Courses tagged with "Calculus I" (279)

Welcome to The Quantum World!

This course is an introduction to quantum chemistry: the application of quantum theory to atoms, molecules, and materials. You’ll learn about wavefunctions, probability, special notations, and approximations that make quantum mechanics easier to apply. You’ll also learn how to use Python to program quantum-mechanical models of atoms and molecules.

HarvardX has partnered with DataCamp to create assignments in Python that allow students to program directly in a browser-based interface. You will not need to download any special software, but an up-to-date browser is recommended.

This course has serious prerequisites. You will need to be comfortable with college-level chemistry and calculus. Some prior programming experience is also encouraged.

The Quantum World is ideal for:

• Chemistry majors who want extra material alongside an on-campus course
• Chemistry majors at an institution that does not offer quantum chemistry
• Physics or CompSci majors who want to branch out to chemistry
• Graduate students refreshing on quantum mechanics before their qualifying exams
• Professional chemists who want to brush up on their skills

Explore the solar system using concepts from physics, chemistry, biology, and geology. Learn the latest from Mars, explore the outer solar system, ponder planets outside our solar system, and search for habitability in the universe.

This is the first term of a theoretical treatment of the physics of solids. Topics covered include crystal structure and band theory, density functional theory, a survey of properties of metals and semiconductors, quantum Hall effect, phonons, electron phonon interaction and superconductivity.

This is the second term of a theoretical treatment of the physics of solids. Topics covered include linear response theory; the physics of disorder; superconductivity; the local moment and itinerant magnetism; the Kondo problem and Fermi liquid theory.

ME209.1x is a basic course in thermodynamics, designed for students of mechanical engineering. We will study the terms and concepts used in thermodynamics, with precise definitions. The three laws of thermodynamics (zeroth, first, and second) will be explored in detail, and the properties of materials will be studied. Many useful relations will be derived. The topics include:

• basic concepts and definitions
• the work interaction
• the first law, energy, and the heat interaction
• the zeroth law, temperature, and scales of temperature
• properties of gases and liquids, equations of state
• the second law, thermodynamic temperature scales, and entropy
• relations between properties
• open thermodynamic systems

There will be emphasis on problem-solving. Students will need to spend significant effort on solving exercises.

The course is designed for students in mechanical engineering. However, others (both engineers and scientists) are likely to find it useful. The course has also been found to be useful to teachers of thermodynamics.

Please note that this course is self-paced and you can enroll at any time.  At normal pace, this course requires 12 weeks of study, about 10 hours a week.

The idea behind topological systems is simple: if there exists a quantity, which cannot change in an insulating system where all the particles are localized, then the system must become conducting and obtain propagating particles when the quantity (called a "topological invariant") finally changes.

The practical applications of this principle are quite profound, and already within the last eight years they have lead to prediction and discovery of a vast range of new materials with exotic properties that were considered to be impossible before.

What will you gain from this course?

• Learn about the variety of subtopics in topological materials, their relation to each other and to the general principles.
• Learn to follow active research on topology, and critically understand it on your own.
• Acquire skills required to engage in research on your own, and to minimize confusion that often arises even among experienced researchers.

What is the focus of this course?

• Applications of topology in condensed matter based on bulk-edge correspondence.
• Special attention to the most active research topics in topological condensed matter: theory of topological insulators and Majorana fermions, topological classification of "grand ten” symmetry classes, and topological quantum computation
• Extensions of topology to further areas of condensed matter, such as photonic and mechanical systems, topological quantum walks, topology in fractionalized systems, driven or dissipative systems.

What tools does this course use?

• Simple thought experiments that rely on considerations of symmetry or continuity under adiabatic deformations
• Computer simulations similar to those used in actual research will give a more detailed and visual understanding of the involved concepts
• Dissecting research papers that teaches you to simply understand the idea even in the rather involved ones.

This course is a joint effort of Delft University of Technology, QuTech, NanoFront, University of Maryland, and Joint Quantum Institute.

FAQs

Are there any books that are required for the course?

No, the course will only rely on materials and software freely available online.

Is it possible to get credit for this course at my university?

