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By whitelisting SlideShare on your ad-blocker, you are supporting our community of content creators. The term "ordinary" is used in contrast with the term . A second-order differential equation involves two derivatives of the equation. Ordinary differential equations are used in the real world to calculate the movement of electricity, the movement of an item like a pendulum, and to illustrate thermodynamics concepts. A brine solution is pumped into the tank at a rate of 3 gallons per minute and a well-stirred solution is then pumped out at the same rate. \(p(0)=p_o\), and k are called the growth or the decay constant. Wikipedia references: Streamlines, streaklines, and pathlines; Stream function <quote> Streamlines are a family of curves that are instantaneously tangent to the velocity vector of the flow. If you enjoyed this post, you might also like: Langtons Ant Order out ofChaos How computer simulations can be used to model life. You could use this equation to model various initial conditions. You can then model what happens to the 2 species over time. So, with all these things in mind Newtons Second Law can now be written as a differential equation in terms of either the velocity, v, or the position, u, of the object as follows. First we read off the parameters: . They can describe exponential growth and decay, the population growth of species or the change in investment return over time. 40K Students Enrolled. I don't have enough time write it by myself. The constant r will change depending on the species. The three most commonly modelled systems are: In order to illustrate the use of differential equations with regard to population problems, we consider the easiest mathematical model offered to govern the population dynamics of a certain species. You can read the details below. Laplaces equation in three dimensions, \({\Delta ^2}\phi = \frac{{{\partial ^2}\phi }}{{{\partial ^2}x}} + \frac{{{\partial ^2}\phi }}{{{\partial ^2}y}} + \frac{{{\partial ^2}\phi }}{{{\partial ^2}z}} = 0\). [11] Initial conditions for the Caputo derivatives are expressed in terms of This equation represents Newtons law of cooling. application of calculus in engineering ppt. To see that this is in fact a differential equation we need to rewrite it a little. Ask Question Asked 9 years, 7 months ago Modified 9 years, 2 months ago Viewed 2k times 3 I wonder which other real life applications do exist for linear differential equations, besides harmonic oscillators and pendulums. 221 0 obj <>/Filter/FlateDecode/ID[<233DB79AAC27714DB2E3956B60515D74><849E420107451C4DB5CE60C754AF569E>]/Index[208 24]/Info 207 0 R/Length 74/Prev 106261/Root 209 0 R/Size 232/Type/XRef/W[1 2 1]>>stream The value of the constant k is determined by the physical characteristics of the object. `E,R8OiIb52z fRJQia" ESNNHphgl LBvamL 1CLSgR+X~9I7-<=# \N ldQ!`%[x>* Ko e t) PeYlA,X|]R/X,BXIR The constant k is called the rate constant or growth constant, and has units of inverse time (number per second). A tank initially holds \(100\,l\)of a brine solution containing \(20\,lb\)of salt. %PDF-1.5 % Thus when it suits our purposes, we shall use the normal forms to represent general rst- and second-order ordinary differential equations. Thefirst-order differential equationis defined by an equation\(\frac{{dy}}{{dx}} = f(x,\,y)\), here \(x\)and \(y\)are independent and dependent variables respectively. hn6_!gA QFSj= Learn faster and smarter from top experts, Download to take your learnings offline and on the go. I[LhoGh@ImXaIS6:NjQ_xk\3MFYyUvPe&MTqv1_O|7ZZ#]v:/LtY7''#cs15-%!i~-5e_tB (rr~EI}hn^1Mj C\e)B\n3zwY=}:[}a(}iL6W\O10})U Answer (1 of 45): It is impossible to discuss differential equations, before reminding, in a few words, what are functions and what are their derivatives. Applications of SecondOrder Equations Skydiving. 115 0 obj <>stream which is a linear equation in the variable \(y^{1-n}\). In this article, we are going to study the Application of Differential Equations, the different types of differential equations like Ordinary Differential Equations, Partial Differential Equations, Linear Differential Equations, Nonlinear differential equations, Homogeneous Differential Equations, and Nonhomogeneous Differential Equations, Newtons Law of Cooling, Exponential Growth of Bacteria & Radioactivity Decay. 