Bezout Etienne1730.3.31~1783.9.27) is a French mathematician. When I was a teenager, I loved mathematics and mainly engaged in the research of equation theory. He was one of the first mathematicians to realize the value of determinant. It is proved for the first time that homogeneous linear equations have non-zero solutions if the coefficient determinant is equal to zero. In his first paper "Several Types of Equations", he used the elimination method to link the problem of N-degree equations with the problem of solving simultaneous equations, and provided some solutions to N-degree equations. He also solved two binary equations with degree higher than 1 by elimination method, and proved Bezu theorem about the number of equations.
From 1086 to 1093, Shen Kuo of China in Song Dynasty put forward "gap product" and "meeting circle" in Meng Qian's Bi Tan, and began to study high-order arithmetic progression.
1 1 century, Al Karhi of Arabia solved the root of quadratic equation for the first time.
1 1 century, Kayam of Arabia completed a book Algebra and systematically studied cubic equations.
1 1 century, the Egyptian Al Haissam solved the "Haissam" problem, that is, two lines on a circular plane should intersect at a point on the circumference and form an equal angle with the normal of that point.
1 1 In the middle of the century, Jia Xian of the Song Dynasty in China created a method of "increasing, multiplying and opening" to open any higher order power, and listed the binomial theorem coefficient table, which was an early discovery of modern combinatorial mathematics. The so-called "Yang Hui Triangle" refers to this method.
/kloc-in the 0/2nd century, the Indian Maijialuo wrote the book Risawati, which is an important work in oriental arithmetic and calculation.
1202, Peponacci of Italy published The Book of Calculations, which introduced Indo-Arabic symbols to the West.
1220, Peponacci of Italy published the book Geometry Practice, which introduced many examples that were not found in Arabic materials.
1247, Qin of the Song Dynasty in China wrote * * * 18 "Shu Shu Jiu Zhang", which popularized the multiplication, division and expulsion methods. The solution of the simultaneous congruence formula proposed in the book is more than 570 years earlier than that in the west.
During the period of 1248, China Song Dynasty Li Zhi wrote twelve volumes of "Measuring the Circle Sea Mirror", which was the first work to systematically discuss "Tianshu".
126 1 year, Yang Hui of Song Dynasty in China wrote "Detailed Explanation of Nine Chapters Algorithm", and used "superposition" to find the sum of several kinds of higher-order arithmetic progression.
1274, Yang Hui of the Song Dynasty in China published the book "The Origin and End of Multiplication and Division", which described the agile method of "Jiugui" and introduced various calculation methods of multiplication and division.
1280, the yuan dynasty "calendar" compiled the sun and moon azimuth table (China, Wang Xun, Guo Shoujing, etc. ) By appealing for differences.
/kloc-Before the middle of 0/4th century, China began to use abacus.
1303, Siyuan Jade Mirror, written by Zhu Shijie in China in Yuan Dynasty, was three volumes, which promoted Tianyuan Art to Siyuan Art..
1464, J. Miller of Germany systematically summarized trigonometry in On Various Triangles (published in 1533).
1494, Pachouri published Arithmetic Integral, which reflected people's understanding of arithmetic, algebra and trigonometry at that time.
1545, Italians cardano and Fernow published the general algebraic solution formula of cubic equation in Dafa.
From 1550 to 1572, Bombelli published Algebra, which introduced imaginary numbers and completely solved the algebraic problem of cubic equations.
Around 159 1 year, the Vedas in Germany used letters to represent the general symbols of numerical coefficients for the first time in Wonderful Algebra, which promoted the general discussion of algebraic problems.
1596 ~ 16 13 years, Otto and Pittis kus completed the hexadecimal tables of six trigonometric functions at intervals of 10 second.
16 14 years, Naipur in England formulated the logarithm.
16 15 years, Kepler, Germany, published "solid geometry of wine barrels", and studied the rotating volume of conical curves.
1635, cavalieri, an Italian, published The Geometry of Essential Continuum, which avoided infinitesimal and expressed the simple form of calculus in the form of no branches.
