Courses tagged with "Structural engineering" (124)

How did Newton describe the orbits of the planets? To do this, he created calculus.  But he used a different coordinate system more appropriate for planetary motion.  We will learn to shift our perspective to do calculus with parameterized curves and polar coordinates. And then we will dive deep into exploring the infinite to gain a deeper understanding and powerful descriptions of functions.

How does a computer make accurate computations? Absolute precision does not exist in the real world, and computers cannot handle infinitesimals or infinity. Fortunately, just as we approximate numbers using the decimal system, we can approximate functions using series of much simpler functions. These approximations provide a powerful framework for scientific computing and still give highly accurate results. They allow us to solve all sorts of engineering problems based on models of our world represented in the language of calculus.

1. Changing Perspectives
   1. Parametric Equations
   2. Polar Coordinates
2. Series and Polynomial Approximations
   1. Series and Convergence
   2. Taylor Series and Power Series

This course, in combination with Parts 1 and 2, covers the AP* Calculus BC curriculum.

Learn more about our High School and AP* Exam Preparation Courses

Calculus 1A: Differentiation

Calculus 1B: Integration

This course was funded in part by the Wertheimer Fund.

*Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.

In this course, we go beyond the calculus textbook, working with practitioners in social, life and physical sciences to understand how calculus and mathematical models play a role in their work.

Through a series of case studies, you’ll learn:

• How standardized test makers use functions to analyze the difficulty of test questions;
• How economists model interaction of price and demand using rates of change, in a historical case of subway ridership;
• How an x-ray is different from a CT-scan, and what this has to do with integrals;
• How biologists use differential equation models to predict when populations will experience dramatic changes, such as extinction or outbreaks;
• How the Lotka-Volterra predator-prey model was created to answer a biological puzzle;
• How statisticians use functions to model data, like income distributions, and how integrals measure chance;
• How Einstein’s Energy Equation, E=mc² is an approximation to a more complicated equation.

With real practitioners as your guide, you’ll explore these situations in a hands-on way: looking at data and graphs, writing equations, doing calculus computations, and making educated guesses and predictions.

This course provides a unique supplement to a course in single-variable calculus. Key topics include application of derivatives, integrals and differential equations, mathematical models and parameters.

This course is for anyone who has completed or is currently taking a single-variable calculus course (differential and integral), at the high school (AP or IB) or college/university level. You will need to be familiar with the basics of derivatives, integrals, and differential equations, as well as functions involving polynomials, exponentials, and logarithms.

This is a course to learn applications of calculus to other fields, and NOT a course to learn the basics of calculus. Whether you’re a student who has just finished an introductory Calculus course or a teacher looking for more authentic examples for your classroom, there is something for you to learn here, and we hope you’ll join us!

Using Desmos in this Course This course uses Desmos (https://www.desmos.com/), an online graphing calculator, to illustrate examples. Your use of the Desmos platform or any content hosted by Desmos is subject to the Desmos terms of service at https://www.desmos.com/terms and privacy policy at https://www.desmos.com/privacy.

If you do not wish to use the Desmos platform or view content hosted by Desmos, you may not be able to complete the course. This course does NOT require you to make your own individual user account on Desmos. Desmos is a separate entity and is not directly affiliated with HarvardX or edX.

HarvardX requires individuals who enroll in its courses on edX to abide by the terms of the edX honor code. HarvardX will take appropriate corrective action in response to violations of the edX honor code, which may include dismissal from the HarvardX course; revocation of any certificates received for the HarvardX course; or other remedies as circumstances warrant. No refunds will be issued in the case of corrective action for such violations. Enrollees who are taking HarvardX courses as part of another program will also be governed by the academic policies of those programs.

HarvardX pursues the science of learning. By registering as an online learner in an HX course, you will also participate in research about learning. Read our research statement to learn more.

Harvard University and HarvardX are committed to maintaining a safe and healthy educational and work environment in which no member of the community is excluded from participation in, denied the benefits of, or subjected to discrimination or harassment in our program. All members of the HarvardX community are expected to abide by Harvard policies on nondiscrimination, including sexual harassment, and the edX Terms of Service. If you have any questions or concerns, please contact harvardx@harvard.edu and/or report your experience through the edX contact form.

Videos on a first course in calculus (Differential Calculus).

Videos on a second course in calculus (Integral Calculus).

Calculus One is a first introduction to differential and integral calculus, emphasizing engaging examples from everyday life.

In this college level Algebra course, you will learn to apply algebraic reasoning to solve problems effectively. You’ll develop skills in linear and quadratic functions, general polynomial functions, rational functions, and exponential and logarithmic functions. You will also study systems of linear equations. This course will emphasize problem-solving techniques, specifically by means of discussing concepts in each of these topics.