0 What is Developmentally Appropriate Practice (DAP) in Early Childhood Education? This is called exponential growth. Every home has wall clocks that continuously display the time. The differential equation \({dP\over{T}}=kP(t)\), where P(t) denotes population at time t and k is a constant of proportionality that serves as a model for population growth and decay of insects, animals and human population at certain places and duration. Accurate Symbolic Steady State Modeling of Buck Converter. In recent years, there has been subject so far-reaching of research in derivative and differential equation because of its performance in numerous branches of pure and applied mathematics. Ordinary differential equations applications in real life include its use to calculate the movement or flow of electricity, to study the to and fro motion of a pendulum, to check the growth of diseases in graphical representation, mathematical models involving population growth, and in radioactive decay studies. Applications of Matrices and Partial Derivatives, S6 l04 analytical and numerical methods of structural analysis, Maths Investigatory Project Class 12 on Differentiation, Quantum algorithm for solving linear systems of equations, A Fixed Point Theorem Using Common Property (E. An example application: Falling bodies2 3. Q.1. Grayscale digital images can be considered as 2D sampled points of a graph of a function u (x, y) where the domain of the function is the area of the image. Slideshare uses What is an ordinary differential equation? If we assume that the time rate of change of this amount of substance, \(\frac{{dN}}{{dt}}\), is proportional to the amount of substance present, then, \(\frac{{dN}}{{dt}} = kN\), or \(\frac{{dN}}{{dt}} kN = 0\). Letting \(z=y^{1-n}\) produces the linear equation. This course for junior and senior math majors uses mathematics, specifically the ordinary differential equations as used in mathematical modeling, to analyze and understand a variety of real-world problems. Students must translate an issue from a real-world situation into a mathematical model, solve that model, and then apply the solutions to the original problem. Students are asked to create the equation or the models heuristics rather than being given the model or algorithm and instructed to enter numbers into the equation to discover the solution. When \(N_0\) is positive and k is constant, N(t) decreases as the time decreases. Such a multivariable function can consist of several dependent and independent variables. 2.2 Application to Mixing problems: These problems arise in many settings, such as when combining solutions in a chemistry lab . by MA Endale 2015 - on solving separable , Linear first order differential equations, solution methods and the role of these equations in modeling real-life problems. Many cases of modelling are seen in medical or engineering or chemical processes. Ive also made 17 full investigation questions which are also excellent starting points for explorations. In the description of various exponential growths and decays. They are present in the air, soil, and water. Where, \(k\)is the constant of proportionality. They are used in a wide variety of disciplines, from biology, economics, physics, chemistry and engineering. Now lets briefly learn some of the major applications. Video Transcript. HUmk0_OCX- 1QM]]Nbw#`\^MH/(:\"avt (i)\)At \(t = 0,\,N = {N_0}\)Hence, it follows from \((i)\)that \(N = c{e^{k0}}\)\( \Rightarrow {N_0} = c{e^{k0}}\)\(\therefore \,{N_0} = c\)Thus, \(N = {N_0}{e^{kt}}\,(ii)\)At \(t = 2,\,N = 2{N_0}\)[After two years the population has doubled]Substituting these values into \((ii)\),We have \(2{N_0} = {N_0}{e^{kt}}\)from which \(k = \frac{1}{2}\ln 2\)Substituting these values into \((i)\)gives\(N = {N_0}{e^{\frac{t}{2}(\ln 2)}}\,. It involves the derivative of a function or a dependent variable with respect to an independent variable. This is a linear differential equation that solves into \(P(t)=P_oe^{kt}\). Enjoy access to millions of ebooks, audiobooks, magazines, and more from Scribd. 3.1 Application of Ordinary Differential Equations to the Model for Forecasting Corruption In the current search and arrest of a large number of corrupt officials involved in the crime, ordinary differential equations can be used for mathematical modeling To . Numerical case studies for civil enginering, Essential Mathematics and Statistics for Science Second Edition, Ecuaciones_diferenciales_con_aplicaciones_de_modelado_9TH ENG.pdf, [English Version]Ecuaciones diferenciales, INFINITE SERIES AND DIFFERENTIAL EQUATIONS, Coleo Schaum Bronson - Equaes Diferenciais, Differential Equations with Modelling Applications, First Course in Differntial Equations 9th Edition, FIRST-ORDER DIFFERENTIAL EQUATIONS Solutions, Slope Fields, and Picard's Theorem General First-Order Differential Equations