Leonhard EulerLeonhard Euler

Notation Made Easier: Modern Notation

BY: DuncanIS

Euler’s WorksEuler’s Works Introduced the concept of function and the notation Introduced the concept of function and the notation f(x).f(x).

• This made it easier to denote the function This made it easier to denote the function ff to the argument to the argument x.x.

Introduced the letterIntroduced the letter ‘ ‘ee’ ’ to denote the base of the natural to denote the base of the natural logarithm.logarithm.

Pioneered the use of the Pioneered the use of the ΣΣ for Summations. for Summations.

Set into order the use of Set into order the use of ii for imaginary units, the square root of for imaginary units, the square root of (-1)(-1)

Works (cont’d)Works (cont’d) Uniformed the use of ‘Uniformed the use of ‘ππ’, ’,

though he did not discover though he did not discover the ratio of circles the ratio of circles circumfrence.circumfrence.

Standardized Trigonometric Standardized Trigonometric values into familiar terms values into familiar terms such as such as • Sin & cosecant (csc)Sin & cosecant (csc)• Cos & secant (sec)Cos & secant (sec)• Tan & cotangent (cot)Tan & cotangent (cot)• Angles A,B,C, and their sides Angles A,B,C, and their sides

a,b,c.a,b,c.

Modern NotationModern Notation As a teacher of Modern Notation As a teacher of Modern Notation

Leonhard will introduce the study of Leonhard will introduce the study of such symbols such as such symbols such as ππ,,ΣΣ, , ii, , f(x) and f(x) and so on.so on.

The course will review history of The course will review history of math and its previous notations.math and its previous notations.

It will delve into the study of Newton It will delve into the study of Newton and Leibniz, the founder of and Leibniz, the founder of Mathematics.Mathematics.

Modern Notation Pt.2Modern Notation Pt.2 Introduce the Study of the theory of Introduce the Study of the theory of

functions, in particular that offunctions, in particular that of• ExponentialExponential• Logarithmic Logarithmic • Trigonometric FunctionsTrigonometric Functions

Study of Study of • Infinite series Infinite series • Negative logarithmsNegative logarithms• Imaginary numbers Imaginary numbers

Probing that ‘e’ is irrational.Probing that ‘e’ is irrational.

Why Leonhard?Why Leonhard? I believe that Leonhard Euler would be the I believe that Leonhard Euler would be the

best teacher for the subject of Modern best teacher for the subject of Modern Notation, because of his publications and Notation, because of his publications and standardization of the symbols he is known standardization of the symbols he is known for. for.

He can also give an explanation to his a He can also give an explanation to his a famed number theory in which he proposed famed number theory in which he proposed the the equation xthe the equation xnn+y+ynn=z=znn has no solutions has no solutions for n greater than 2. This study is based of for n greater than 2. This study is based of the study of Pierre de Fermat.the study of Pierre de Fermat.

Konigsberg BridgeKonigsberg Bridge One of this man’s greatest One of this man’s greatest

feats was in 1736 when he feats was in 1736 when he was able to solve the was able to solve the problem of the seven problem of the seven bridges in Konigsberg.bridges in Konigsberg.

Euler proved that was no Euler proved that was no way to find a path through way to find a path through the town that crosses each the town that crosses each bridge exactly once and bridge exactly once and returns to the starting point.returns to the starting point.

Above all…Above all…

He also had He also had money in his money in his likeness!!!likeness!!!

It was used It was used Switzerland. It Switzerland. It was displayed on was displayed on the Swiss 10 frank the Swiss 10 frank note in its 6note in its 6thth series.series.

Leonard EulerLeonard Euler

Course 1Course 1

Modern Notation Modern Notation Course 2Course 2

Modern Notation and ApplicationsModern Notation and Applications