Calculus: Applications of Derivatives

Name: Calculus: Applications of Derivatives
Rating: 5.0 (3 reviews)

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

Created byMostafa M. Madbouly

Last updated 6/2024

English

English [Auto],

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

Course content

5 sections • 10 lectures • 1h 2m total length

Lecture 1: The linear Approximation6:42
Explore linear approximation using tangent lines to estimate function values, with L(x)=f(a)+f'(a)(x−a); relate changes in x to changes in y, including radius, volume, and area examples.
Section 1: The linear Approximation7:56
Apply linear approximation with tangent lines using f(a) and f'(a) to form L(x) = f(a) + f'(a)(x-a). Explore how derivatives estimate changes in volume and area for shapes.

Lecture 2: Finding Maximum & Minimum9:59
Learn how to find local and global maxima and minima by locating critical points, applying the first and second derivative tests, and considering endpoints within intervals.
Section 2: Finding Maximum & Minimum6:23
Use derivatives to locate maxima and minima: maximize rectangle area with a 200 perimeter and compare to circle area, minimize cylinder surface area for volume 16, and maximize building volume.

Lecture 3: Parabolas, Ellipses, and Hyperbolas12:09
Explore parabolas, ellipses, and hyperbolas through equations, centers, and axes; apply to graphs of circles and ellipses with focus points, and real-world problems like projectile height.
Section 3: Parabolas, Ellipses, and Hyperbolas5:20
Derive ellipse and circle equations and apply hyperbola parameters to real-world navigation problems, calculating coordinates and focus-based distances for a bridge, lighthouse, and ship scenario.

Lecture 5: L'Hopital's Rule3:35
Learn l'hôpital's rule for indeterminate limits such as 0/0 and inf/inf, using derivatives to compute limits. The lecture shows first and higher-order derivatives yielding results like 1 and 2.
Section 5: L'Hopital's Rule1:55
Apply l'hôpital's rule to resolve 0/0 limits in the velocity ratio, differentiate to compare rates of change, and conclude car a's speed is almost double car b's.

Requirements

Having knowledge about solving 2nd Degree equations using factorization methods
Know how to find first derivative of any function
Know how to graph a function first & second degree functions
Know about what are limits, and how they're solved

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,

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)

Calculus: Applications of Derivatives

What you'll learn

Explore related topics

Course content

The Linear Approximation2 lectures • 15min

Finding Maximum & Minimum2 lectures • 16min

Parabolas, Ellipses, and Hyperbolas2 lectures • 17min

The Mean Value Theorem2 lectures • 8min

L'hopital's Rule2 lectures • 6min

Requirements

Description

Who this course is for: