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.

Advanced lesson: Line Integrals

  • 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. 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.

    • 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!

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