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The Birth of Calculus

7 February 2018 in MAE 113: Calculus for the Liberal Arts | No comments

This is a BBC video from 1986 on the development of calculus. For those that are interested in history, the presenter is looking at the original notes of Leibniz while he was developing calculus. He formalized the rules of differentiation within a 3 week timeframe.

Tags: BBC, Calculus, history, MAE 113, youtube, Youtube clip

A second (more elegant) proof of the Quotient Rule

6 February 2018 in MAE 113: Calculus for the Liberal Arts | No comments

The quotient rule proof can be quite tedious if we are only allowed to use the definition of the derivative. In this post, this presents an alternative way of proving the quotient rule if we are allowed to use the product rule.

The Quotient Rule: $\left( \dfrac{f(x)}{g(x)}\right)' = \dfrac{f'(x) \cdot g(x) - f(x) \cdot g'(x)}{[g(x)]^2}$

Read the rest of this entry »

Tags: Calculus, MAE 113, proof

A proof of the quotient rule

6 February 2018 in MAE 113: Calculus for the Liberal Arts | No comments

The quotient rule proof can be quite tedious if we are only allowed to use the definition of the derivative.

The Quotient Rule: $\left( \dfrac{f(x)}{g(x)}\right)' = \dfrac{f'(x) \cdot g(x) - f(x) \cdot g'(x)}{[g(x)]^2}$

Read the rest of this entry »

Tags: Calculus, MAE 113, proofs

Assignment 4

6 February 2018 in MAE 113: Calculus for the Liberal Arts | 2 comments

Assignment 4 was handed out in class. You can see a copy here with the additional solutions here.

I had a question about some of the solutions. Read the rest of this entry »

Tags: assignment, Calculus, MAE 113

Assignment 3

29 January 2018 in MAE 113: Calculus for the Liberal Arts | No comments

Assignment 3 has been handed out and it can be found here.

Tags: assignment, Calculus, limits, MAE 113

Limits

24 January 2018 in MAE 113: Calculus for the Liberal Arts | No comments

Some students have asked if there was online material that they could read or study.

Limits: This follows my explanation of a limit closely. Read examples 1 and 2.
Left and right handed limits: Read examples 1 and 3. Practice problems here with solutions. Remember that the left-handed limit is the limit as $x$ approaches the value $a$ from the left-hand side; $\displaystyle\lim_{x \to a^{-}}f(x)$ . We use the $-$ symbol to denote the left-hand side. The right-handed limit is the limit of $f(x)$ as $x$ approaches the value $a$ from the right-hand side; $\displaystyle\lim_{x \to a^+} f(x)$ . We use the $+$ symbol to denote the right-hand side.
Limit properties: Read examples 1 and 2.
Computing Limits: More practice problems with solutions.
Continuity: Read examples 1 and 2. Practice problems here with solutions (try problems 1 and 2).