Join today for the 2025 Spring Semester
Differential Equations for Accelerated Teens
Jan 6, 2025- May 30, 2025
*Mondays
2:45-4pm ET
and Wednesdays
3:45-5pm ET
This is a Spring Semester college level Introduction to Differential Equations course for accelerated young learners!
* The primary text is TBD (I'm currently assessing options).
*Prerequisites are strong knowledge of Calculus I and II. Multivariable Calculus can be helpful, but is not required.
* The primary text is TBD (I'm currently assessing options).
*Prerequisites are strong knowledge of Calculus I and II. Multivariable Calculus can be helpful, but is not required.
What's included?
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Two live class meetings per week via zoom, with prep videos to watch as needed
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Small class size capped at 12 students
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Interactive live sessions recorded weekly via video
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Submit online or handwritten practice exercises weekly
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Weekly formal writing response exercises with written feedback from Dr. Finotti
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Two (optional) midterm exams and an end of semester cumulative final exam (required for the graded track)
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A set live weekly office hour with Dr Finotti
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A class site that allows students to interact with each other between classes, ask questions, and share ideas!
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Option between a graded track or completion certificate track
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Optional reading and video resources to learn more about common real-world uses for Multivariable Calculus
Revel in a Fascinating Subject with Peers Who Enjoy Math Too!
In our regular live zoom meetings and through the class community message board, our multivariable students will have the opportunity to explore the subject they love with a small group of like-minded peers. We'll be primarily using the Thomas' Calculus text.
Class size will be capped at 12 students so that every student will have the necessary support and opportunity to interact and be heard. The class meetings will often be interactive with an instructor that encourages a growth-mindset, supportive, mistakes-encouraged environment. We'll always aim for an appropriate level of challenge to keep the group growing!
The level of rigor in this class will be that of a rigorous university level Multivariable Calculus course. The pace of the class will be that of a college level course, so it moves fast! If you have any concern about whether or not your child is ready for this course, please feel free to contact us here.
Class size will be capped at 12 students so that every student will have the necessary support and opportunity to interact and be heard. The class meetings will often be interactive with an instructor that encourages a growth-mindset, supportive, mistakes-encouraged environment. We'll always aim for an appropriate level of challenge to keep the group growing!
The level of rigor in this class will be that of a rigorous university level Multivariable Calculus course. The pace of the class will be that of a college level course, so it moves fast! If you have any concern about whether or not your child is ready for this course, please feel free to contact us here.
Differential Equations -- Now we're really cooking with gas!
I think Steven Strogatz said it all best in the following excerpt from his book "Infinite Powers":
"It’s a mysterious and marvelous fact that our universe obeys laws of nature that always turn out to be expressible in the language of calculus as sentences called differential equations. Such equations describe the difference between something right now and the same thing an instant later or between something right here and the same thing infinitesimally close by. The details differ depending on what part of nature we’re talking about, but the structure of the laws is always the same. To put this awesome assertion another way, there seems to be something like a code to the universe, an operating system that animates everything from moment to moment and place to place. Calculus taps into this order and expresses it.
Isaac Newton was the first to glimpse this secret of the universe. He found that the orbits of the planets, the rhythm of the tides, and the trajectories of cannonballs could all be described, explained, and predicted by a small set of differential equations. Today we call them Newton’s laws of motion and gravity. Ever since Newton, we have found that the same pattern holds whenever we uncover a new part of the universe. From the old elements of earth, air, fire, and water to the latest in electrons, quarks, black holes, and superstrings, every inanimate thing in the universe bends to the rule of differential equations. I bet this is what Feynman meant when he said that calculus is the language God talks. If anything deserves to be called the secret of the universe, calculus is it."
While we will be restricting our selves to the study of differential equations of one independent variable in this course, this is still adequate for application to a wide array of interesting real-world problems. And we set the foundation for future study in Partial Differential Equations (differential equations in which the unknown function has more than one variable), which are used routinely in cutting-edge real-world applications today.
While this course has a reputation for being a "cookbook" math course -- meaning it is approached as "if you have this type of equation, then do this to solve it", there is quite a bit of meaning to glean from the equations themselves and their solutions. My research area was Partial Differential equations, so this topic is a particular passion of mine and I have plenty to share in this regard.
This course will also include a short study of systems of differentials equations (which is not always included in a differential equations course), in which the students will do applied projects. They can either design their own project (contingent upon approval by the instructor), or choose from a list of project options. We'll devote some class time to having the students present the final results of their project studies.
"It’s a mysterious and marvelous fact that our universe obeys laws of nature that always turn out to be expressible in the language of calculus as sentences called differential equations. Such equations describe the difference between something right now and the same thing an instant later or between something right here and the same thing infinitesimally close by. The details differ depending on what part of nature we’re talking about, but the structure of the laws is always the same. To put this awesome assertion another way, there seems to be something like a code to the universe, an operating system that animates everything from moment to moment and place to place. Calculus taps into this order and expresses it.
Isaac Newton was the first to glimpse this secret of the universe. He found that the orbits of the planets, the rhythm of the tides, and the trajectories of cannonballs could all be described, explained, and predicted by a small set of differential equations. Today we call them Newton’s laws of motion and gravity. Ever since Newton, we have found that the same pattern holds whenever we uncover a new part of the universe. From the old elements of earth, air, fire, and water to the latest in electrons, quarks, black holes, and superstrings, every inanimate thing in the universe bends to the rule of differential equations. I bet this is what Feynman meant when he said that calculus is the language God talks. If anything deserves to be called the secret of the universe, calculus is it."
While we will be restricting our selves to the study of differential equations of one independent variable in this course, this is still adequate for application to a wide array of interesting real-world problems. And we set the foundation for future study in Partial Differential Equations (differential equations in which the unknown function has more than one variable), which are used routinely in cutting-edge real-world applications today.
While this course has a reputation for being a "cookbook" math course -- meaning it is approached as "if you have this type of equation, then do this to solve it", there is quite a bit of meaning to glean from the equations themselves and their solutions. My research area was Partial Differential equations, so this topic is a particular passion of mine and I have plenty to share in this regard.
This course will also include a short study of systems of differentials equations (which is not always included in a differential equations course), in which the students will do applied projects. They can either design their own project (contingent upon approval by the instructor), or choose from a list of project options. We'll devote some class time to having the students present the final results of their project studies.
Meet the instructor
Dr. Heather Finotti
Heather has been teaching mathematics for 27 years. She has a PhD in Mathematics and experience teaching all ages and in all stages of learning and life. She loves supporting people in finding their own unique relationship with mathematics, and helping students who already love to learn math really learn to soar!
The last six years she's worked primarily with accelerated learners, both through private tutoring and teaching group classes. If you'd like to learn more about her, check out this page.
Patrick Jones - Course author
Ready to Enroll?
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