Ana1 - From Prof Dirk Ferus PDF

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Summary

From Prof Dirk Ferus...

Description

z=x+iy

iy i |z| 1

x

15 12.5 10 7.5 5 2.5 1

2

3

4

5

6

4

3

2

1

1

2

3

4

5

6

1 0.8 0.6 0.4 0.2

1

2

3

4

5

6

x 1 2

1 _ 2

1_ 4

3 1 _ 6

4

n 1 _ 2n

y

n+1

1 0.5

-3

-2

-1

1 -0.5 -1

2

3

J f(J)

7 6 5 4 3 2 1 -4

-3

-2

-1

1

2

3 2 1

1 -1 -2 -3

2

3

4

5

6

7

15

12.5

10

x

x

0.5

2 7.5

5

2.5

-4

-2

2

4

1

sin x

0.5 -4

-2

2

4

-0.5

cos x

-1

π/2

t =?

1

sin t π

cos t

0 2π

3π/2

-4

4

4

3

3

2

2

1

1

-2

2

4

-4

-2

2

-1

-1

-2

-2

-3

-3

-4

-4

3

1 2.5

0.5 2

0.5

1

1.5

2

2.5

1.5

3

1

-0.5

0.5

-1 -1

-0.5

0.5

1

1.5

1 1

0.5

-1.5

-1

-0.5

0.5

0.5 -0.5

1

1.5

-1

-0.5

0.5

-0.5

-1

-1 -1.5

1

4

4

1.5

3

1

2

0.5

1

-1.5

-1

-0.5

0.5

1

1.5

-4 -1

-2

-3

-4

-2

-0.5 -1 -1.5

2

4

3.5 3

cosh x 3

2.5 2

2 1.5 1 1 0.5 -2

-1

1

2

-2

-1

1 -1

cosh x

sinh x -2

-3

2

1 0.5 -4

-2 -0.5 -1

2

4

(cosh t,sinh t)

F=t

1.0

∆f

∆x

x 0

x

f(x)

x* xn+1 xn

x 0

a

a

ξ

b

b

b β

α a

a

c

b

x y

z

0.06

0.06

0.05

0.05

0.04

0.04 0.03

0.03

0.02

0.02

0.01

0.01 0.5

1

1.5

2

0.5

1

1.5

2

f

a

b

f

+

+

a

b -

f

a

b

1

0

2

| a=x

| x 0

1

| x 2

| x3

| b=x

4

0.7 0.6 0.5 0.4 0.3 0.2 0.1

1

2

3

4

0.6 0.4 0.2

-0.6

-0.4

-0.2 -0.2 -0.4 -0.6

0.2

0.4

0.6

4 3.5 3 2.5 2 1.5 1 0.5 1

2

3

4

5

6

0.6 0.5 0.4 0.3 0.2 0.1

1

2

3

4

5

4 3.5

1/x2

3 2.5 2 1.5

1/ √x

1 0.5 1

2

3

4...