1637, Descartes published Geometry, put forward analytic geometry, and introduced variables into mathematics, which became a "turning point in mathematics".
1638, Fermat in France began to solve minimax problems by differential method.
1638, Galileo of Italy published "On the Mathematical Proof of Two New Sciences", studied the relationship between distance, velocity and acceleration, and put forward the concept of infinite set. This book is regarded as an important scientific achievement of Galileo.
1639, De Shag of France published the draft of "Trying to study what happens at the intersection of a cone and a plane", which is an early work of modern projective geometry.
164 1 year, Pascal of France discovered Pascal's theorem about the hexagon inscribed in a cone.
1649, Pascal of France made Pascal calculator, which is the pioneer of modern computer.
1654, Pascal and Fermat in France studied the basis of probability theory.
1655, Varis published arithmetica infinitorum, which extended algebra to analysis for the first time.
In 1657, Huygens of the Netherlands published an early paper on probability theory, on calculus of probability games.
1658, Pascal of France published "General Theory of Cycloids", which made a full study of "Cycloids".
In 1665 ~ 1676, Newton (1665 ~ 1666) lived in Leibniz (1673 ~ 1676) and Leibniz (/).
1669, Newton and Raphson in Britain invented Newton-Raphson method for solving nonlinear equations.
1670, Fermat of France put forward Fermat's last theorem.
1673, Huygens in the Netherlands published an oscillating clock, in which the evolute line and the evolute line of a plane curve were studied.
1684, Leibniz, Germany, published a book about differential method, which is a new method for finding minimax and tangents.
1686, Leibniz, Germany, published a book about integration methods.
169 1 year, Jean Bernoulli of Switzerland published Elementary Differential Calculus, which promoted the application and research of calculus in physics and mechanics.
1696, Robida of France invented the "Robida Rule" for finding the limit of infinitives.
1697, johann bernoulli solved some variational problems and discovered the steepest descent line and geodesic line.
1704, Newton published the counting of cubic curves, and used infinite series and flow number method to find the area and length of curves.
17 1 1 year, Newton published "Analysis of Using Series and Flow Number". .
17 13, Jaya Bernoulli of Switzerland published the first book on probability theory, Guess.
17 15 years, Boo Taylor of Britain published the incremental method, etc.
173 1 year, a Frenchman, Crelo, published The Study of Double Curvature Curves, which was the first attempt to study spatial analytic geometry and differential geometry.
1733, the normal probability curve was discovered by De Le Havel in Britain.
1734, British Becker published "Analytical Scholars" with the subtitle "To Mathematicians who don't believe in God", attacking Newton's flow method and causing the so-called second mathematical crisis.
1736, Newton published the method of flow number and infinite series.
1736, Euler of Switzerland published the Theory of Mechanics or Analytic Description of Motion, which is the first work to develop Newton's particle dynamics by analytical method.
1742, maclaurin of Britain introduced the power series expansion method of functions.
1744, Euler of Switzerland deduced Euler equation of variational method and found some minimal surfaces.
1747, French D'Alembert and others initiated the theory of partial differential equations from the study of string vibration.
From 65438 to 0748, Euler of Switzerland published the Outline of Infinite Analysis, which is one of Euler's major works.
From 1755 to 1774, Euler of Switzerland published three volumes of differential and integral. This book includes the theory of differential equations and some special functions.
From 1760 to 176 1, Lagrange of France systematically studied the variational method and its application in mechanics.
1767, Lagrange of France discovered the method of separating the real roots of algebraic equations and the method of finding their approximate values.
1770 ~ 177 1 year, Lagrange of France used permutation groups to solve algebraic equations, which was the beginning of group theory.
1772, Lagrange of France gave the initial special solution of three-body.
1788, Lagrange of France published Analytical Mechanics, which applied the newly developed analytical methods to the mechanics of particles and rigid bodies.
1794, Legendre, France published a widely circulated elementary geometry textbook "Geometry Outline".
1794, Gauss of Germany studied the measurement error and put forward the least square method, which was published in 1809.
1797, Lagrange of France published analytic function theory, and established differential calculus without limit concept by algebraic method.
