Programa especializado: Mathematics for Engineers

This course is all about matrices, and concisely covers the linear algebra that an engineer should know. The mathematics in this course is presented at the level of an advanced high school student, but typically students should take this course after completing a university-level single variable calculus course. There are no derivatives or integrals in this course, but students are expected to have attained a sufficient level of mathematical maturity. Nevertheless, anyone who wants to learn the basics of matrix algebra is welcome to join.

The course contains 38 short lecture videos, with a few problems to solve after each lecture. And after each substantial topic, there is a short practice quiz. Solutions to the problems and practice quizzes can be found in instructor-provided lecture notes. There are a total of four weeks in the course, and at the end of each week there is an assessed quiz. Download the lecture notes: http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf Watch the promotional video: https://youtu.be/IZcyZHomFQc

This course is about differential equations and covers material that all engineers should know. Both basic theory and applications are taught. In the first five weeks we will learn about ordinary differential equations, and in the final week, partial differential equations.

The course is composed of 56 short lecture videos, with a few simple problems to solve following each lecture. And after each substantial topic, there is a short practice quiz. Solutions to the problems and practice quizzes can be found in instructor-provided lecture notes. There are a total of six weeks in the course, and at the end of each week there is an assessed quiz. Download the lecture notes: http://www.math.ust.hk/~machas/differential-equations-for-engineers.pdf Watch the promotional video: https://youtu.be/eSty7oo09ZI

Vector Calculus for Engineers covers both basic theory and applications. In the first week we learn about scalar and vector fields, in the second week about differentiating fields, in the third week about multidimensional integration and curvilinear coordinate systems. The fourth week covers line and surface integrals, and the fifth week covers the fundamental theorems of vector calculus, including the gradient theorem, the divergence theorem and Stokes’ theorem. These theorems are needed in core engineering subjects such as Electromagnetism and Fluid Mechanics.

Instead of Vector Calculus, some universities might call this course Multivariable or Multivariate Calculus or Calculus 3. Two semesters of single variable calculus (differentiation and integration) are a prerequisite. The course is organized into 53 short lecture videos, with a few problems to solve following each video. And after each substantial topic, there is a short practice quiz. Solutions to the problems and practice quizzes can be found in instructor-provided lecture notes. There are a total of five weeks to the course, and at the end of each week there is an assessed quiz. Download the lecture notes: http://www.math.ust.hk/~machas/vector-calculus-for-engineers.pdf Watch the promotional video: https://youtu.be/qUseabHb6Vk

Numerical Methods for Engineers covers the most important numerical methods that an engineer should know. We derive basic algorithms in root finding, matrix algebra, integration and interpolation, ordinary and partial differential equations. We learn how to use MATLAB to solve numerical problems. Access to MATLAB online and the MATLAB grader is given to all students who enroll.

We assume students are already familiar with the basics of matrix algebra, differential equations, and vector calculus. Students should have already studied a programming language, and be willing to learn MATLAB. The course contains 74 short lecture videos and MATLAB demonstrations. After each lecture or demonstration, there are problems to solve or programs to write. The course is organized into six weeks, and at the end of each week there is an assessed quiz and a longer programming project. Download the lecture notes: http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Watch the promotional video: https://youtu.be/qFJGMBDfFMY