and Solutions, DIFFERENTIAL_EQUATIONS_WITH_BOUNDARY-VALUE_PROBLEMS_7th_.pdf, Differential equations with modeling applications, [English Version]Ecuaciones diferenciales - Zill 9ed, [Dennis.G.Zill] A.First.Course.in.Differential.Equations.9th.Ed, Schaum's Outline of Differential Equations - 3Ed, Sears Zemansky Fsica Universitaria 12rdicin Solucionario, 1401093760.9019First Course in Differntial Equations 9th Edition(1) (1).pdf, Differential Equations Notes and Exercises, Schaum's Outline of Differential Equation 2ndEd.pdf, [Amos_Gilat,_2014]_MATLAB_An_Introduction_with_Ap(BookFi).pdf, A First Course in Differential Equations 9th.pdf, A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. In the field of medical science to study the growth or spread of certain diseases in the human body. 149 10.4 Formation of Differential Equations 151 10.5 Solution of Ordinary Differential Equations 155 10.6 Solution of First Order and First Degree . This graph above shows what happens when you reach an equilibrium point in this simulation the predators are much less aggressive and it leads to both populations have stable populations. hbbd``b`z$AD `S The applications of differential equations in real life are as follows: In Physics: Study the movement of an object like a pendulum Study the movement of electricity To represent thermodynamics concepts In Medicine: Graphical representations of the development of diseases In Mathematics: Describe mathematical models such as: population explosion G*,DmRH0ooO@ ["=e9QgBX@bnI'H\*uq-H3u `IV So we try to provide basic terminologies, concepts, and methods of solving . Does it Pay to be Nice? Can you solve Oxford Universitys InterviewQuestion? The differential equation, (5) where f is a real-valued continuous function, is referred to as the normal form of (4). So, our solution . Solve the equation \(\frac{{\partial u}}{{\partial t}} = \frac{{{\partial ^2}u}}{{\partial {x^2}}}\)with boundary conditions \(u(x,\,0) = 3\sin \,n\pi x,\,u(0,\,t) = 0\)and \(u(1,\,t) = 0\)where \(0 < x < 1,\,t > 0\).Ans: The solution of differential equation \(\frac{{\partial u}}{{\partial t}} = \frac{{{\partial ^2}u}}{{\partial {x^2}}}\,..(i)\)is \(u(x,\,t) = \left( {{c_1}\,\cos \,px + {c_2}\,\sin \,px} \right){e^{ {p^2}t}}\,..(ii)\)When \(x = 0,\,u(0,\,t) = {c_1}{e^{ {p^2}t}} = 0\)i.e., \({c_1} = 0\).Therefore \((ii)\)becomes \(u(x,\,t) = {c_2}\,\sin \,px{e^{ {p^2}t}}\,. Graphical representations of the development of diseases are another common way to use differential equations in medical uses. Homogeneous Differential Equations are used in medicine, economics, aerospace, automobile as well as in the chemical industry. A partial differential equation is an equation that imposes relations between the various partial derivatives of a multivariable function. The principal quantities used to describe the motion of an object are position ( s ), velocity ( v ), and acceleration ( a ). CBSE Class 9 Result: The Central Board of Secondary Education (CBSE) Class 9 result is a crucial milestone for students as it marks the end of their primary education and the beginning of their secondary education. Q.2. 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. Q.3. Innovative strategies are needed to raise student engagement and performance in mathematics classrooms. Population growth, spring vibration, heat flow, radioactive decay can be represented using a differential equation. Nonhomogeneous Differential Equations are equations having varying degrees of terms. The. BVQ/^. 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 cant get food from other sources). This is the route taken to various valuation problems and optimization problems in nance and life insur-ance in this exposition. If after two years the population has doubled, and after three years the population is \(20,000\), estimate the number of people currently living in the country.Ans:Let \(N\)denote the number of people living in the country at any time \(t\), and let \({N_0}\)denote the number of people initially living in the country.\(\frac{{dN}}{{dt}}\), the time rate of change of population is proportional to the present population.Then \(\frac{{dN}}{{dt}} = kN\), or \(\frac{{dN}}{{dt}} kN = 0\), where \(k\)is the constant of proportionality.