D'Alembert d’Alember was born on November 17th 1717 in Paris,
France. During his studies in the College des Quatre Nations he grew very interested on Mathematics, mainly because the school’s library was excellent. There d’Alembert had the oppotunity to study mathematicians like Descartes.
D'Alember's interest on Mathematics was mixed with his interest on the study of Physics. This interest had significant results. He improved Newton's definition of force in his book “Traité de dynamique” published in 1743. This book is very important because it proveded the foundation for mechanics. He believed that mechanics was a very important part of mathematics just as geometry or algebra is to mathematics.
France. During his studies in the College des Quatre Nations he grew very interested on Mathematics, mainly because the school’s library was excellent. There d’Alembert had the oppotunity to study mathematicians like Descartes.
D'Alember's interest on Mathematics was mixed with his interest on the study of Physics. This interest had significant results. He improved Newton's definition of force in his book “Traité de dynamique” published in 1743. This book is very important because it proveded the foundation for mechanics. He believed that mechanics was a very important part of mathematics just as geometry or algebra is to mathematics.
One of the most significant contributions of d'Alembert to the world of Mathematics was his studies on Partial Differential Equations (PED). This man was not only the pioneer of the PDE, but he was also the pioneer of the use of PDE on Physics. His studies on PDE made him win the 1747 pize of the Prussian Academy. He submited his work on PDE in an article called “Reflecions
sur la cause generable des vents” to the Prussian Academy.
The book contained d’Alembert’s formula for the general solution to the one-dimensional wave equation, which can be observed in the left.
D'Alembert's work contains simplifications that led the results to be at odds with observation. It was mainly based on poor physical evidence. However, Euler saw d’Alembert’s work and the power of the methods that had just introduce, his interest grew until he made significant improvements to the work provided by d’Alembert.
sur la cause generable des vents” to the Prussian Academy.
The book contained d’Alembert’s formula for the general solution to the one-dimensional wave equation, which can be observed in the left.
D'Alembert's work contains simplifications that led the results to be at odds with observation. It was mainly based on poor physical evidence. However, Euler saw d’Alembert’s work and the power of the methods that had just introduce, his interest grew until he made significant improvements to the work provided by d’Alembert.
The following YouTube video shows how to obtain d'Alembert's formula to the PDE of the wave lenght.
Another of the significant contributions of d’Alembert to the world of mathematics was an article called “Differentiel”, which was written in 1754. On this article, d’Alembert argued that the theory of limits should be put in a firm foundation. He defined the derivative of a function as the limit of a quotient of increments.
This idea led him to the test of convergence, which now is better known as d’Alembert’s ratio test. This was his was the last work on the area of mathematics because in the last years of his life d’Alembert turned to the study of literature and philosophy. However, he came to regret this decision. In a letter that he send to Lagrange in 1777, he said that he regretted not continue working on Geometry, which was the only occupation that truly interested him.
This idea led him to the test of convergence, which now is better known as d’Alembert’s ratio test. This was his was the last work on the area of mathematics because in the last years of his life d’Alembert turned to the study of literature and philosophy. However, he came to regret this decision. In a letter that he send to Lagrange in 1777, he said that he regretted not continue working on Geometry, which was the only occupation that truly interested him.