Content in this course will be adaptive, allowing you to achieve mastery in a certain concept before moving on to the next. Utilizing the ALEKS learning system, students in this personalized, self-paced course will be instructed on the topics they are most ready to learn while also providing individualized coaching as you move through each topic.

This 3 credit hour course satisfies the Mathematical Studies (MA) general studies requirement at Arizona State University. This course may satisfy a general education requirement at other institutions; however, it is strongly encouraged that you consult with your institution of choice to determine how these credits will be applied to their degree requirements prior to transferring the credit.

Our lives are full of combinations. Combinatorial mathematics is just the science to deal with combinations of discrete items. As an ancient field, the history of combinatorial mathematics can be traced back over 4000 years to the age of the Great Yu in ancient China. Today, combinatorial mathematics is regarded as the basis of computer science since the algorithms in programming heavily rely on the analysis of the discrete elements.

FAQ

I don’t speak Chinese, can I learn the course?

All the materials are in English. Though the original video was recorded in Chinese, the course team record the corresponding dubbing in English. All the audio and subtitles are processed to fit the English dubbing as much as possible, so that you can enjoy this wonderful course in English.

What are the textbook and the reference books for this course?

There is no textbook requirement for this course. The handouts distributed every week are critical. The following books are references

• Richard A. Brualdi; Introductory Combinatorics (5^th edition), Pearson, 2009
• J.H.van Lint and R.M. Wilson; A course in Combinatorics, Cambridge University Press, 2001
• 卢开澄,《组合数学》第四版,清华大学出版社

What is the grading breakdown?

• 70% quizzes and exercises
• 30% final exam

How can I get the certificate?

If your final score is no less than 60.

Do I need to know how to program to learn this class?

Not necessary. This course is a math course which is based on fundamental theory. But to help the students to have the intuitive feel of the effects of the theory, we also provide a code lib that you can compare different implementations by running different programs.    

In this advanced math course, you will learn how to build solutions to important differential equations in physics and their asymptotic expansions. Armed with the tools mastered in this course, you will have a solid command of the methods of tackling differential equations and integrals encountered in theoretical and applied physics and material science.

The course is for engineering and physics majors. The course instructors are active researchers in theoretical solid-state physics.

Ce cours donne les connaissances fondamentales liées aux fonctions trigonométriques, logarithmiques et exponentielles. Il est articulé autour de 9 chapitres:

1. L'angle et sa mesure
2. Les fonctions trigonométriques sinus et cosinus et leurs inverses
3. Les fonctions trigonométriques tangente et cotengente et leurs inverses
4. Les formules trigonométriques (addition, bissection, etc)
5. Les oscillations harmoniques
6. Les équations trigonométriques
7. Les relations dans le triangle (théorème du sinus, du cosinus)
8. Continuité et dérivabilité des fonctions trigonométriques
9. Les fonctions logarithmiques et exponentielles

Le cours propose une approche très détaillée et précise des notions fondamentales liées aux fonctions trigonométriques, logarithmiques et exponentielles. La présentation des concepts et des propositions est soutenue par une grande gamme de figures et d'animations, ainsi que par des exemples qui illustrent la mise en oeuvre des connaissances acquises.

EX101x is for all of those struggling with data analysis. That crazy data collection from your boss? Megabytes of sensor data to analyze? Looking for a smart way visualize your data in order to make sense out of it? We’ve got you covered!

Using video lectures and hands-on exercises, we will teach you cutting-edge techniques and best practices that will boost your data analysis and visualization skills.

We will take a deep dive into data analysis with spreadsheets: PivotTables, VLOOKUPS, Named ranges, what-if analyses, making great graphs - all those will be covered in the first weeks of the course. After that, we will investigate the quality of the spreadsheet model, and especially how to make sure your spreadsheet remains error-free and robust.

Finally, once we have mastered spreadsheets, we will demonstrate other ways to store and analyze data. We will also look into how Python, a programming language, can help us with analyzing and manipulating data in spreadsheets.

EX101x is created using Excel 2013 and Windows. Most assignments can be made using another spreadsheet program and operating system as well, but we cannot offer full support for all configurations.

The goal of this course is to help you to overcome data analysis challenges in your work, research or studies. Therefore we encourage you to participate actively and to raise real data analysis problems that you face in our discussion forums. 

This course is part of the Data Analysis XSeries.

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.

Are you interested in pursuing a degree in Data Science, but unsure whether you have the necessary Math and Programming skills? This assessment will help you identify your current readiness in three core areas required for the study of Data Science; Calculus, Linear Algebra, and Programming.

You can take this assessment at your own pace and receive a private score report that identifies your readiness in each specific area. We will also provide, when necessary, recommendations for additional free online study.

