BEX Calculus Course

Lesson 4

Pattern Visualization Step-by-Step Change Calculus Lingo

Line

f(x) = x

f(x) = 4x

Pattern X-Ray Timelapse Step-by-step change Single Step Zoom

Line

f(x) = x

f(x) = 4xx dx

1

X-Ray Strategy Visualization Step-by-Step Layout Single Step Zoom

Ring-by-ring

Slice-by-slice

Board-by-board

r

p

x

dp

dx

dx

1

r

Derivative Symbol Mindset

Think about the resulting step-by-step pattern

Think about the actual ratio of changes

Lesson 5: Building Squares

1 3 5 7

1 + 3 + 5 + 7 + 9 5x5

=

5 + 7 + 9 5x5

=

2x2-

The integral (accumulating a set of changes) Can be found with the anti-derivative[a function where F’(x) = f(x)]

Applying a sequence of changes (f(x))from a to b

Getting a function that changes the same way (F(x))and taking the difference

Is the same as

x

Area = ½ * 40 * x = 20x

20

x

Area = 20x

40

Size: 10x10

Perimeter: 40

Area: 100

x

1x

1d Perimeter Change 2d Area Change

Pixelation

a

…