Ask for a short essay on the application of calculus (two thousand words is enough) and a short essay on advanced mathematics.
What is calculus? It is a mathematical idea, in which' infinite subdivision' is differential and' infinite summation' is integral. Infinity is the limit, and the thought of limit is the basis of calculus, that is, to look at problems with a moving thought. For example, the instantaneous speed of a bullet flying out of a gun bore is the concept of differentiation, and the sum of the distances traveled by a bullet at each instant is the concept of integration.
If the whole mathematics is compared to a big tree, then elementary mathematics is the root of the tree, each branch of mathematics is the branch, and the main part of the trunk is calculus. Calculus is one of the greatest achievements of human wisdom. Since the17th century, with the progress of society and the development of productivity, as well as many problems to be solved in navigation, astronomy and mine construction, mathematics has also begun to study the quantity of change, and mathematics has entered the era of "variable mathematics", that is, calculus has been continuously improved and become a discipline. In the whole17th century, dozens of scientists did pioneering research for the creation of calculus, but it was Newton and Leibniz who made calculus an important branch of mathematics.
Calculus became a subject in17th century, but the idea of differential and integral existed in ancient times. In the 3rd century BC, Archimedes (287-2 12 BC), an ancient Greek mathematician and mechanic, had already contained the seeds of calculus in his works such as Measurement of Circle and On Spheres and Cylinders. When he studied and solved the problems of arcuate area under parabola, area under spiral and volume of hyperbola of revolution, he implied the idea of modern integration. As the basic limit theory of calculus, it was discussed in great detail as early as ancient China. For example, in the book "Zhuangzi" written by Zhuang Zhou, "One foot of space is inexhaustible." During the Three Kingdoms period, Liu Hui proposed in "Cutting Circle" that "if you cut it carefully, the damage will be small. If you can't cut it, you will be encircled and have nothing to lose". In his book 16 15, The New Science of Measuring the Volume of Barrels, he regarded the curve as a straight line with infinitely increasing sides. The area of a circle is the sum of the areas of an infinite number of triangles, which is a masterpiece of typical limit thought. Cavalieri, an Italian mathematician, published The Geometry of Continuity in 1635, and regarded the curve as an infinite number of line segments (indispensable). All these made ideological preparations for the birth of calculus later.
/kloc-the development of productivity in the 0/7th century promoted the development of natural science and technology. Not only the existing mathematical achievements have been further consolidated, enriched and expanded, but also because of the need of practice, we began to study the moving objects and the changing quantity, thus obtaining the concept of variables and studying the generality of the changing quantity and its dependence. /kloc-in the second half of the 7th century, isaac newton (1642- 1727), a great British mathematician and physicist, studied calculus from the perspective of physics on the basis of creative research by predecessors. In order to solve the problem of motion, he created a mathematical theory directly related to physical concepts, which Newton called "flow counting", but it was actually. Newton's main works on "flow counting" include "Finding the area of a curved polygon", "Calculation method using infinite polynomial equation" and "Flow counting and infinite pole number". These concepts are mathematical reflections of mechanical concepts. Newton thought that any movement exists in space and depends on time, so he took time as an independent variable and time-related solid variables as a flow. Not only that, he also regarded geometric figures-lines, angles and shapes-as the result of mechanical displacement. Therefore, all variables are flow.
Newton pointed out that "flow counting" basically includes three types of problems.
(l) "Knowing the relationship between streams and finding the relationship between them" is equivalent to differential calculus.
(2) Know the equation representing the relationship between streams and find the relationship between corresponding streams. This is equivalent to integral calculus. Newton integral method includes not only solving the original function, but also solving the differential equation.
(3) The application scope of "flow number technology" includes calculating the maximum and minimum values of curves, finding the tangent and curvature of curves, finding the length of curves and calculating the area of curved edges.
Newton has fully realized that the operations in the above two kinds of problems (1) and (2) are reciprocal operations, so he established the connection between differential calculus and integral calculus.
Newton mentioned "flow counting" in a manuscript on May 20, 1665, so some people took this day as the symbol of the birth of calculus.
Leibniz made calculus more concise and accurate.
German mathematician Leibniz (G.W. Leibniz1646-1716) discovered calculus independently from geometry. Before Newton and Leibniz, who made pioneering contributions to the birth of calculus, at least dozens of mathematicians had studied calculus. However, our work is fragmented, incoherent and lacks unity. Leibniz's way and method of establishing calculus are different from Newton's. Leibniz introduced the concept of calculus by studying the tangent of the curve and the area surrounded by the curve, and got the algorithm. Newton combined kinematics more in the application of calculus, and his attainments were better than Leibniz's, but Leibniz's expression was far better than Newton's, which not only revealed the essence of calculus concisely and accurately, but also effectively promoted the development of higher mathematics.
