Read and Watch 1

15.5.1: Directional Derivatives (16:01)

15.5.2: Example Computing Directional Derivatives (09:16)

15.5.3: Introducing the Gradient with Examples (06:16)

15.5.5: Interpreting the Gradient, Max Rate of Ascent (07:56)

15.6.1: Interpreting Differentiability (09:24)

Read and Watch 2

15.6.5: Linear Approximation with Example (09:26)

15.6.6: Differentials with Example (09:02)

15.6.7: Example Application of Differentials to Manufacturing Error (14:34)

Practice

Use the practice problems at the end Section 15.5 and 15.6 in our text to practice what you've learned this week. The problems generally increase in difficulty in each subsection. The problems towards the end of the section get increasingly more involved, so I recommend working a few problems from each of the earlier subsections, checking your answers against the back of the book, and then venturing as far as you desire.

Review and Reflect

Take a look at the learning objectives for this week (found in the overview above). After completing everything above, assess how well you feel you meet each objective (say, on a scale from 1-5, 1 being the least comfortable and 5 being confident with having met the objective). The idea here is to make a record of how you feel about each objective so that you can easily go back to it before, say, an exam or at the end of the chapter and easily see what topics you should review. It can also be helpful if you are having trouble understanding a concepts later in the course.

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