1799, French gaspard monge founded descriptive geometry, which has been widely used in engineering technology.
1799, Gauss of Germany proved a basic theorem of algebra: algebraic equations with real coefficients must have roots.
Differential equation: generated roughly at the same time as calculus. In fact, finding the original function of y ′ = f (x) is the simplest differential equation. I Newton himself has solved the two-body problem: the motion of a single planet under the gravity of the sun. He idealized two objects as particles and got three second-order equations with three unknown functions, which were proved to be plane problems by simple calculation, that is, two second-order differential equations with two unknown functions. With the method now called "first integration", the problem of solving it is completely solved. /kloc-the elastic problem was put forward in the 0/7th century, and the catenary equation, vibrating string equation and so on were derived. In a word, many problems in mechanics, astronomy, geometry and other fields have led to differential equations. Now even many social science problems will lead to differential equations, such as population development model and traffic flow model. Therefore, the study of differential equations is closely related to human society. At first, mathematicians focused on finding the general solution of differential equations, but it proved to be generally impossible, so they gradually gave up this extravagant hope and turned to find definite solutions: initial value problems, boundary value problems, mixed problems and so on. But even for the first-order ordinary differential equation, the elementary solution (integral form) is proved impossible, so we turn to quantitative method (numerical calculation) and qualitative method to solve the theoretical problems such as the existence and uniqueness of the solution first.
Equations are familiar to those who have studied middle school mathematics; There are various equations in elementary mathematics, such as linear equation, quadratic equation, higher order equation, exponential equation, logarithmic equation, trigonometric equation, equation and so on. These equations are to find out the relationship between the known number and the unknown number in the studied problem, list one or more equations containing one unknown number or several unknown numbers, and then find out the solutions of the equations.
However, in practical work, there are often some problems that are completely different from the above equations. For example, if a substance moves and changes under certain conditions, it is necessary to seek the law of its movement and change; When an object falls freely under the action of gravity, it is necessary to seek the law that the falling distance changes with time; When a rocket flies in space driven by an engine, it needs to seek its flight orbit, and so on.
Mathematically, the motion of matter and its changing law are described by functional relations, so this kind of problem is to find one or several unknown functions that meet certain conditions. In other words, all these problems are not simply to find one or several fixed values, but to find one or several unknown functions.
The basic idea of solving this kind of problems is very similar to that of solving equations in elementary mathematics. It is also to find out the relationship between known function and unknown function in the studied problem, and get the expression of unknown function from one or several listed equations containing unknown function. But it is different from the solution equation in elementary mathematics in many aspects, such as the form of the equation, the specific method of solving it, the nature of the solution and so on.
Mathematically, solving such equations requires knowledge of differential and derivative. Therefore, any equation that represents the relationship between the derivative and the independent variable of an unknown function is called a differential equation.
Differential equations are generated almost simultaneously with calculus. When Scottish mathematician Naipur founded logarithm, he discussed the approximate solution of differential equation. Newton used series to solve simple differential equations when establishing calculus. Later, Swiss mathematician Jacob? 6? 1 Bernoulli, Euler, French mathematicians Crelo, D'Alembert, Lagrange and others continue to study and enrich the theory of differential equations.
The formation and development of ordinary differential equations are closely related to the development of science and technology such as mechanics, astronomy and physics. The new development of other branches of mathematics, such as complex variable function, Lie group and combinatorial topology, has a far-reaching impact on the development of ordinary differential equations, and the current development of computers provides a very powerful tool for the application and theoretical research of ordinary differential equations.
When Newton studied celestial mechanics and mechanical mechanics, he used the tool of differential equation to get the law of planetary motion in theory. Later, French astronomer Le Verrier and British astronomer Adams used differential equations to calculate the position of Neptune, which had not been discovered at that time. All these make mathematicians more convinced of the great power of differential equations in understanding and transforming nature.
When the theory of differential equation is gradually improved, it can accurately express the basic laws of things' changes. As long as the corresponding differential equations are listed, there is a way to understand them. Differential equations have become the most important branch of mathematics.