Differential Calculus in 1 dimension and higher dimensions

Informal minicourse, January 2014.
Thursday, January 9, 16, and 23, 6-8 PM, WWH 312.
No credit, no grades, no assignments graded.
Instructor: Ernest Davis davise@cs.nyu.edu.

If you are interested in taking this, please email me in advance.

Textbook: Online Calculus Textbook (MIT Open Courseware).

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List of Topics

(Note: The references to the text may be inaccurate, since I'm just working off the table of contents.)

Meeting 1: January 9

Definition of derivative. Basic applications. Text: 1.1-1.3, 1.7, 2.1
Numerical differentiation (i.e. (f(x+e)- f(x))/e). First-order approximation (i.e. f(x+e) = f(x) + e*f'(x) +o(e).) Text: 3.1.
Basic rules (powers, f+g. f*g, f/g). Text: 2.2, 2.3, 2.5.
Chain rule f(g(x)). Text: 4.1
Exponential and logarithm (Note: omitting trigonometric functions). Text: 6.1, 6.2

Suggested exercises Note: I've listed odd-numbered exercises because the solutions are online. Somewhat annoyingly, a lot of the more interesting problems are even-numbered.
Section 2.1, p. 49: 5, 7, 71, 21
Section 2.2, p. 56: 3, 5, 7, 9, 13
Section 2.5, p. 77: 1, 5, 19, 23, 29, 31, 39 (except d)
Section 3.1, p. 96: 11, 19, 23, 25
Section 4.1, p. 158: 1
Section 6.2, p. 241: 1, 3, 5, 9

Meeting 2: January 16

Maximum and minimum as zeros of derivative. Text: 3.2.
Higher-order derivatives and their significance. Text: 3.3
Definition of an integral, fundamental theorem of calculus. Text: 5.1, 5.2

Selected exercises
Section 3.2 p. 103: 1, 5, 9, 17, 23, 25, 39
Section 3.3 p. 111: 11, 13, 27, 45
Section 5.2 p. 186: 1, 3, 5

Meeting 3: January 23

Partial derivative. Text: 13.1-13.3
Chain rule. Text: 13.5
Tangent to a curve. Text: 12.1
Directional derivative and Gradient. 13.4
Max and min as points of zero gradient. Text: 13.6
Jacobian, time permitting (ties in nicely with linear algebra, for those who have taken Math Techniques). Not in text.
Gradient descent, time permitting. Not in text.

Selected exercises
Section 13.2 p. 479: 1, 3, 5, 7, 13, 17
Section 13.5 p. 503: 13, 15, 19, 21
Section 13.3 p. 488: 1, 3, 5
Section 12.1 p. 452: 1, 5 Section 13.4 p. 495: 1, 13, 15
Section 13.6 p. 512: 1, 5, 13.