\(\frac{{dN}}{{dt}} kN = 0\)which has the solution \(N = c{e^{kt}}. Ordinary di erential equations and initial value problems7 6. Population Models Several problems in Engineering give rise to some well-known partial differential equations. endstream endobj 209 0 obj <>/Metadata 25 0 R/Outlines 46 0 R/PageLayout/OneColumn/Pages 206 0 R/StructTreeRoot 67 0 R/Type/Catalog>> endobj 210 0 obj <>/Font<>>>/Rotate 0/StructParents 0/Tabs/S/Type/Page>> endobj 211 0 obj <>stream Almost all of the known laws of physics and chemistry are actually differential equations , and differential equation models are used extensively in biology to study bio-A mathematical model is a description of a real-world system using mathematical language and ideas. Summarized below are some crucial and common applications of the differential equation from real-life. Written in a clear, logical and concise manner, this comprehensive resource allows students to quickly understand the key principles, techniques and applications of ordinary differential equations. Anscombes Quartet the importance ofgraphs! endstream endobj 87 0 obj <>stream Application of differential equation in real life Dec. 02, 2016 42 likes 41,116 views Download Now Download to read offline Engineering It includes the maximum use of DE in real life Tanjil Hasan Follow Call Operator at MaCaffe Teddy Marketing Advertisement Advertisement Recommended Application of-differential-equation-in-real-life 2022 (CBSE Board Toppers 2022): Applications of Differential Equations: A differential equation, also abbreviated as D.E., is an equation for the unknown functions of one or more variables. 4.4M]mpMvM8'|9|ePU> Leading AI Powered Learning Solution Provider, Fixing Students Behaviour With Data Analytics, Leveraging Intelligence To Deliver Results, Exciting AI Platform, Personalizing Education, Disruptor Award For Maximum Business Impact, Copyright 2023, Embibe. }9#J{2Qr4#]!L_Jf*K04Je$~Br|yyQG>CX/.OM1cDk$~Z3XswC\pz~m]7y})oVM\\/Wz]dYxq5?B[?C J|P2y]bv.0Z7 sZO3)i_z*f>8 SJJlEZla>`4B||jC?szMyavz5rL S)Z|t)+y T3"M`!2NGK aiQKd` n6>L cx*-cb_7% It includes the maximum use of DE in real life. Hi Friends,In this video, we will explore some of the most important real life applications of Differential Equations.Time Stamps-Introduction-0:00Population. Similarly, the applications of second-order DE are simple harmonic motion and systems of electrical circuits. They are used in a wide variety of disciplines, from biology, economics, physics, chemistry and engineering. Newtons Law of Cooling leads to the classic equation of exponential decay over time. mM-65_/4.i;bTh#"op}^q/ttKivSW^K8'7|c8J Hence the constant k must be negative. This is useful for predicting the behavior of radioactive isotopes and understanding their role in various applications, such as medicine and power generation. A Differential Equation and its Solutions5 . Thus \({dT\over{t}}\) > 0 and the constant k must be negative is the product of two negatives and it is positive. The negative sign in this equation indicates that the number of atoms decreases with time as the isotope decays. Even though it does not consider numerous variables like immigration and emigration, which can cause human populations to increase or decrease, it proved to be a very reliable population predictor. If you read the wiki page on Gompertz functions [http://en.wikipedia.org/wiki/Gompertz_function] this might be a good starting point. N~-/C?e9]OtM?_GSbJ5 n :qEd6C$LQQV@Z\RNuLeb6F.c7WvlD'[JehGppc1(w5ny~y[Z A differential equation is one which is written in the form dy/dx = . In general, differential equations are a powerful tool for describing and analyzing the behavior of physical systems that change over time, and they are widely used in a variety of fields, including physics, engineering, and economics. Hence, just like quadratic equations, even differential equations have a multitude of real-world applications. chemical reactions, population dynamics, organism growth, and the spread of diseases. The applications of second-order differential equations are as follows: Thesecond-order differential equationis given by, \({y^{\prime \prime }} + p(x){y^\prime } + q(x)y = f(x)\). For a few, exams are a terrifying ordeal. What are the applications of differential equations?Ans:Differential equations have many applications, such as geometrical application, physical application. \h@7v"0Bgq1z)/yfW,aX)iB0Q(M\leb5nm@I 5;;7Q"m/@o%!=QA65cCtnsaKCyX>4+1J`LEu,49,@'T 9/60Wm If a quantity y is a function of time t and is directly proportional to its rate of change (y'), then we can express the simplest differential equation of growth or decay. 