This assessment is free, unproctored, and not offered for credit; it is designed for enrichment and self-assessment for anyone interested in pursuing data science as a career.​

En esta era de la información, los datos están disponibles en todos lados y crecen a una tasa exponencial. ¿Cómo podemos darle sentido a todos los datos? ¿Cómo aprovechamos los datos en el momento de tomar decisiones? ¿Cómo utilizamos los datos para que nos ayuden a guiar la gestión y planificación de nuestras políticas? Tanto si eres ciudadano como planificador de políticas, deberías poder responder a estas preguntas.

En este curso podrás fortalecer tus capacidades de uso, comprensión e interpretación de datos, utilizando la plataforma desarrollada por el BID “Números para el Desarrollo”, que presenta datos e indicadores socioeconómicos de la región de América Latina y el Caribe. A través de estas herramientas, podrás comprender cómo mejorar el proceso de toma de decisiones en la gestión pública.

Al finalizar el curso, contarás con instrumentos para navegar entre los datos, realizar e interpretar visualizaciones y comprender los diferentes tipos de análisis de datos según la política a implementar.

Tranquilo, no se trata de un curso de estadística, sino de adquirir los conocimientos necesarios para interpretar gráficas, reportes estadísticos y comprender su lenguaje. Y, lo más importante: adquirirás las bases para fundamentar tus decisiones en datos comprobables, más allá de tu intuición.

El curso está basado en ejemplos para que puedas ir comprendiendo los diferentes conceptos y metodologías de una manera sencilla, práctica y amena. Encontrarás diferentes actividades prácticas, en las que podrás aplicar los conocimientos adquiridos y practicar con datos y gráficas. Además, te mostraremos casos reales del BID para promover el análisis y presentar las realidades a las que están expuestos los expertos de la región. También te enfrentarás a algunos retos creativos, con los que podrás medir tus capacidades en un nivel de dificultad más elevado.

Finalmente, el curso tiene lecturas y videos que permiten generar una mejor compresión de temas del curso y participar con fundamento en los foros de discusión; en los que se abren espacios para la discusión con tus compañeros alrededor de los temas y retos planteados durante el curso.

Este MOOC ha sido certificado por Quality Matters (QM), organización sin ánimo de lucro reconocida como líder en el aseguramiento de la calidad de la educación en línea. QM ha desarrollado un conjunto de estándares de calidad para el diseño de cursos cuyo cumplimiento ha sido certificado en este MOOC a través de un riguroso proceso de revisión de pares expertos para garantizar la efectividad del aprendizaje.

This overview course is designed to show new students how to take a course on edx.org. You will learn how to navigate the edX platform and complete your first course! From there, we will help you get started choosing the course that best fits your interests, needs, and dreams.

In this interactive pre-Calculus course, you will deepen and extend your knowledge of functions, graphs, and equations from high school algebra and geometry courses so you can successfully work with the concepts in a rigorous university-level calculus course. This course is designed to engage learners in the “doing” of mathematics, emphasizing conceptual understanding of mathematical definitions and student development of logical arguments in support of solutions. The course places major emphasis on why the mathematics topics covered work within the discipline, as opposed to simply the mechanics of the mathematics.

This introductory course has the same rigor as the regular M.I.T. course of the same name, which is one of the first subjects in M.I.T.'s Mechanical Engineering undergraduate curriculum.

In this course, students will learn to analyze and predict the dynamic behavior of objects and systems, their motions and associated forces, and understand mechanical systems of complexity that are representative of engineering practice.  Students will also analyze the kinematics of mechanisms, understand torque and angular momentum in rigid bodies in rotation, and imbalance in rotating systems. Finally students will derive nonlinear equations of motion for a wide variety of mechanical systems, solve them using numerical methods in MATLAB as well as plot and interpret results.

The course combines a unique blend of rigor and realism to produce fundamental skills in an accessible, entertaining format.

Before your course starts, try the new edX Demo where you can explore the fun, interactive learning environment and virtual labs. Learn more.

A wondrously romantic belief is that brilliant thinkers magically produce brilliant ideas: Einstein jostles his hair and relativity falls out. We can enjoy these fanciful visions of leaps of genius, but we should not be fooled into believing that they’re reality.

Brilliant innovators are brilliant because they practice habits of thinking that inevitably carry them step by step to works of genius. No magic and no leaps are involved.

Professor Starbird will discuss how habits of effective thinking and creativity can be taught and learned through puzzles and mathematics. Anyone who practices these habits of mind will inevitably create new insights, new ideas, and new solutions.

Wollen Sie realistische Probleme der Ingenieurmathematik lösen? Das ist ohne Einsatz von Computersoftwarelösungen, wie sie etwa MATLAB bietet, nicht möglich.

