Calculus: Applications of Derivatives

An insight into theories related to derivatives and how they could be applied to real life problems

Description

Hello,

Welcome to Calculus: Applications of Derivatives course.  Many of us has already learned what are derivatives through either college lectures or through self learning.  But what was really important is how could we apply the knowledge we have gained through learning to other applications including studying motions of bodies, predicting fluctuations of stock markets, finding at which speed you’re driving, checking temperature variations, calculating profits or losses, etc…

In this course, we take a quick refresher on what are first derivatives then mention how they could be used in some real life scenarios. Not all examples are real life cases. However, they give you a sense of how we could use derivatives through a set of theories proposed by great math scientists.

The structure of the course is divided into a lecture & a section mode. In each lecture, theories are stated and demonstrated through some examples. Mostly are either real life cases or related to real life problems. Then using sections, we have extra examples that make things more clear.

The course also includes notes which are the problems that are solved during lectures & sections in PDF downloadable format.

The course uses Prof. Gilbert Strang Calculus as a reference. The book is available to download for free from the MIT Open courseware hub.

To get the best out of the course you shall go through lectures, and sections first then start solving the problems on your own. It would be perfect to try on extra problems through the reference book.

Would always be happy to help and wish you get the best out of the course.

Thank you,

What you’ll learn

• Understanding what is linear approximation theoretically
• Examples of real life applications of linear approximation theory
• Learning about finding Maximum and Minimum of curves
• Understanding what are critical points, global or local maximum, and minimum points
• Real life examples of finding glonal or local Max. & Min. points
• Understanding what are equations describing circles, ellipses, parabolas, and hyperbolas
• Using equations of geometric shapes as parabolas, and hyperbolas to solve problems related to real life
• Understanding what is the mean value theorem
• Using some problems related to real life to grasp more of what is mean value theorem
• Learning about l’hopital’s Rule of calculus
• Examples for l’hopital’s Rule using real life scenarios

Who this course is for:

• Calculus students that seek to have more understanding of how derivatives are used in solving real life problems
• Engineering & Economics students who seek to use derivatives as part of their solution tools
• Anyone wants to know about (linear approximation, finding max. and min. , l’hopital’s rule, and mean value theorem)

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