4) In economics to find optimum investment strategies Q.3. Surprisingly, they are even present in large numbers in the human body. Clipping is a handy way to collect important slides you want to go back to later. We've updated our privacy policy. Various disciplines such as pure and applied mathematics, physics, and engineering are concerned with the properties of differential equations of various types. At \(t = 0\), fresh water is poured into the tank at the rate of \({\rm{5 lit}}{\rm{./min}}\), while the well stirred mixture leaves the tank at the same rate. y' y. y' = ky, where k is the constant of proportionality. The most common use of differential equations in science is to model dynamical systems, i.e. VUEK%m 2[hR. hO#7?t]E*JmBd=&*Fz?~Xp8\2CPhf V@i (@WW``pEp$B0\*)00:;Ouu The simplest ordinary di erential equation3 4. Example: \({d^y\over{dx^2}}+10{dy\over{dx}}+9y=0\)Applications of Nonhomogeneous Differential Equations, The second-order nonhomogeneous differential equation to predict the amplitudes of the vibrating mass in the situation of near-resonant. It thus encourages and amplifies the transfer of knowledge between scientists with different backgrounds and from different disciplines who study, solve or apply the . What is the average distance between 2 points in arectangle? THE NATURAL GROWTH EQUATION The natural growth equation is the differential equation dy dt = ky where k is a constant. 9859 0 obj <>stream Electrical systems, also called circuits or networks, aredesigned as combinations of three components: resistor \(\left( {\rm{R}} \right)\), capacitor \(\left( {\rm{C}} \right)\), and inductor \(\left( {\rm{L}} \right)\). Do not sell or share my personal information. 5) In physics to describe the motion of waves, pendulums or chaotic systems. If you want to learn more, you can read about how to solve them here. eB2OvB[}8"+a//By? If the body is heating, then the temperature of the body is increasing and gain heat energy from the surrounding and \(T < T_A\). ), some are human made (Last ye. Embiums Your Kryptonite weapon against super exams! In medicine for modelling cancer growth or the spread of disease They are used to calculate the movement of an item like a pendulum, movement of electricity and represent thermodynamics concepts. Methods and Applications of Power Series By Jay A. Leavitt Power series in the past played a minor role in the numerical solutions of ordi-nary and partial differential equations. We've encountered a problem, please try again. The CBSE Class 8 exam is an annual school-level exam administered in accordance with the board's regulations in participating schools. Nonlinear differential equations have been extensively used to mathematically model many of the interesting and important phenomena that are observed in space. Many interesting and important real life problems in the eld of mathematics, physics, chemistry, biology, engineering, economics, sociology and psychology are modelled using the tools and techniques of ordinary differential equations (ODEs). Ordinary differential equations are applied in real life for a variety of reasons. Sorry, preview is currently unavailable. Application Of First Order Differential Equation, Application Of Second Order Differential Equation, Common Applications of Differential Equations in Physics, Exponential Reduction or Radioactivity Decay, Applications of Differential Equations in Real Life, Application of Differential Equations FAQs, Sum of squares of first n-natural numbers. All content on this site has been written by Andrew Chambers (MSc. Where v is the velocity of the object and u is the position function of the object at any time t. We should also remember at this point that the force, F may also be a function of time, velocity, and/or position. 1 This Course. The graph of this equation (Figure 4) is known as the exponential decay curve: Figure 4. if k<0, then the population will shrink and tend to 0. Chapter 7 First-Order Differential Equations - San Jose State University Everything we touch, use, and see comprises atoms and molecules. Ordinary differential equations applications in real life are used to calculate the movement or flow of electricity, motion of an object to and fro like a pendulum, to explain thermodynamics concepts. To demonstrate that the Wronskian either vanishes for all values of x or it is never equal to zero, if the y i(x) are solutions to an nth order ordinary linear dierential equa-tion, we shall derive a formula for the Wronskian. Since velocity is the time derivative of the position, and acceleration is the time derivative of the velocity, acceleration is the second time derivative of the position. We solve using the method of undetermined coefficients. In the biomedical field, bacteria culture growth takes place exponentially. Differential equations have applications in various fields of Science like Physics (dynamics, thermodynamics, heat, fluid