科技英语---数学篇(全英版)

key word
• • • • • • • • evolution n. v.进化；演化；发展 Euclidean geometry n.欧几里德几何 trigonometry n.三角学 Pythagorean theorem n.勾股定理 Counting Rod n.算筹 prehistoric adj. 史前的；陈旧的 arithmetic n. 算术，算法 astronomy n.天文学
• Discrete-time Fourier transform • Discrete Fourier transform is the special case of discrete-time Fourier transform (DTFT) (sometimes referred to as the latter’s approximate). DTFT discrete in the time domain, cycle in the frequency domain. DTFT can be viewed as the inverse transformation of the Fourier series.
Applications of Fourier transform • Fourier transform in physics, acoustics, optics, structural dynamics, quantum mechanics, number theory, combinatorics, probability theory, statistics, signal processing, cryptography, oceanography, communications, finance and other fields have a wide range of applications. For example, in signal processing, the typical use of the Fourier transform is decomposing a signal into an amplitude component and a frequency component. • We spend a semester studying signals and systems, most of them are around the Fourier series expansion
Different variants of the Fourier transform
.Continuous-time Fourier transform .In general, if the "Fourier Transform" does not add any qualifiers, means the "Continuous Fourier Transform" (the Fourier transform of a continuous function). Continuous Fourier transform of square integrable functions f (t) is expressed as integral or series form of complex exponential function.
Basic properties • linearity
• Time-shifting • differential relationship
• The Convolution Property • Parseval's theorem
• linearity
• The Fourier transform of the sum of the two function is equal to the respective transform • If x(t) X(jw)
• Fourier series
• Continuous form of the Fourier transform is actually the Fourier series (Fourier series) promotion, because integration is actually an extreme form of summation operator only. For periodic function, its Fourier series is existed.
y(t) Y(jw) ax(t)+by(t） aX(jw)+ bY(jw)
The relationship in the Fourier transfomation
Conversion Continuous Fourier transform Fourier series Discrete-time Fourier transform Discrete Fourier transform time Continuous, non-periodic Continuous,periodic Discrete,non-periodic Discrete,periodic frequency Continuous, nonperiodic Discrete,non-periodic Continuous,periodic Discrete,periodic
• In ancient times, the main reason of studying Mathematics calculations is to study astronomy, the rational allocation of land crops, the tax and trade. Mathematics is fromed to understand the relationship between numbers, to measure land and to predict astronomical events . These needs can be simply summarized as the study of Mathematics , about structure, spatial and temporal aspects. • In 17th century Europe produced variable concepts. Therefore, people began to study mutual relations of the changing quantity and graphic.In the process of establishing classical mechanics, calculus method combines precision geometric ideas were invented. With the further development of natural science and technology, in areas such as set theory and mathematical l百度文库gic began to slowly develop.
science.
• For example,researching space derives from the Euclidean geometry. Trigonometry is a combination of space and number, and contains a very famous Pythagorean theorem.
Mathematical history
• About the evolution of mathematical can be seen as abstraction sustainable development, or extension theme. • The Eastern and Western cultures also used a different perspective. European civilization developed geometry, while China developed arithmetic. • The first abstracted concept is probably the number (China's Counting Rod). Between two apples and two oranges have the same perception .It's a kind of a major breakthrough in human thought. • In addition to aware to how to count the number of actual objects, prehistoric humans also learn how to count the number of abstract concepts such as days, seasons and years. Arithmetic (addition, subtraction) are naturally produced.
Famous mathematician and theorems
Fourier transform What is Fourier transform
• Fourier transform is a linear integral transformation, often used when the signal between the time domain (or spatial) and frequency domain transform, there are many applications in physics and engineering. Because the basic idea first proposed by the French scholar systematically Joseph Fourier, so named in its honor.Fourier transform is derived from the study of Fourier series. In the study of the Fourier series, Complex periodic function can be expressed as the sum of a series of simple sine and cosine wave. Fourier transform is a expansion of Fourier series, the periodic of a function represented by it tends to infinity.
Unit
1
Mathematics
Panel members：Tang Manling 通信1204 Zhang Yan 电子1203 Luo Jialiang 光信 Luo Xiuhua 2014.9.15
Contents
• Mathematics abstract
• Mathematical history • Famous mathematician and
theorems
Mathematics abstract
• Mathematics is the study of the concept of quantity, structure and space as well as a discipline, in some ways is a form of