The symbols of calculus created by Leibniz promoted the development of calculus, just as Indo-Arabic numerals promoted the development of arithmetic and algebra. Leibniz is one of the most outstanding symbol creators in the history of mathematics.
Newton's differential and integral symbols are not used now, while Leibniz's symbols are still used today. Leibniz realized earlier and more clearly than others that good symbols can greatly save thinking labor, and the skill of using symbols is one of the keys to the success of mathematics.
Ask for a paper (two thousand words) about describing personal growth report. Time flies like a breeze. It only leaves the calm and temperature after the wind blows. The same is true of time, which leaves only the slightest change in life. One minute it's like this, the next it's like that. What is left is the memory of the last second, and the bits and pieces of this second. Some people have calculated that we have lived for more than 7000 days now. If we count by seconds, then the time we live now will be a big number. But every second we gain something, learn something and let go. This is a question worthy of our consideration. Make your life more fulfilling, instead of leaving regrets. There were our scarred memories and happy days in the past, and scenes kept floating in our minds like movies. Looking back, I want to stay in that second forever, but I want to ignore that paragraph forever. Looking back on myself in the past, let me know myself again and know myself more clearly. In order to better realize the value of life, we must calmly analyze ourselves. Review the past, regain self-confidence and look forward to the future. Believe that my future is not a dream. My future is not a dream, because I believe that my destiny is in my own hands. Only those who don't control themselves will be at the mercy of others and complain about the injustice of heaven. So I want to be a person who controls my own destiny, not someone who is manipulated by others. I believe in myself. Be a strong and persistent person. Be firm in thinking, be interested in music and have a person's determination. A person's life may burn or rot. I can't rot, I want to burn! -osterloff I don't want to rot all my life, so I don't treat myself badly if I do well. Let's go Learn to talk by babbling, learn to walk by stumbling, wear shoes seriously, and read. Those dribs and drabs of growth records have long been fragmented and even forgotten in my mind. But they are a chapter in my life experience book. It enriches my life. It is my seasoning, which makes my life bittersweet. I was a shy girl in primary school. I don't like playing with strangers I don't know why, I'm always afraid of strangers. But I am also a girl who loves to play. Is a person with dual personality. Sometimes it is unpredictable. Parents sometimes feel strange. When I was a child, I was a person who didn't like learning. In my own eyes, I only think that playing is the first, and I only know the fun of playing. Always leave your studies behind. Rest only when you are tired of playing. My parents are worried that I don't like reading. Always trying to trap my playful heart. But all the tricks are useless to me. When I was a child, I liked playing with planes and cars. I always take these things apart to assemble my favorite molds. I like playing many games, but I have nothing I am good at. Time passed slowly, and my mother suddenly became pregnant and told me that I had a sister. My heart sank at that time. I am afraid that my parents will not give me their love, but give it to my sister, or they will share it with my sister. How reluctant I was at that time. I cried. My parents have always advised me that my sister can always accompany you, and my parents' love will not decrease, and they will always love me. I was persuaded by them. Finally my sister was born. My sister is really cute. I found that I really like her. Gradually, I also found that the burden on my shoulders is getting heavier and heavier, because my parents' work has become much better and their work pressure has become greater. I slowly found that I couldn't play by myself and learned to take care of my sister. A few years later, my sister grew up, and I also grew up from an ignorant primary school student to a junior high school student. I gradually learned a lot and grew a lot. At the same time, my ambition gradually sprouted, and I began to study hard. I found that I like to express myself among teachers and classmates. I have always been very concerned about what teachers and classmates think of me. I always try my best in everything, so that my classmates and teachers can affirm me. However, sometimes I can't do it. I always want to do my best, but I can't do it well. I'm always depressed. But I stood up and wiped my sweat. Like a persistent cow, go forward bravely. But those setbacks always make me unhappy. Always feel regret and loss, just like falling into a deep underestimation and collapsing. I remember a parent-teacher meeting after a monthly exam, which I failed. Recalling my mother's hard work every day, I am so tired every day. My heart is sour from time to time and I secretly shed tears. I know it's no use crying. But when I see my mother, I think she works so hard every day. Also for * * *, a lot of hair turned white. Sometimes I ask myself why I worked so hard to get this result. I comfort myself by constantly smoothing myself. Hard work may not succeed, but I will never succeed without hard work. Even if I am rejected, I will continue to work hard and encourage myself. I believe that my destiny is in my own hands, and my future is not a dream. Be a strong and persistent person. I am the best, and I will succeed. I will always believe this. Stones look at mountains, people look at trees and objects, and stones open. Who can resist? Those who aspire to it are also pillars of fame. Climbing the mountain does not stop at difficulties and obstacles, but will reach the high mountain. I must make up my mind and enjoy life. After