mechanics, and electromagnetism), Chemistry (rate of chemical reactions, physical chemistry, and radioactive decay), Biology (growth rates of bacteria, plants and other organisms) and Economics (economic growth rate, and population growth rate). This book presents the application and includes problems in chemistry, biology, economics, mechanics, and electric circuits. Newtons Second Law of Motion states that If an object of mass m is moving with acceleration a and being acted on with force F then Newtons Second Law tells us. The degree of a differential equation is defined as the power to which the highest order derivative is raised. Numberdyslexia.com is an effort to educate masses on Dyscalculia, Dyslexia and Math Anxiety. An ordinary differential equation (also abbreviated as ODE), in Mathematics, is an equation which consists of one or more functions of one independent variable along with their derivatives. The equation that involves independent variables, dependent variables and their derivatives is called a differential equation. Laplace Equation: \({\Delta ^2}\phi = \frac{{{\partial ^2}\phi }}{{{\partial ^2}x}} + \frac{{{\partial ^2}\phi }}{{{\partial ^2}y}} = 0\), Heat Conduction Equation: \(\frac{{\partial T}}{{\partial t}} = C\frac{{{\partial ^2}T}}{{\partial {x^2}}}\). PRESENTED BY PRESENTED TO However, most differential equations cannot be solved explicitly. applications in military, business and other fields. ) Among the civic problems explored are specific instances of population growth and over-population, over-use of natural . Ive just launched a brand new maths site for international schools over 2000 pdf pages of resources to support IB teachers. Electrical systems also can be described using differential equations. This book offers detailed treatment on fundamental concepts of ordinary differential equations. 100 0 obj <>/Filter/FlateDecode/ID[<5908EFD43C3AD74E94885C6CC60FD88D>]/Index[82 34]/Info 81 0 R/Length 88/Prev 152651/Root 83 0 R/Size 116/Type/XRef/W[1 2 1]>>stream This relationship can be written as a differential equation in the form: where F is the force acting on the object, m is its mass, and a is its acceleration. %\f2E[ ^' ?}2y=B%Chhy4Z =-=qFC<9/2}_I2T,v#xB5_uX maEl@UV8@h+o Learn more about Logarithmic Functions here. But how do they function? %PDF-1.6 % With a step-by-step approach to solving ordinary differential equations (ODEs), Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R successfully applies computational techniques for solving real-world ODE problems that are found in a variety of fields, including chemistry, Ordinary differential equations are put to use in the real world for a variety of applications, including the calculation of the flow of electricity, the movement of an object like a pendulum, and the illustration of principles related to thermodynamics. @ How many types of differential equations are there?Ans: There are 6 types of differential equations. Example: \({\delta^2{u}\over\delta{x^2}}+{\delta2{u}\over\delta{y^2}}=0\), \({\delta^2{u}\over\delta{x^2}}-4{\delta{u}\over\delta{y}}+3(x^2-y^2)=0\). Hi Friends,In this video, we will explore some of the most important real life applications of Differential Equations. Systems of the electric circuit consisted of an inductor, and a resistor attached in series, A circuit containing an inductance L or a capacitor C and resistor R with current and voltage variables given by the differential equation of the same form. Additionally, they think that when they apply mathematics to real-world issues, their confidence levels increase because they can feel if the solution makes sense. Some other uses of differential equations include: 1) In medicine for modelling cancer growth or the spread of disease 2. We can express this rule as a differential equation: dP = kP. View author publications . In the prediction of the movement of electricity. Unfortunately it is seldom that these equations have solutions that can be expressed in closed form, so it is common to seek approximate solutions by means of numerical methods; nowadays this can usually be achieved . 300 IB Maths Exploration ideas, video tutorials and Exploration Guides, February 28, 2014 in Real life maths | Tags: differential equations, predator prey. A lemonade mixture problem may ask how tartness changes when The Maths behind blockchain, bitcoin, NFT (Part2), The mathematics behind blockchain, bitcoin andNFTs, Finding the average distance in apolygon, Finding the average distance in an equilateraltriangle. Differential equations have a remarkable ability to predict the world around us.