Lecture 1

Август 23, 2022

Содержание

2. Lecture overview Multivariable functions Interior and boundary points, open and closed region Level Curve, Graph of
3. Multivariable functions
4. Multivariable functions
5. Interior and boundary points, open and closed region
6. Interior and boundary points, open and closed region
7. Interior and boundary points, open and closed region
8. Interior and boundary points, open and closed region
9. Interior and boundary points,open and closed region
10. Level Curve, Graph of function
11. Level Curve, Graph of function
12. Level surface,
13. Limits of multivariable functions
14. Limits along smooth curves
15. Limits of multivariable functions
17. Limits of multivariable functions
19. Limits along smooth curves
20. Theorem: Continuity of multivariable functions
21. Continuity of multivariable functions
22. Continuity of multivariable functions
23. Partial differentiation
24. Partial differentiation
25. Partial differentiation
26. Partial differentiation
27. Partial differentiation
28. Partial differentiation
29. Partial differentiation
30. Partial differentiation
31. Partial differentiation dx f ( x, y) = x cos y + yex df = cos
32. Partial differentiation
33. Partial differentiation
34. Chain rules for partial differentiation Definition (chain rules):
35. Chain rules for partial differentiation
36. Chain rules for partial differentiation Definition (chain rules) for partial derivatives:
37. Chain rules for partial differentiation
38. Chain rules for partial differentiation
39. Chain rules for partial differentiation
40. Chain rules for partial differentiation
42. Скачать презентацию

Слайд 2

Lecture overview
Multivariable functions
Interior and boundary points, open and closed region
Level Curve,

Graph of function
Limits of multivariable functions
Continuity of multivariable functions
Partial differentiation
Chain rules for partial differentiation

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Multivariable functions

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Multivariable functions

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Interior and boundary points, open and closed region

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Interior and boundary points, open and closed region

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Interior and boundary points, open and closed region

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Interior and boundary points, open and closed region

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Interior and boundary points,open and closed region

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Level Curve, Graph of function

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Level Curve, Graph of function

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Level surface,

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Limits of multivariable functions

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Limits along smooth curves

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Limits of multivariable functions

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Limits of multivariable functions

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Limits along smooth curves

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Theorem:
Continuity of multivariable functions

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Continuity of multivariable functions

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Continuity of multivariable functions

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Partial differentiation

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Partial differentiation

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Partial differentiation

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Partial differentiation

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Partial differentiation

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Partial differentiation

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Partial differentiation

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Partial differentiation

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Partial differentiation
dx
f ( x, y) = x cos y + yex
df =

cos y + yex

d df = d (cos y + yex )

x

dy dx dy
d 2 f

dy dx

= −sin y + e

fyx

= −sin y + ex

dy

x

d 2 f

dx dy

= −sin y + e

fxy

= −sin y + ex

f ( x, y) = x cos y + yex
df = −x sin y + ex
d df = d (−x sin y + ex )
dx dy dx

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Partial differentiation

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Partial differentiation

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Chain rules for partial differentiation
Definition (chain rules):

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Chain rules for partial differentiation

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Chain rules for partial differentiation
Definition (chain rules) for partial derivatives:

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Chain rules for partial differentiation

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Chain rules for partial differentiation

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Chain rules for partial differentiation

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Chain rules for partial differentiation