Not by default, but we invite anyone to use the course materials as a basis for a graduate course, with course materials studied as preparation and followed by a classroom discussion. Such courses are planned at universities of Copenhagen, Delft, Leiden, and University of Maryland. Following such a course will obviously give you credit points.

Would it not be better to take a more formal approach, and to describe the math in a more rigorous and systematic way?

While advanced math is certainly relevant for some researchers, in our experience it is the simple things that are the most confusing. We aim for the course to stay accessible and relevant to advanced undergraduate/beginner graduate students, both the theorists and experimentalists.

I do not know enough about condensed matter physics, but I have attended an exciting talk/read a cool article, and I'd like to learn more. Would the course be useful for me?

We are not sure. On the one hand, we will aim the course at people familiar with basic condensed matter physics and the necessary math, hence we will always assume that we don't need to explain e.g. band structures from scratch. However, a good share of the course materials are just discussions which would give you some sort of overview and understanding what this is all about.

Why didn't you discuss my favorite topic, which is certainly relevant and exciting?

Hey, that's a great idea! We aim to start from covering the basic questions, and then let the course evolve together with the field. So if you want, please help us by preparing the materials that would be helpful for the course, and they will become a bonus topic. By the way, same holds if you spot an error, or know how to improve the course: everything about this course is open, so don't hesitate to contribute.

LICENSE
The course materials of this course are Copyright Delft University of Technology and are licensed under a Creative Commons Attribution-ShareAlike (CC-BY-SA) 4.0 International License.

This course is about the Laplace Transform, a single very powerful tool for understanding the behavior of a wide range of mechanical and electrical systems: from helicopters to skyscrapers, from light bulbs to cell phones. This tool captures the behavior of the system and displays it in highly graphical form that is used every day by engineers to design complex systems.

This course is centered on the concept of the transfer function of a system. Also called the system function, the transfer function completely describes the response of a system to any input signal in a highly conceptual manner. This visualization occurs not in the time domain, where we normally observe behavior of systems, but rather in the “frequency domain.” We need a device for moving from the time domain to the frequency domain; this is the Laplace transform.

We will illustrate these principles using concrete mechanical and electrical systems such as tuned mass dampers and RLC circuits.

This course offers you the opportunity to gain a deeper understanding of the life and work of the young Albert Einstein and especially his mind-bending special theory of relativity.

In this nuclear energy course, we will tackle provocative questions such as:

• Is nuclear energy a good substitute for fossil fuels to reduce our CO2 emission or not?
• Can nuclear reactors operate safely without any harm to the public and environment?
• How much nuclear waste is produced and how long does it need to be stored safely?
• How can we make nuclear energy clean and more sustainable?
• How much are nuclear energy costs?

You will learn the physics behind nuclear science, how to gain energy from nuclear fission, how nuclear reactors operate safely, and the life cycle of nuclear fuel: from mining to disposal. In the last part of the course, we will focus on what matters most in the public debate: the economic and social impact of nuclear energy but also the future of energy systems.

Practically, we will:

• Teach you about nuclear science and technology (radiation and radioactivity, nuclear reactions, nuclear reactors and fuel cycle, economics of nuclear energy, and the sociality aspects)
• Show you short videos about the theory and practical implementation of nuclear energy
• Stimulate discussion and debate about nuclear energy
• Ask you to formulate your own opinion about nuclear energy and its role in society

The GENTLE consortium has sponsored and prepared this course. GENTLE is focused on maintaining the current high level of nuclear safety, and developing a highly skilled and well informed nuclear workforce, following the conclusion of the Council of the EU that it “it is essential to maintain in the European Union a high level of training in the nuclear field“ to deal with reactor fleet safely, decommission obsolete plants, be involved in new builds where policy dictates, and deal with the legacy and future radioactive wastes.

LICENSE

The course materials of this course are Copyright Delft University of Technology and are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike (CC-BY-NC-SA) 4.0 International License.

This cross-disciplinary course deals with the undetermined, the unpredictable- or what appears to be such. Learn about the usefulness of randomness in communication and computation, the intrinsic randomness of quantum phenomena, the unpredictability of the weather, and the implications of the neural activity of the brain on our "free will".

