There are several phenomena which fit this pattern. Orthogonal trajectories, therefore, are two families of curves that always intersect perpendicularly. Population Models Can you solve Oxford University’s Interview Question? Game Theory and Evolution. 5) In physics to describe the motion of waves, pendulums or chaotic systems. Algebra, Calculus etc) and each area then has a number of graded questions. Change ), You are commenting using your Facebook account. If you want to learn more, you can read about how to solve them here. Malthus used this law to predict how a species would grow over time. Change ). The Practice Exams section takes you to ready made exams on each topic – again with worked solutions. I was thinking of modelling traffic flow using differential equations, are there anything specific resources that you would recommend to help me understand this better? Change ), You are commenting using your Twitter account. Overview of applications of differential equations in real life situations. With such ability to describe the real world, being able to solve differential equations is an important skill for mathematicians. ( Log Out / Includes: Fourteen full investigation questions – each one designed to last around 1 hour, and totaling around 35 pages and 500 marks worth of content. is there anywhere that you would recommend me looking to find out more about it? Modelling the spread of Coronavirus (COVID-19), Rational Approximations to Irrational Numbers – A 78 Year old Conjecture Proved, Hollow Cubes and Hypercubes investigation, Ramanujan’s Taxi Cab and the Sum of 2 Cubes, Finding the volume of a rugby ball (or American football), The Shoelace Algorithm to find areas of polygons, IB Applications and Interpretations SL and HL Resources, IB Analysis and Approaches SL and HL Resources, Stacking cannonballs – solving maths with code, Normal Numbers – and random number generators, The Gini Coefficient – measuring inequality, Zeno’s Paradox – Achilles and the Tortoise. very nice article, people really require this kind of stuff to understand things better, How plz explain following????? 3) In chemistry for modelling chemical reactions APPLICATIONS OF DIFFERENTIAL EQUATIONS 2 the colony to grow. The picture above is taken from an online predator-prey simulator . I would really recommend everyone making use of this – there is a mixture of a lot of free content as well as premium content so have a look and see what you think. This also has some harder exams for those students aiming for 6s and 7s and the Past IB Exams section takes you to full video worked solutions to every question on every past paper – and you can also get a prediction exam for the upcoming year. ( Log Out / You could use this equation to model various initial conditions. In real life, the applications of linear equations are vast. Real life use of Differential Equations. The following steps are involved while restating a situation into a mathematical statement: The short answer is any problem where there exists a relationship between the rate of change in something to the thing itself. Quadratic regression and cubic regression. If you’re already thinking about your coursework then it’s probably also time to start planning some revision, either for the end of Year 12 school exams or Year 13 final exams. They are used in a wide variety of disciplines, from biology, economics, physics, chemistry and engineering. IB Maths Resources from British International School Phuket, Does it Pay to be Nice? They are used in a wide variety of disciplines, from biology, economics, physics, chemistry and engineering. As you can see this particular relationship generates a population boom and crash – the predator rapidly eats the prey population, growing rapidly – before it runs out of prey to eat and then it has no other food, thus dying off again. The above graph shows almost-periodic behaviour in the moose population with a largely stable wolf population. If you enjoyed this post, you might also like: Langton’s Ant – Order out of Chaos How computer simulations can be used to model life. Blog at WordPress.com.Ben Eastaugh and Chris Sternal-Johnson. 4) In economics to find optimum investment strategies I was thinking of using related rates as my ia topic but Im not sure how to apply related rates into physics or medicine. 2) In engineering for describing the movement of electricity This has more parameters to control. The constant r will change depending on the species. There’s a really great website that I would strongly recommend students use – you choose your subject (HL/SL/Studies if your exam is in 2020 or Applications/Analysis if your exam is in 2021), and then have the following resources: The Questionbank takes you to a breakdown of each main subject area (e.g. Differential equations have a remarkable ability to predict the world around us. Advice on using Geogebra, Desmos and Tracker. Home; Free Mathematics Tutorials. Useful websites for use in the exploration, A selection of detailed exploration ideas. The graph above shows the predator population in blue and the prey population in red – and is generated when the predator is both very aggressive (it will attack the prey very often) and also is very dependent on the prey (it can’t get food from other sources). Application of differential equations? This function is a modified exponential model so that you have rapid initial growth (as in a normal exponential function), but then a growth slowdown with time. We present examples where differential equations are widely applied to model natural phenomena, engineering systems and many other situations. Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. Change ), You are commenting using your Google account. 5) In physics to describe the motion of waves, pendulums or chaotic systems. You can then model what happens to the 2 species over time. More complicated differential equations can be used to model the relationship between predators and prey. Differential equations have a remarkable ability to predict the world around us. I have a paper due over this, thanks for the ideas! A differential equation is one which is written in the form dy/dx = ………. Thank you. What I like about this is that you are given a difficulty rating, as well as a mark scheme and also a worked video tutorial. Applying Differential Equations Applications of First‐Order Equations; Applications of Second‐Order Equations ; Applications of First‐Order Equations. There are also more complex predator-prey models – like the one shown above for the interaction between moose and wolves. Together this is around 100 pages of content. Exponential and trigonometric regression. Follow IB Maths Resources from British International School Phuket on WordPress.com.