Calculus: Single Variable Part 4 - Applications
University of Pennsylvania
list 5 sequences
assignment Level : Introductive
chat_bubble_outline Language : English
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verified_user Fee-based Certificate
timer 30 hours in total

About the content

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach. In this fourth part--part four of five--we cover computing areas and volumes, other geometric applications, physical applications, and averages and mass. We also introduce probability.

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  • Week 1 - Computing Areas and Volumes
    Having seen some calculus before, you may recall some of the motivations for integrals arising from area computations. We will review those classical applications, while introducing the core idea of this module -- a differential element. By computing area and ...
  • Week 2 - Other Geometric Applications
    There's more to geometry than just area and volume! In this module, we will take things "to the next level", ascending to higher dimensions. Coming back to the 3-d world, we will return to problems of length and area, but this time in the context of curves and...
  • Week 3 - Physical Applications
    There is so much more to applications of integrals than geometry! So many subjects, from physics to finance, have, at heart, the need for setting up and computing definite integrals. In this short but intense module, we will cover applications including work, ...
  • Week 4 - Averages and Mass
    There is a statistical aspect to integrals that has not yet been brought up in this course: integrals are ideal for computing averages. Motivated by physical problems of mass, centroid, and moments of inertia, we will cover applications of integrals to average...
  • Week 5 - An Introduction to Probability
    This capstone module gives a very brief introduction to probability, using what we know about integrals and differential elements. Beginning with common-sense uniform probabilities, we move on to define probability density functions and the corresponding proba...


Robert Ghrist
Mathematics and Electrical & Systems Engineering


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The University of Pennsylvania (commonly referred to as Penn) is a private university, located in Philadelphia, Pennsylvania, United States. A member of the Ivy League, Penn is the fourth-oldest institution of higher education in the United States, and considers itself to be the first university in the United States with both undergraduate and graduate studies.


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