Into the Unknown
Differential Equations Part I Basic Theory Korea Advanced Institute of Science and Technology It is impossible to appreciate the beauty of mathematics without knowing differential equations, nor become and qualify as a skillful engineer. You probably have begun studying them ever since high school. This course provides basic terminologies, concepts, and methods of solving various…
Mathematics for Engineers: The Capstone Course The Hong Kong University of Science and Technology This course is the apex of the entire specialization. It is truly a rewarding journey. I am so excited to learn some basic concepts in computational fluid dynamics (CFD), and to visualize fluid flow around a cylinder with MATLAB. Math is…
Numerical Methods for Engineers The Hong Kong University of Science and Technology This is an excellent course to consolidate your mathematics knowledge with Matlab programming skills. In real life it is usually extremely difficult to find roots, compute quadrature, or solve ordinary differential equations. It is critical to gain the skills to effectively use Matlab….
Combinatorics and Probability US San Diego You may already have some experience that, in daily life, brute force by counting items one-by-one is almost the worst method to find the the you want. A mathematical field called combinatorics is a powerful tool to help you think before getting your hand dirty. Moreover a solid grasp…
Vector Calculus for Engineers The Hong Kong University of Science and Technology We can’t emphasize enough the importance of Vector Calculus. A solid understanding lays the foundations for further learning of electromagnetism, fluid mechanics and many disciplines. This course is one of the best I have met. I can’t help but recommend to those who…
Differential Equations for EngineersThe Hong Kong University of Science and Technology By highlighting both theories and applications in practice, this amazing course might be your excellent choice to grasp the differential equations in shortest time. You are actually learning math and physics at the same time, building your own mapping between the 2 disciplines. I…
Gradient Theorem The fundamental theorem of single variable calculus was the one that told you “the integral of the derivative of a function is just going to be the function itself.” The gradient theorem is a generalization of the fundamental theorem of calculus to vector calculus, i.e. calculus of several variables. Suppose a scalar field 蠁, we could use…
Line Integrals Scalar Fields We have a curve C in the x-y plane, we can represent a point on this curve then by a vector r. To do a line integral, we break the curve into small pieces ds, you have a small element of length ds and a value of f on that element, we multiply…
Logic for EconomistsUniversity of Amsterdam The logo of University of Amsterdam is cool, so is this succinct course. In this course you only experience black board, white chalk and the hushed tone of the professor. No distraction, you just focus on the “logic”! The course covers a few of the most basic concepts, they are…
Fourier Series Sometimes complicated motions can actually be composed of motions of many different frequencies. The type of mathematical analysis that’s useful is called Fourier series. Fourier series is a way of representing a function – an infinite series of cosine and sines. You can view these as a linear superposition of waves of various frequencies. We use orthogonality…
Systems of Homogeneous Linear First-order ODEs The system of linear first order homogeneous equations can be written in matrix form. To solve it we’re going to use An ansatz X(t) = V e位t . We’re going to look for solutions of the ansatz. The principle of superposition. When we find solutions of the ansatz, we’ll multiply…
Multidimensional Integration In Vector Calculus, we have to worry about integrating over two or three variables: double integrals or triple integrals. Double integral can be interpreted as a volume, like a single integral is the area under the curve. When the limits don’t depend on any variable, and we could do integrals separately. Polar coordinates Polar coordinates…
Laplace transform Laplace transform is a technique for solving differential equations. By using the Laplace transform you can convert a differential equation into another space where the equation is easier to solve. Laplace transform is a linear transformation and it is invertible. The strength of the Laplace transform technique, is to solve the differential equations where you…
Partial derivatives Partial derivative is to differentiate functions of multiple variables. Assume a function f = f(x, y), you are differentiating f with respect x, that is the usual definition of a derivative of a function of one variable, but y is held constant. There is something called mix partial. It does not depend on…
Propositional Logic A proposition (often denoted by capital letters P, Q, etc) is a statement, that can be either true or false. Its negation 卢P is obtained by prepending “it is not true that …” to P. If you negate twice, you get P back again: 卢(卢P) = P . Two propositions are equivalent P…