In diesem Kurs zeigen wir, wie Sie die in MATLAB zur Verfügung stehenden Funktionen benutzen können, um zahlreiche typische Problemstellungen aus der Höheren Mathematik zu lösen bzw. zu visualisieren. Sie entwickeln ein tiefes Verständnis für die mathematischen Problemstellungen und deren Lösungen. Das aktive Erstellen von Programmen unterstützt das sogfältige und genaue Arbeiten der Studierenden – die Lösungsstrategien werden nicht nur nachvollzogen, sondern erarbeitet.

Es sind keine Voraussetzungen nötig. Nehmen Sie an dem Kurs teil und erwerben Sie eine Schlüsselqualifikation, die Ihnen nicht nur im Studium, sondern auch im Berufsleben von entscheidendem Nutzen sein wird.

Are you interested in improving your mechanics or introducing yourself to the subject all together? Join our unique course, devised by the Ural Federal University. Through our innovative approach, you will receive the basic traditional material by engaging in practically-oriented tasks and learn the strictly theoretical mathematical analysis of basic concepts. You will be introduced to mathematical modelling of engineering designs, standard machines, and mechanisms using 2D and 3D diagrams. The course begins with statics, which is the science of forces.

By the end of the course you will be able to:

• write down equilibrium conditions of structural elements and units of machines and mechanisms.
• perform the substitution of one system of forces that acts upon the structural elements and components of mechanisms with another equivalent one.
• create 2D and 3D diagrams of equilibrium in the standard engineering objects.
• choose appropriate mathematical models for calculating geometric parameters and force loads in the problems related to equilibrium of the engineering structures.
• apply combinations of mathematical operations according to the obtained mathematical models, when creating and solving equations describing equilibrium of the engineering structures.

The weekly course includes video lectures on theoretical concepts, video demonstrations of the solutions of practical problems, tasks for students’ training, individual task, interim and final tests.

This course is part of the Microsoft Professional Program Certificate in Data Science.

If you’re considering a career as a data analyst, you need to know about histograms, Pareto charts, Boxplots, Bayes’ theorem, and much more. In this applied statistics course, the second in our Microsoft Excel Data Analyst XSeries, use the powerful tools built into Excel, and explore the core principles of statistics and basic probability—from both the conceptual and applied perspectives. Learn about descriptive statistics, basic probability, random variables, sampling and confidence intervals, and hypothesis testing. And see how to apply these concepts and principles using the environment, functions, and visualizations of Excel.

As a data science pro, the ability to analyze data helps you to make better decisions, and a solid foundation in statistics and basic probability helps you to better understand your data. Using real-world concepts applicable to many industries, including medical, business, sports, insurance, and much more, learn from leading experts why Excel is one of the top tools for data analysis and how its built-in features make Excel a great way to learn essential skills.

Before taking this course, you should be familiar with organizing and summarizing data using Excel analytic tools, such as tables, pivot tables, and pivot charts. You should also be comfortable (or willing to try) creating complex formulas and visualizations. Want to start with the basics? Check out DAT205x: Introduction to Data Analysis using Excel. As you learn these concepts and get more experience with this powerful tool that can be extremely helpful in your journey as a data analyst or data scientist, you may want to also take the third course in our series, DAT206x Analyzing and Visualizing Data with Excel. This course includes excerpts from Microsoft Excel 2016: Data Analysis and Business Modeling from Microsoft Press and authored by course instructor Wayne Winston.

This course is also part of the Microsoft Excel for the Data Analyst XSeries.

Do you want to learn how to harvest health science data from the Internet? Or learn to understand the world through data analysis? Start by learning R Statistics!

Skilled professionals who can process and analyze data are in great demand today. In this course you will explore concepts in statistics to make sense out of data. You will learn the practical skills necessary to find, import, analyze and visualize data. We will take a look under the hood of statistics and equip you with broad tools for understanding statistical inference and statistical methods. You will also perform some really complicated calculations and visualizations, following in the footsteps of Karolinska Institute’s researchers.

Statistical programming is an essential skill in our golden age of data abundance. Health science has become a field of big data, just like so many other fields of study. New techniques make it possible and affordable to generate massive data sets in biology. Researchers and clinicians can measure the activity for each of 30000 genes of a patient. They can read the complete genome sequence of a patient. Thanks to another trend of the decade, open access publishing, the results of such large scale health science are very often published for you to read free of charge. You can even access the raw data from open databases such as the gene expression database of the NCBI, National Center for Biotechnology Information.

We will dive into this data together. Learn how to use R, a powerful open source statistical programming language, and see why it has become the tool of choice in many industries in this introductory R statistics course.