The topic of this problem is Nodal Analysis. The problem itself is to determine the nodal equations for each node in the circuit below. First of all, we acknowledge that, when we're performing nodal analysis, we're doing Kirchhoff's Current Law. And we're summing the currents in to each of the nodes in the circuit. So the first thing we want to do is we want to find the nodes in the circuit. So if we do that we noticed that we have a node 1, on the left hand side of the circuit. We have a node 2, in the center of the circuit. We have a node 3 which has already been designated as the node on the right hand side of the circuit. And we have the ground node at the bottom of the circuit and we know that the ground node voltage is always zero volts. It's our reference point for the analysis. So we're going to write the nodal equations for this circuit. And we're going to use Kirchhoff's Current Law, since that's the basis for nodal analysis. And in this instance, we're going to sum the currents out of the nodes. We know that Kirchhoff's Current Law can be applied using either analysis of the currents flowing into the nodes or an analysis of the current flowing out of the nodes just so we're consistent throughout the problem. So we're going to sum the currents out of each nodes starting with node 1. So for node 1 we have I sub 1 flowing out. That's going to be a positive since it's flowing out. And we also have the current, which is slowing through R1 from left to right, which is flowing out of node 1. So it's going to be (V1- V2) / R1 = 0. Our second equation for node 2, is going to be in a similar way. The four currents which are flowing out of node 2. The currents flowing out of node 2 are going to be (V2 -V1) / R1. As for the current flowing right to left through R1. We also have the current flowing down through R2 which is V2- 0 for the ground node, divided by R2. We have the current flowing out through R3 which is (V2- V3) / R3. And we have a current flowing out through R4, which is V2 again, minus V3 over R4 equal to zero. So that's our second independent equation. So we have these unknown nodal voltages V1 and V2 and V3. So we have two independent equations, we need our third independent equation that we get from node 3 in order to solve for our unknown nodal voltages V1, V2 and V3. So we're going to sum the currents again, out of node 3. So it's -I sub 2, because that current source is flowing into node 3. And we're going to add to that the current which is flowing out of that node through the resistance R4, which is (V3- V2) / R4. And we have the current which is flowing out of node 3 through the resistance R3 which is (V3- V2) / R3 = 0. So now we have our three equations and three unknowns. If we had values for the current sources and for the resistances, then we can solve for V1, V2 and V3 by combining like terms and then using either matrix analysis or process of elimination of variables in order to find the nodal voltages V1, V2 and V3.