Upcoming Paid Online Courses (2)
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.
Data driven decision-making systems allow instructional designers to engage in continuous improvement of course design to optimize student learning.
In this education and teacher training course, part of the Instructional Design and Technology MicroMasters program we will delve into data driven decision-making and you will learn data mining techniques to collect actionable data. You will learn how to analyze learner statistics to improve the impact of design and technology on learning.
It’s important for instructional designers to have systematic plans for gathering data and learner analysis to guide ongoing course adjustments to improve teaching and learning. Data is critical to the continuous improvement process.
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