# The Essentials of Calculus

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Lesson 1: Limits

Formal (or less formal) definitions:

• Infinity is the concept of a number grater than any numeric value.
• limit is a value that a graph gets infinitely close to as the independent variable (usually x) gets infinitely close to a specific value from either side (positive or negative).  i. e. the “limit of the f(x) as x approaches a” is the value that the  f(x) gets infinitely close to as x gets infinitely close to a.
• Calculus is algebra with additional logic and algorithms designed for computing incomputable quantities.
• End behavior is the limit of a function as the independent variable approaches positive or negative infinity.
• If a function f is continues at a point a, then the limit of the f of x as x approaches a is the f of a.

Lesson 2: Removable Discontinuities

Formal (or less formal) definitions:

• A removable discontinuity is a part of a graph at which the limit exists, but the graph does not; i.e. a singular point at which a graph does not exist but where the graph approaches that same point from both sides.

• A line integral is an integral of a curve that is weighted according to a surface of one higher dimension generally, but not always, with respect to the length of the curve (ds).
• line integrals lesson transcript

## 2 thoughts on “The Essentials of Calculus”

1. Charlotte Hoather says:

Shame you’re not doing master classes in Maths mechanics my younger brother is struggling with it. He thought he was taking pure maths with Statistics and got A’s in Core 1 and 2 but he dislikes mechanics which dragged his overall grade down to a B just a few marks short at AS.

I love Maths and took it at AS level.

• 0over0 says:

Mechanics is such a practical subject; most of what I study is rather impractical. Has your brother considered watching some of Walter Lewis’ lecture series?

I’m glad to hear you like math!