Online courses directory (4)
How long should the handle of your spoon be so that your fingers do not burn while mixing chocolate fondue? Can you find a shape that has finite volume, but infinite surface area? How does the weight of the rider change the trajectory of a zip line ride? These and many other questions can be answered by harnessing the power of the integral.
But what is an integral? You will learn to interpret it geometrically as an area under a graph, and discover its connection to the derivative. You will encounter functions that you cannot integrate without a computer and develop a big bag of tricks to attack the functions that you can integrate by hand. The integral is vital in engineering design, scientific analysis, probability and statistics. You will use integrals to find centers of mass, the stress on a beam during construction, the power exerted by a motor, and the distance traveled by a rocket.
1. Modeling the Integral
- Differentials and Antiderivatives
- Differential Equations
- Separation of Variables
2. Theory of Integration
- Mean Value Theorem
- Definition of the Integral and the First Fundamental Theorem
- Second Fundamental Theorem
- Areas and Volumes
- Average Value and Probability
- Arc Length and Surface Area
4. Techniques of Integration
- Numerical Integration
- Trigonometric Powers, Trig Substitutions, Completing the Square
- Partial Fractions, Integration by Parts
This course, in combination with Part 1, covers the AP* Calculus AB curriculum.
This course, in combination with Parts 1 and 3, covers the AP* Calculus BC curriculum.
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.
This is an introductory course to learn programming with Java designed to teach how to code good programs in Java, understanding “good” as both correct and efficient. Basic principles of software engineering will be introduced to make it easier for our future self and others to reuse code. Ethical issues and the intellectual property of our programs will also be addressed in the last part of this course. Examples and case studies will be provided, so that learners can implement simple but increasingly complex programs in Java.
Emphasis is put on immediate feedback and on having a fun experience. Programming knowledge is not only useful to be able to program today’s devices such as computers and smartphones. It also opens the door to computational thinking, i.e. the application of computing techniques to every-day processes.
This course is designed taking into account the subset and recommendations of the College Board in order to prepare learners for the Advanced Placement (AP) Computer Science A exam..
Louv1.2x and its predecessor computer-2751#.VBBX97xdUnQ">Louv1.1x together give an introduction to all major programming concepts, techniques, and paradigms in a unified framework. We cover the three main programming paradigms: functional, object-oriented, and declarative dataflow.
The two courses are targeted toward people with a basic knowledge of programming. It will be most useful to beginning programming students, but the unconventional approach should be insightful even to seasoned professionals.
Louv1.1x (Fundamentals) covers functional programming, its techniques and its data structures. You’ll use simple formal semantics for all concepts, and see those concepts illustrated with practical code that runs on the accompanying open-source platform, the Mozart Programming System.
Louv1.2x (Abstraction and Concurrency) covers data abstraction, state, and concurrency. You’ll learn the four ways to do data abstraction and discuss the trade-offs between objects and abstract data types. You’ll be exposed to deterministic dataflow, the most useful paradigm for concurrent programming, and learn how it avoids race conditions.
To learn more about the practical organization of the two courses, watch the introductory video.
Video games as a medium go back more than 50 years to mainframe computers. Even the central design of video games can be traced back to the first games themselves.
To be a good game designer, it’s essential to have an understanding of the video game design industry’s fascinating history.
We’ve partnered with The Strong National Museum of Play to give you a unique look into the history of all things video game. The International Center for the History of Electronic Games at The Strong is the largest and most comprehensive public assemblage of video games and related materials in the world. The staff are celebrated experts in the field and the ICHEG is visited by scholars of video games from around the world. You’ll gain amazing insight into the history of video games with a guided exploration of key artifacts from the collection of more than 100,000 electronic games and materials.
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