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Lecture 4 Partial Derivatives Calculus II Topic 2: Differential Calculus in Several Variables Calculus II Santiago de Vicente 1

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Calculus II Topic 2: Differential Calculus in Several Variables Calculus II Santiago de Vicente 1 Functions of Several Variables: Differents pents depending direction Calculus II Santiago de Vicente 2 Watching a two variables Function as a function of x only Calculus II Santiago de Vicente 3 Santiago de Vicente 4 Calculus II Partial Derivatives: Definition Calculus II Santiago de Vicente 5 Geometrical Interpretation (1 of 2) Calculus II Santiago de Vicente 6

TRANSCRIPT

Lecture 4 Partial Derivatives

Calculus II

Topic 2:

Differential Calculus in Several Variables

Calculus II Santiago de Vicente 1

Functions of Several Variables: Differents pents depending direction

Calculus II Santiago de Vicente 2

Watching a two variables Function as a function of x only

Calculus II Santiago de Vicente 3

Calculus II Santiago de Vicente 4

Watching a two variables Function as a function of y only

Partial Derivatives: Definition

Calculus II Santiago de Vicente 5

Geometrical Interpretation (1 of 2)

Calculus II Santiago de Vicente 6

Geometrical Interpretation (2 of 2)

Calculus II Santiago de Vicente 7

Partial Derivatives in General

Calculus II Santiago de Vicente 8

Partial Derivatives: Usual Notations

Calculus II Santiago de Vicente 9

Calculus II Santiago de Vicente 10

Examples

Calculus II Santiago de Vicente 11

Examples

Calculus II Santiago de Vicente 12

Geometrical Application

Calculus II Santiago de Vicente 13

More Examples

Calculus II Santiago de Vicente 14

Traces of a Plane

Calculus II Santiago de Vicente 15

Traces of a Plane

Calculus II Santiago de Vicente 16

Second-Order Partial Derivatives

Calculus II Santiago de Vicente 17

Traces of a Surface

Calculus II Santiago de Vicente 18

The Schwarz (Claireaut) Theorem

Calculus II Santiago de Vicente 19

Traces of a Surface

Calculus II Santiago de Vicente 20

Drawing a Cylinder

Calculus II Santiago de Vicente 21

Drawing General Cylinders

Calculus II Santiago de Vicente 22

Ellipsoid

Calculus II Santiago de Vicente 23

Elliptic Paraboloid

Calculus II Santiago de Vicente 24

Hyperboloid of one sheet

Calculus II Santiago de Vicente 25

Hyperbolic Paraboloid

Calculus II Santiago de Vicente 26

Hyperbolic Paraboloid

Calculus II Santiago de Vicente 27

Hyperbolic Paraboloid

Calculus II Santiago de Vicente 28

Hyperbolic Paraboloid

Calculus II Santiago de Vicente 29

Hyperbolic Paraboloid

Calculus II Santiago de Vicente 30

Hyperboloid of two sheets

Calculus II Santiago de Vicente 31

The Cone

Calculus II Santiago de Vicente 32

The Cone

Calculus II Santiago de Vicente 33

The Cone

Calculus II Santiago de Vicente 34

The Cone

Calculus II Santiago de Vicente 35

Finding the Directional Derivative using his Definition

Calculus II Santiago de Vicente 36

The Cone

Calculus II Santiago de Vicente 37

The Cone

Calculus II Santiago de Vicente 38

The Cone

Calculus II Santiago de Vicente 39

The Cone

Calculus II Santiago de Vicente 40

The Cone

Calculus II Santiago de Vicente 41

The Cone

Calculus II Santiago de Vicente 42

The Cone

Calculus II Santiago de Vicente 43

The Cone

Calculus II Santiago de Vicente 44

The Cone

Calculus II Santiago de Vicente 45

The Cone

Calculus II Santiago de Vicente 46

The Cone

Calculus II Santiago de Vicente 47

The Cone

Calculus II Santiago de Vicente 48

The Cone

Calculus II Santiago de Vicente 49

The Cone

Calculus II Santiago de Vicente 50

The Cone

Calculus II Santiago de Vicente 51

The Cone

Calculus II Santiago de Vicente 52

The Cone

Calculus II Santiago de Vicente 53

The Cone

Calculus II Santiago de Vicente 54

The Cone

Calculus II Santiago de Vicente 55

The Cone

Calculus II Santiago de Vicente 56

The Cone

Homework

Calculus II Santiago de Vicente 57