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Calculus by Mind Map: Calculus
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1.4 Parametric Equations




Lines & Other Curves


Average Rates of Change


1.2 Functions & Graphs

Domain & Range

Viewing & Intrepreting Graphs

Even & Odd Functions

Piecewise Functions

Absolute Value Function

Composite Functions

Radian Measure

Slope of a line

1.3 Exponential Functions

Exponential Growth & Decay

The Number e


Instantaneous rates of change

3.1 Derivative of a Function

Definition of a derivative

Graphing Derivative from Data

One-sided derivatives

3.4 Velocity and other rates of change

Motion along a line

Relationship between graphs of and the graph of their derivative

Sensitivity to change

Derivatives in Economics

Derivative Notation

Chapter 2

2.1 Rates of Change and Limits

A Secant line is a line segment that connects to two points on a function.  Its slope provides the average rate of change of the function.   A Tangent line on the other hand is a line that touches only one point on the graph, and provides the instantaneous rate of change.

Average and Intantaneous Speed

Definition of a limit

Properties of Limits, Limit Examples

One sided and two sided limits, `1

Sandwich Theorem

2.2 Limits involving infinity


Direct Substitution Property

Finite Limts

More Sandwichs

Infinte Limits

End Behavior models

Seeing Limits

2.3 Continuity

Continuity at a point

Continuous Functions

Algebraic Combinations


Intermediate Value Theorm for continuous functions

2.4 Rates of Change and Tanget Lines

Tanget to a Curve

Slope of a Curve

Normal to a Curve

Speed Revisited


Chapter 3

3.2 Differentiablity

Derivatives might not exist

differentiability implies local linearity

Derivatives on Calculator

Differentiability implies Continuity

Intermediate Value Theorem for Derivatives

3.3 Rules for Differentiation

Postive integer powers, multiples, sums, and differences

Products and quotients, Derivative of the Sine Function

Negative integer powers of x

Second and higher order derivatives

3.5 derivatives of trig functions

Derivative of the Cosine Function

Simple Harmonic Motion


Derivatives of other Trig Functions

3.6 Chain Rule

Derivative of a Composite Function

Outside-in rule

Repeated use of the chain rule

Slopes of parametric curves

Power chain rule

New node

New node

3.7 Implicit Differentiation

Implicitly defined functions

Lenses, Tangents and Normal lines

Derivatives of higher order

Rational Powers of Differentiable functions

3.8 Derivaties of Inverse trig functions

Derivatives of inverse functions

Derivatives of the arcsin

Derivative of the arctangent

Derivative of the arcsecant

Derivatives of the other three

3.9 Derivaties of Exponential & Logarithmic Functions

Derivative of e^x

Derivative of a^x

Derivative of ln (x)

Derivative of log (x)

Power rule for arbitrary real powers

Key terms & Review

Chapter 4

Chapter 5


Sample Tests

I chose this link because it provides sample tests provided by my teacher, these tests have helped me so far in the semester, so I think they will help in my preparation for the final. I consider this scholarly or at least semi scholarly, my professor is the head of the Math Department at CCU, James Solazzo.

Recommended Examples

This PDF is a list of exercises my teacher has recommended, these will help me become familiar with the types of problems, and skill sets I will need to be prepared for the final. I consider this scholarly or at least semi scholarly, my professor is the head of the Math Department at CCU, James Solazzo.


Chapter 1

1.1 Lines


Parallel Lines, Perpendicular lines

Finding Inverse Functions

Equations of Lines

1.5 Functions & Logarithms

One-to-one functions

Inverse Functions

Logarithmic Functions

Properties of Logarithms


Key Terms & Review

1.6 Trigonometric Functions

Graphs of Trigonometric Functions

Peroid of trigonometric functions

Even & Odd Trig Functions

Transformations of Trig Functions

Inverse Trig functions