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Mathematics with Worked Examples

A companion site for the book, "Teaching Math with Examples"

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Category: Calculus

Implicit Differentiation Examples

Here are some example-ish tasks I used to introduct implicit differentiation. First, a warm up, to help students notice and … More

derivative

Comparing Explicit and Implicit Differentiation

Here was the original problem from Calc Medic: The thought of comparing two strategies made me think of the Compare … More

derivative

The Product Rule

Nothing especially groundbreaking here, though maybe there’s something interesting in the use of examples to cover this territory. The next … More

derivative, product rule

Finding stationary points

derivative, stationary points

Expressing a^x as a power of e

I like this example because it shows how worked examples can be used to help students make sense of a … More

derivative, exponential

Chain Rule for Exponentials

This is just a bit sloppier than I’d like. But the core idea is to draw similarities between polynomial and … More

chain rule, derivative

Basic Integration

I tend to teach integration towards the beginning of the course. Here is an early example. I tend to default … More

integration

Derivatives with fractional exponents

For this one, I tried to structure the steps. I wanted to make explicit that there are two distinct stages. … More

derivative

Derivative of Multiplied and Divided Factors

For this one, I left the final step off. I figured my students could figure that out on their own … More

derivative

Basic Derivative Mistake

The example below comes from the Mathematics Enhancement Programme. But — oh no! — a mistake. (I use these materials … More

derivative, example, mistake

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