# Online courses directory (9)

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.

This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.

Note: This course was previously called "Mathematical Methods for Engineers I."

Concepts in Nanotechnology is a six-week introduction to nanotechnology. The course is designed at a pre-college level, with no college level chemistry, math, or physics experience required. You will learn what nanotechnology is and what it means for something to be a nanomaterial. You will also learn about the applications and commercial products that use nanotechnology. This is an exciting opportunity to delve into the nano-world. Prerequisites: The course is taught entirely in English and aimed at a U.S. high school level. You need to be familiar with the basic concepts of chemistry, such as the theory of atoms and the periodic table of elements. Basic algebra skills, such as how to deal with equations containing variables, fractions, and exponents is necessary. No prerequisite knowledge in nanotechnology, materials science, or physics is required.

Statics is the study of methods for quantifying the forces between bodies. Forces are responsible for maintaining balance and causing motion of bodies, or changes in their shape. You encounter a great number and variety of examples of forces every day, such as when you press a button, turn a doorknob, or run your hands through your hair. Motion and changes in shape are critical to the functionality of man-made objects as well as objects the nature. Statics is an essential prerequisite for many branches of engineering, such as mechanical, civil, aeronautical, and bioengineering, which address the various consequences of forces. This course contains many interactive elements, including: simulations; “walk-throughs” that integrate voice and graphics to explain a procedure or a difficult concept; and, most prominently, computer tutors in which students practice problem solving with hints and feedback. This course uses algebra and trigonometry and is suitable for use with either calculus- or non-calculus-based academic statics courses. Completion of a beginning physics course is helpful for success in statics, but not required. Many key physics concepts are included in this course.

This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis.

Users may find additional or updated materials at Professor Carter's 3.016 course Web site.

This class introduces elementary programming concepts including variable types, data structures, and flow control. After an introduction to linear algebra and probability, it covers numerical methods relevant to mechanical engineering, including approximation (interpolation, least squares and statistical regression), integration, solution of linear and nonlinear equations, ordinary differential equations, and deterministic and probabilistic approaches. Examples are drawn from mechanical engineering disciplines, in particular from robotics, dynamics, and structural analysis. Assignments require MATLAB^{®} programming.

Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with structured programming is assumed. The examples will use MATLAB®.

## Acknowledgements

The instructor would like to thank Robert Ashcraft, Sandeep Sharma, David Weingeist, and Nikolay Zaborenko for their work in preparing materials for this course site.

Principles of Electric Circuits (20220214x) is one of the kernel courses in the broad EECS subjects. Almost all the required courses in EECS are based on the concepts learned in this course, so it’s the gateway to a qualified EECS engineer.

The main content of this course contains linear and nonlinear resistive circuits, time domain analysis of the dynamic circuits, and the steady state analysis of the dynamic circuits with sinusoidal excitations. Important concepts, e.g. filters, resonance, quiescent point, etc., cutting-edge elements, e.g. MOSFETs and Op Amps, etc., systematic analyzing tools, e.g. node method and phasor method, etc., and real-world engineering applications, e.g. square wave generator and pulse power supply for railgun, etc., will be discussed in depth.

In order to facilitate the learning for students with middle school level, we prepare the necessary knowledge for calculus and linear algebra in week 0. With your effort, we can show you the fantastic view of electricity.

电路原理课程是电类各专业最重要的一门学科基础课，后续各专业基础课和专业课都建立在这门课程的知识体系之上，因此是电类专业本科生的“看家 课”之一。电路原理课程的主要内容包括：线性电阻电路分析、非线性电阻电路分析、动态电路的时域分析和正弦激励下动态电路的稳态分析4大部分。清华大学电 路原理课程的教学包括电路分析基本方法、当代电路元器件、电路原理的实际工程应用等，为学生提供了扎实的基础和丰富的应用。

为方便至只有中学知识的学生学习，电路原理MOOC专门利用第0周准备必要的微积分、线性代数和大学物理电学的基础。我们有信心：你能领悟电世界的奇妙。

This course forms an introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory, optimization techniques, calculus of variations and linear algebra. The topics covered in any particular year depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in mechanical engineering. This year, the subject focuses on selected topics from linear algebra and the calculus of variations. It is aimed mainly (but not exclusively) at students aiming to study mechanics (solid mechanics, fluid mechanics, energy methods etc.), and the course introduces some of the mathematical tools used in these subjects. Applications are related primarily (but not exclusively) to the microstructures of crystalline solids.