structure into …Machine Dynamics and VibrationsFree vibration is the motion a system performs when it is disturbed from equilibrium and then left t…
Programming
Programming with PythonA program is a recipe that the computer follows line by line. In Python you store values in variable…Intermediate ProgrammingObject-oriented programming (OOP) lets you bundle data together with the functions that belong to it…Discrete MathematicsComputers are built on logic: true and false, and and or. Sets are how mathematics collects things. …Databases, Networks and SecurityAlmost every app stores its data in a database: users, orders, measurements. A relational database s…Machine Learning and Data AnalysisMachine learning means letting the computer find patterns in data instead of us writing the rules. Y…
Mathematics and Science
PhysicsAnything that moves back and forth around an equilibrium position – a mass on a spring, a pendulum, …CalculusThe derivative measures how fast a quantity changes. Geometrically, it is the slope of the tangent l…Linear Algebra and Differential EquationsA matrix is a table of numbers, but its most important interpretation is as a linear map: takes a ve…Statistics and Risk AnalysisProbability theory gives you tools to handle uncertainty: how likely is it that a component fails, t…Multivariable CalculusA function of several variables, such as , describes something that depends on more than one quantit…Laplace, Fourier and PDEsThe Laplace transform turns a function of time, , into a function of a complex variable : . The key …Numerical MethodsMany practical engineering equations, such as arising from pipe friction, beam stresses or equilibri…General ChemistryChemical reactions occur in fixed numerical ratios between molecules, but in the lab we weigh substa…
Electrical and Automation
Electric CircuitsA DC circuit has voltage and current that do not change direction: batteries, solar panels and elect…Embedded Systems and InstrumentationComputers and microcontrollers store and compute with everything as binary numbers (0s and 1s). To r…RoboticsA robot arm must always know where its tool is and which way it points, both in its own frame and in…Control EngineeringIn control engineering we describe how a system (a motor, a temperature process, a robot arm) respon…ElectronicsA diode is a component that lets current through in (almost) only one direction, and a transistor le…Electric Power and MachinesElectricity from the power station is sent out at high voltage and transformed down in several steps…
Society and Sustainability
Energy and Fluids
Fluid MechanicsHydrostatics deals with fluids at rest. Even though nothing is flowing, the fluid still exerts press…Heat TransferConduction is the transport of heat through a substance without the substance itself moving – the he…
Product Development and Economics
Engineering EconomicsMoney has a time value: 100 NOK today is worth more than 100 NOK in a year, because the amount can e…Product DevelopmentProduct development doesn't start with a solution, but with understanding what the user actually nee…
Start here: foundations
Foundations of MathematicsAll engineering mathematics rests on ordinary arithmetic. Before you can differentiate, solve equati…Foundations of PhysicsAll of physics is about measuring and calculating with quantities such as length, time, mass, speed …
Civil Engineering
Building and StructuresBefore you can design a beam or a floor, you need to know which loads it must carry. In Norway we fo…Geotechnical EngineeringEverything we build stands on soil or rock. Geotechnical engineering is about how soil behaves when …
Medicines
Drug CalculationsAlmost every error in drug calculations comes from the wrong unit, not from difficult maths. You mus…PharmacologyPharmacokinetics is what the body does to the drug: absorption, distribution, metabolism and excreti…
Body and health
Anatomy and PhysiologyThe body is built from cells that work together in tissues and organs. For the cells to function, th…Microbiology and Infection ControlMicroorganisms are bacteria, viruses, fungi and parasites. Most are harmless and many are useful (th…Pathology and DiseaseCardiovascular diseases are among the most common causes of illness and death. You must recognise th…
Clinical nursing
Clinical NursingVital signs are the measurements that most quickly tell whether a patient is stable: respiratory rat…Law, Ethics and CommunicationThe Norwegian Health Personnel Act sets out your duties as a health professional. The most important…
Mathematics
Mathematics 1TAlgebra is calculating with letters. You must be able to simplify expressions, factorise, and solve …Mathematics R1The logarithm answers the question "which exponent do I need?". It is used to solve equations where …Mathematics R2Integration is the opposite of differentiation. The definite integral gives the area between the gra…Mathematics S1In S1 you need solid algebra: fractions with letters, factorising, and first- and second-degree equa…Mathematics S2🔗 Shared curriculum with R2. The questions are the same, but your progress counts separately for ea…Mathematics 1PPercent means "per hundred". Sales, interest, pay rises and inflation are all percentage calculation…Mathematics 2PStatistics is collecting, ordering and interpreting numbers: grades, pay, temperatures. Measures of …
Physics, chemistry and biology
Physics 1The equations of motion describe motion with constant acceleration, for example free fall and a car …Chemistry 1The atom has a nucleus with protons and neutrons, and electrons around it. The number of protons dec…Biology 1All living things are made of cells. Cells take up nutrients, produce energy, build proteins and div…Physics 2A projectile moves in two directions at once: constant velocity horizontally and free fall verticall…Chemistry 2Many reactions go both ways. At equilibrium they go equally fast in both directions, and the concent…Biology 2DNA is the recipe, proteins do the work. The path from gene to protein has two steps: transcription …
Common core subjects
Natural ScienceScience is a way of finding out how the world works: we ask questions, make hypotheses and test them…GeographyMaps are simplified pictures of reality. Geographers use maps, coordinates and digital tools (GIS) t…Social StudiesNorway is a representative democracy: we elect representatives who govern on our behalf. Power is di…HistoryHistory is not only what happened, but how we know it. Historians use sources and assess them critic…Religion and EthicsReligion and ethics is about how people interpret life: faith, worldviews, values and what is right …
Law
Legal MethodLegal method is the recipe lawyers use to find out what the law is: which sources may be used and ho…Constitutional Law and Human RightsThe Constitution of 1814 is Norway's highest law. It divides power between three branches, so that n…Contract and Sales LawA contract is formed when an offer is met by an acceptance. Chapter 1 of the Contracts Act has the r…Tort LawTort law decides when someone who caused harm must pay for the loss. Three conditions are required, …Administrative LawThe public administration is all the public bodies that make decisions about us: NAV, the municipali…Criminal LawFor someone to be punished, four conditions must be met. The Penal Code of 2005 contains the rules.…
Business and administration
Business EconomicsHow many units must a company sell to break even? The answer comes from the contribution margin: wha…AccountingThe accounts tell you how things went. The income statement shows revenue and expenses over a period…Mathematics for EconomistsEconomists use functions for cost, revenue and demand. The derivative is called marginal (what happe…StatisticsDescriptive statistics summarise data with a few numbers: where is the centre, and how much do the d…EconomicsIn a market, price and quantity are determined by supply and demand. Where the curves cross, the mar…