Calculus is the mathematics of change. In algebra we covered linear functions, the word linear refers to straight lines, straight lines represent change, but change that is at a constant rate (i.e. like a car driving at a constant speed).
In calculus we will start to look at functions and lines where the change… changes! For example, if a car driving at a constant speed is represented by a straight linear line, then we will use calculus to look at a car driving where its speed is changing (like if it was going down hills or being stuck behind cyclists etc.)
The three concepts that will be introduced in Calculus that allow us to analyse this change are Limits, Derivatives and Integrals - very big smart words. We will take it step by step and start by reviewing what we learned in algebra.
Differentiation & Integration
Lesson 1 looks at differentiation, integration and limit theoretically including using differentiation to find the slope of a tangent. More specifically, it covers:
- Theoretical Definition of the Slope of a Tangent
- Using Integration to Find the Area Under a Line
- Sketching a Tangent to a point on a line and estimating its slope
- Example: Average rate of change between two points
Lines
Lesson 2 starts with a review of the Real Number Line and the distance between two points thereon. It continues with:
- The Cartesian Plane
- Midpoint between points on a Cartesian Plane
- Slope Between Points on Cartesian Plane
- Equation for Line
Angles
Lesson 3 begins with a recap of perpendicular lines and then continues with a look at:
- Finding equation for a line when knowing a point on the line and the equation of another parallel line
- Angles Between Intersecting Lines
- Proof of equation for angle between lines
- Finding point of intersection and angle between two lines
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