graduating from junior high school, I can't compete with my parents. After entering high school life, everything changed. The pace of reading suddenly became so fast. I always can't keep up with the teacher's rhythm, constantly explore my own learning methods, and finally have some results. The teacher is also very instructive, so I have been working hard. Strict with herself, she always goes all out to the tasks assigned by the teacher, but some still can't get the results she imagined. My classmates said I was too demanding. Maybe. The responsibility of class cadres is much heavier, and they constantly explore how to enhance the cohesion of the class. It is always not enough to rely on your own efforts, so it is very important to find the cohesion of the class. While managing the class, I also study hard. I think learning is still the primary position, after all, the most important battlefield for the college entrance examination. But the college entrance examination is still quite disappointing. I am annoyed that I don't have ideal grades, and I can't figure out why fate should treat me like this. I don't understand or understand why what I get is always unsatisfactory. What my future will be like. But some words from the teacher made me feel relieved. No matter how bad the environment is, as long as my heart of persistence and never giving up is still there, no matter what setbacks I experience, it will not hinder my progress. No matter how bad the environment is, I can break out of my own sky. Now I am a college student. Maybe I'm not mature yet, but after years of exercise, I believe I can have my own day. Because I always believe that fate is in my own hands, and my future is not a dream. My college life has just begun, and I believe I still have a long way to go. Maybe there will be more unexpected setbacks and many accidents waiting for me, so I will meet them with the best attitude. Being clear about one's big goals in life has a direct promoting effect on grasping them. Carefully plan every step of life. There is a saying: "everything is established in advance, and it will be abolished if it is not planned", which is true. Without any preparation for what you have done or will do, you are preparing for failure. Only by fully understanding yourself can we face life better. My class has a good mass base, strong communication skills, cheerful and lively personality and good organizational skills. Be patient and be good at observing things around you. My character is honest, upright and modest, but there is no lack of arrogance. I am conscientious, diligent and responsible. Be good at listening to other people's opinions. And other people's troubles, is a good listener. Have a strong thirst for knowledge, do things seriously and responsibly, have a strong ability to adapt to the environment from beginning to end, have a wide range of interests and can do a lot of things, but there are still many places to be improved. Strengthen communication with others, increase your social scope, and actively participate in various beneficial activities on various occasions to make yourself more confident and excited, and less silent and stage fright. People have more friends and more experiences. Sometimes it depends on the occasion. If you want to speak loudly, you should speak loudly, but sometimes you shouldn't speak loudly. You should strictly control your behavior and be self-disciplined. Strengthen exercise and strengthen physical fitness. I have great prospects for my study and future. Studied hard in high school and entered the university. My learning energy still exists. I study hard and master professional skills. At the same time, looking at the economy and culture of various countries is conducive to laying a solid foundation for future study. Seriously complete the tasks assigned by the teacher. After serving as a scientific research committee member, I finished my research seriously. I hope I can get the desired results through my own efforts. I actively participate in extracurricular activities, various activities organized by classes, student union competitions, and join clubs to broaden my social scope. At the same time, read some famous books and magazines, broaden your horizons and improve your outlook on life, world outlook and values. Become a citizen with four possessions and an outstanding contemporary college student. I will constantly improve myself, change myself, enrich myself, enrich my life, correct my shortcomings and improve my advantages. Make yourself more confident, confident and persistent. Improve your outlook on life, world outlook and values. Constantly exercise yourself and improve yourself. Don't waste yourself, don't waste your life, believe that fate is in your own hands, and believe that the future is not a dream. School is only an external factor, and it depends on yourself to really do a good job in your major, doesn't it? You make your own life, you can't complain, you can't complain. Only with your heart and your faith can you change your destiny. I think our school is quite good, the teachers are excellent, and there are many excellent students who can learn from each other and guide each other. The scenery is beautiful. Very pleasant. This is a good learning environment. In college, I still have to study hard, acquire solid knowledge and lay a solid foundation for my future work, because I know that the journey to find a job will be very difficult in the future, so I should pay close attention to charging myself now to avoid hitting a wall in the future. Looking back on my past, I regain my confidence. I believe that my destiny is in my own hands. Quote osterloff's words; A person's life may burn or rot, I can't rot, I am willing to burn! I believe that after four years of college baptism, I will become more confident and I will face every setback I face with the most beautiful smile. Confidence is my most powerful shield. Please, my future is not a dream.
How to write a graduation thesis on microbial inspection of dairy products? Ask god for help