PHYS201x follows introductory physics courses with a more detailed treatment of oscillators, waves on strings, and electromagnetic waves. In addition to deriving and solving the wave equation, mathematical methods will be introduced on making approximations, describing oscillations with complex numbers, and synthesizing functions with Fourier series. Optical reflection and refraction will be derived, as well as the lens equation and elements of geometrical optics. Optical interference, diffraction, and polarization will be covered in detail, including the role of diffraction in image formation. PHYS201x will have weekly video lectures that explain the material through detailed derivations and demonstrations. There will be weekly homework, a discussion forum, and two exams. Eight weeks of content will be presented, and one week devoted to each self-paced exam.

Моделирование биологических молекул - одна из бурно развивающихся областей современной науки. В курсе даются основы строения биомолекул, примеры применения программных пакетов для молекулярного моделирования, разъясняются подходы к математическому описанию молекулярных систем и разбирается программная реализация этих подходов на центральном и графическом процессорах.

Курс посвящен изучению базовых законов электростатики и магнитостатики.

Курс освещает базовые законы электромагнитной индукции и электрических колебаний

以深入淺出的概念說明日常生活與科學應用中常見的光學現象，特色在於大量的範例以及實驗展示。

Hydraulics is one of the basic courses of civil engineering, hydraulic engineering, environmental engineering, architecture, and engineering physics. This science focuses on the laws of fluid dynamics and their interactions with the boundaries.

The main objective of this course is to develop the following:

• Understanding of the basic concepts and related theories of hydraulics
• Innovation consciousness and scientific literacy
• Analysis and the ability to solve the hydraulic problems met in practice 

The course content focuses on basic theories:

• Physical and mechanical properties of fluid
• Hydrostatics
• Hydrokinematics
• Hydrodynamics
• Dimensional analysis and similitude
• Flow resistance and energy loss

Hydraulics will expose you to important and interesting applications of mathematics and mechanics in engineering. You’ll participate in experiments and view videos in this class. If you take this course, you will not only gain expertise, but also have fun and know more about the nature about hydraulics in a fun and engaging way.

《水力学》是水利、土木、环境、建筑和工程物理等相关专业的技术基础课，它以水为主要对象研究流体运动的规律以及流体与边界的相互作用。本课程的主要任务是培养学生在三个方面的知识与能力：(1) 掌握水力学基本概念和基本理论；(2) 培养创新意识和科学素养；(3) 培养分析和解决工程实际中水力学问题的能力和实验技能。课程内容包括：基础部分、专题部分和实验部分。基础部分：1.流体的物理力学性质；2.静力学；3.运动学；4.动力学基础；5.量纲分析和相似理论；6.流动阻力和能量损失。专题部分：1.有旋流动和有势流动；2.边界层理论基础与绕流运动；3.孔口、管嘴出流有压管流。实验部分：包括常规教学实验和设计型（创新）实验。    

电磁学是普通物理系列中最重要的基础课之一，是高等学校每一个理工科学生必修课程，本课程包括静电场、导体与电介质、恒定电流、恒磁场、磁介质、电磁感应、交流电、电磁场与电磁波等内容，首次系统地向学生介绍“场”的概念和处理“场”的方法，对学生今后学习和工作有深远的影响。本课程作为北京大学首次向中学开放的中国大学先修课（AP课程）之一，为有志于学习物理及相关专业的学有余力的优秀中学生，培养学科兴趣，提高科学素养，打下扎实的物理基础提供学习的环境和应有的资源。

本课程以通俗的语言介绍粒子物理的主要内容和最前沿的研究。课程涉及的主要内容包括： 物质和反物质， 夸克和强相互作用，中微子和弱相互作用，对称性和它的作用， 粒子物理的标准模型，粒子天文学， 暗物质。 This course gives an brief introduction of the main content and the frontier of particle physics in popular language. It includes: matter and antimatter, quark and strong interaction, neutrino and weak interaction, symmetry and its applications, standard model of particle physics, particle astronomy, dark matter etc.