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AKINDELE AKINROPO: Hello. My name is Akindele O. Akinropo. I'm an urban planner studying sustainable development in Malaysia. The study of this course in this video compares shopping at two malls. The first one is Jusco mall located in the heart of Bukit Indah in Johor, and the other is Alamanda in Putrajaya, the administrative headquarters of Malaysia. In this video, I want to share with you my research on the sustainable dimensions of shopping malls. Sustainable development means different things to different people. However, it generally refers to using environmental resources in a way that allows other generations to continue to use and preserve it. Shopping in malls can be sustainable under certain conditions. For instance, the processes of siting, building, and using malls need to be properly organized within the urban system to promote city livability and environmental performance. Mall sustainability will be guaranteed when site and operation discourage carbon...

Hello. My name is Krishna Rajagopal and I'm MIT's Dean for Digital Learning. Ordinarily, I would be recording this update for the OCW community from our offices on campus but as these are not ordinary times I find myself delivering this message to you from my home in the same way that so many MIT faculty along with educators all around the world are right now teaching their students from home during this global pandemic. From the beginning, OpenCourseWare was meant to be a resource for anyone who wants to learn, whenever and wherever they need it. We've always believed in the urgency of our mission but never before have we seen the stakes rise so immediately as we have these past several weeks. With millions even billions of people around the world asked to stay apart, stay at home, and adapt to sudden changes in the way we all live, work, connect, and learn. This has brought particular challenges for educators and needs for all of us as learners. Here at MIT ...

MARKUS KLUTE: Hello. So with this recording I'd like to introduce the topic of flavor symmetry, what we mean by that. So when the neutron was discovered, it was noted that the mass of the neutron is very close to the mass of the proton. And so it seems like those two particles are somehow related. Even so, the electric charge is different. The proton is charged, the neutron is neutral. And you can see here that the masses are really very, very close, about 1 MeV or about 1% difference in mass. So Heisenberg proposed, and that was in the 1930s, to regard them as two states of the same particle. They were really so different that you could think that they are basically the same, just a rotation from one end to the other. And that's exactly what he did, considering them as one particle, a nucleon, where the proton is described as a doublet, with an up doublet, and the neutron as a down doublet, similar to an up quark and a down quark in electron and neutrino later on...

CLEVE MOLER: Hello. I'm Cleve Moler, one of the founders and chief mathematician at the MathWorks. This series of videos is about solving ordinary differential equations in MATLAB. We can begin by recalling the definition of derivative. The derivative of a function at a point is the slope of the tangent line to the graph of the function at that point. Our numerical approximations will rely upon the slope of the secant to the graph. That's a line through two points separated by a distance h. We'll have a lot to say about the step size h as we go along. What's important to realize is that as h goes to 0, the slope of the secant approaches the slope of tangent. The wiggly equals sign means approximately equal to. T0 is the point where we are finding the approximation. The value of the derivative at t0 is approximately equal to the slope of the secant. The slope of the secant is the change in the y value over the change in the t value. The change in y value is...

LINAN CHEN: Hello. Welcome back to recitation. I'm sure you are becoming more and more familiar with the determinants of matrices. In the lecture, we also learned the geometric interpretation of the determinant. The absolute value of the determinant of a matrix is simply equal to the volume of the parallelepiped spanned by the row vectors of that matrix. So today, we're going to apply this fact to solve the following problem. I have a tetrahedron, T, in this 3D space. And the vertices of T are given by O, which is the origin, A_1, A_2, and A_3. So I have highlighted this tetrahedron using the blue chalk. So this is T. And our first goal is to compute the volume of T using the determinant. And the second part is: if I fix A_1 and A_2, but move A_3 to another point, A_3 prime, which is given by this coordinate, I ask you to compute the volume again. OK. So since we want to use the fact that the determinant is related to the volume, we have to figure out which volume...

LINAN CHEN: Hello. Welcome back to recitation. I'm sure you are becoming more and more familiar with the determinants of matrices. In the lecture, we also learned the geometric interpretation of the determinant. The absolute value of the determinant of a matrix is simply equal to the volume of the parallelepiped spanned by the row vectors of that matrix. So today, we're going to apply this fact to solve the following problem. I have a tetrahedron, T, in this 3D space. And the vertices of T are given by O, which is the origin, A_1, A_2, and A_3. So I have highlighted this tetrahedron using the blue chalk. So this is T. And our first goal is to compute the volume of T using the determinant. And the second part is: if I fix A_1 and A_2, but move A_3 to another point, A_3 prime, which is given by this coordinate, I ask you to compute the volume again. OK. So since we want to use the fact that the determinant is related to the volume, we have to figure out which volume...