A reference against which the math department can assess how well this course has taught you calculus at the end of the semester.
Preview
The secret true purpose of calculus: computer animated snakes!
OK, maybe this isn’t quite the only reason for calculus, but it illustrates a lot of things we will look at this course. Specifically, this course extends much of what you know about calculus to more than 2 dimensions.
The snake’s basic shape is a curve, but in 3 dimensions rather than 2. We will talk about ways of describing such curves.
But the snake isn’t just a curved line, it has volume and a surface. We will also talk about ways of describing surfaces in 3 dimensions.
Realistically drawing the snake involves knowing things about the orientations of pieces of the surface, e.g., what directions tangents or perpendiculars to the surface point -- this is an extension of ideas about derivatives and tangents to 2D curves that you already know.
The snake, being a closed surface, has a volume, and you can work with 3D volumes via integration, extending what you know about integrals and area (not something that’s particularly important to computer animation though).
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How this course will work and the underlying approach to learning.
Solving distinct problems with same concept in different ways.
But it’s good to understand the underlying concepts before solving problems.
Seeing example solutions.
Working with examples based on real world applications.
Looking for patterns of similarity/difference in solution processes between problems.
Many of these ideas correspond well with my own experience learning and teaching, and with research on learning.
Particularly the importance of doing things with the ideas you’re learning, not just hearing or reading about them.
So this course will have a lot of opportunities to practice calculus, notably through in-class problem solving and discussion, and frequent out-of-class problem sets.