Makenna's introduction on Calculus

Calculus

Table of Contents

Introduction

• Review on Algebra 1-2

• Function Review

• Function Example

• Average Rate of Change

• What does rate of change mean?

• Average Rate of Change Intuition and Derivation

Calculus

Introduction

This course will be based towards those who have basic Alegbra 2 knowledge, including polynomials mainly. If you know summation you can skip over the summation part of this course.

Review on Algebra 1-2

Function Review

We normally define real single variate ( having only one variable ) functions as some , How to use functions,

Function Example

Average Rate of Change

What does rate of change mean?

In a linear standpoint we can think of the rate of change as some slope, some over some values.

Average Rate of Change Intuition and Derivation

We can think about average rate of change most simply by imagining a line connecting some and where and are our intervals, the rate of change is the slope of that line. To get an equation for that we want to define some over , whereas is our and our is some , in all we get this.

Formula

Sequences review

Sequences Introduction

You can think of a sequence as a pattern with elements.

Sequence Example:

In this sequence the pattern is adding one to the past element.

Summations

Intro to Summations

Summations are a way of adding things up, maybe if you recall from Algebra 1, sequences, summations are a type of sequences.

Notation of Summations

is the index, is the indedx start, is the index end

Summation Example

Like before we can represent some sequences as summations, in our sequences example we can rewrite that as a summation

means that the index starts at , and the n value is which means it stops at

Limits

Derivatives

What are Derivatives?

Derivatives are known as the instantaneous rate of change. But what does that mean?

Intuitive Approach

Say we have some curve now if we want to plot

Lets plot a line on

Lets plot another line now on

Connect the lines

Bring the second line closer to the first line

Bring the second line to the limit of 2

Formal definition

Introduction to Derivatives

Integrals