 Let us go to the modeling basics. Let us also learn and join this nice trilogy. Actually, teaching is very easy. I will be done teaching in another 5 minutes of the modeling basics. Essentially, all system dynamics model consists of exactly three elements. One is the stock or level which accumulates over time. Second is flow or a rate which causes stocks to change over time. So, we have stocks, we have flows and then we have auxiliary variables, information which help define other instantaneous variables or calculations. So, on the visual representation of them, we can look at it like this where the rectangle you see is called as stock. So, all stocks are represented as rectangles and the thick arrow with a valve you see is the inflow. I mean the direction of arrow represents inflow to the stock and direction of arrow can represent the outflow of the stock. At the end of it, you see kind of cloud kind of thing. This kind of represents an infinite sink and an infinite source, sorry, kind of presence. An example could be something as simple like you know if you are modeling inventory then production rate affects inventory and shipment rate affects inventory. How it affects is intuitive, right? As the production rate is more, inventory is going to increase. As shipment rate is more, then inventory is going to fall down. So, we can represent it simply as these rectangles for stocks and these thick arrows with a valve to represent the rates, close. And these are the only three constructs you need to model, however complex a system you want. Whatever we discussed yesterday, we know we had looked at the examples for the road traffic and road congestion modeling to various other examples we have been studying. We are just going to be modeling it as stocks, close and auxiliary variables. So, if you want to imagine, say for example, hydraulic metaphor, you can imagine a kind of a water tank, I have inflow to the tank, inflow to the tank and then I have an outflow to the tank. So, very simplistic kind of metaphor of course, so you can whenever there is inflows and outflows, we are used to looking at it with say some set of valves within the system. So, this is the same idea that we are using it here and in this way. So, again these are flows, so it is called stock or level, it means the same thing, flow or rate or some books even measure it as flow rate, it depends on what you look. So, it all means the same thing, flow rate or flow rate. The quick load of caution, see here this, though it is a hydraulic metaphor, you know that for example, when inflow is kind of say stops and outflow is always on, then after a point the tank will become empty and then no further water will flow, right. So, if it becomes empty, no further outflow occurs, so that is for the hydraulic metaphor. But if you look at this just the basic model of it, it is nothing but a set of equation. So, in equations especially when you are trying to simulate it, the inflows and outflows can take positive or negative values, there is nothing which restricts it. So, if you take outflows positive then stock will reduce, but outflows negative that means stock is going to increase. So, there is no other check that is done automatically with the computer here, we are back to the real basics of how we are viewing as the equations. For example, we can view it as an integral, view it as integral, you can say stock at time t, this is an integral of time 0 to current time t, inflow of time s minus inflow of time s ds plus initial value of stock, the t is 0 is the let us say initial, so the underlying model is nothing but a you know integral or you can write it as a differential equation or you can write it as d stock by dt, nothing but net change in stock is nothing but your net flow, nothing but your inflow time t minus outflow, so once you make a mapping of your model in terms of stocks and flows, automatically you have defined these differential equations into the system. The system is the stock is going to change by the inflows and outflows precisely in this manner. And once you have set up a differential equation we can simulate it, some of you have done numerical analysis you may know it, others the beauty of it is you do not need to know, you can give it a system and it will simulate it for you, simplest approach could be an Euler method, it will simulate it for you. So we will see a bit of it, so you understand how the underlying model works, but beyond that we do not need to implement the simulator first, we can try to use the simulator to model the systems and the model. So you remember this, so stock can only change through this double headed valve arrows, I mean this directional arrows and it represents your inflows as well as your outflows and stocks are what is going to be differentiable here, so change in stock is defined as inflows minus outflows, so stock can only be changed through flows nothing else. So we have the decide, we have seen this is a negative feedback system where we have water level and we have decide water level, there is no the gap, I decide how fast I want to open the tap and the water is going to flow in and as an decide water level is reached as actual water level reaches a desired water level, I turn down the faucet and then automatically or manually water, so this in stocks, so what is the stock here? Water level is the stock and what is the flow here? There is a word flow in it, there is only one variable water flow, so better guess the same thing and that is the only thing which is influencing water level and it all stocks can only be changed by the flows, so if the water level is the stock then whatever is coming in the end could be the flow. So we simply define as water flow or water flow rate affecting the water level, then there are other variables, so I can simply map it as let us have decide water level which is an information that I have outside the system and I have defined as a variable here, variable here, I identified the gap, see at the same causal links and then the gap is again connected to the affects the flow rate. So now this is also what we call as a stock flow representation of the model, so this is a causal loop representation but just by moving to the stock flow representation the problem becomes much more grounded, actually you know okay, water level is something that I need to measure, so as soon as when it goes both ways, the stock is, stocks are things that we can actually measure, okay, so let us measure that, so that is the stock, how does the stock change based on water that is flowing, what is the information and need to control it, so I need to know about the decide water level, then I need to somehow figure out the gap, so then those comes as what we call as information of auxiliary variable, so just by these three elements we can actually come up with a much richer representation of the same example, we did in causal loop but with a stock flow representation, so many papers you may find that people quickly jump into stock flow representation to represent the same thing without bothering about the underlying equation, how this gap affects the water flow rate we do not know, right now we have time for it, so this is the representation. Now let us quickly understand the role of stocks and then look at some examples.