Even as the finite encloses an infinite series
And in the unlimited limits appear,
So the soul of immensity dwells in minutia
And in narrowest limits no limits inhere.
What joy to discern the minute in infinity!
The vast to perceive in the small, what divinity!
-Jacob Bernoulli, “Treatise on Infinite Series”
Course Objectives
In this course, we will explore some of the calculus discoveries that gave Jacob Bernoulli a feeling of joy and divinity. This course covers three main topics: the integral, sequences and series, and differential equations. An integral is a conceptual tool to add up many tiny increments, producing a value that might represent an area, volume, or total amount of change. A series is a different kind of infinite sum, using calculus tools to approximate or evaluate functions we can’t compute any other way. A differential equation is a type of problem where we try to understand the behavior of a function based on its rate of change.
This course will help you:
• Further develop your ability to collaborate and communicate ideas (written and verbally)
• Learn to think and solve problems like a mathematician
• Translate real-world problems into specific mathematical questions
• Appreciate the incredible beauty of Calculus.
And in the unlimited limits appear,
So the soul of immensity dwells in minutia
And in narrowest limits no limits inhere.
What joy to discern the minute in infinity!
The vast to perceive in the small, what divinity!
-Jacob Bernoulli, “Treatise on Infinite Series”
Course Objectives
In this course, we will explore some of the calculus discoveries that gave Jacob Bernoulli a feeling of joy and divinity. This course covers three main topics: the integral, sequences and series, and differential equations. An integral is a conceptual tool to add up many tiny increments, producing a value that might represent an area, volume, or total amount of change. A series is a different kind of infinite sum, using calculus tools to approximate or evaluate functions we can’t compute any other way. A differential equation is a type of problem where we try to understand the behavior of a function based on its rate of change.
This course will help you:
• Further develop your ability to collaborate and communicate ideas (written and verbally)
• Learn to think and solve problems like a mathematician
• Translate real-world problems into specific mathematical questions
• Appreciate the incredible beauty of Calculus.
- Teacher: Ian Whitehead