Shanghai Jiao Tong University, formerly known as Nan Yang Public School, was founded in 1896. Ever since the recruitment of the first class of students in April 1898, mathematics courses have been offered at SJTU. The Department of Mathematics was established in 1928. Since its establishment, the department has made important contributions to modern mathematics in China. The first annual meeting of the Chinese Mathematical Society was held at SJTU. In 1952, among the nationwide reconstruction of universities, most faculty and students from SJTU were relocated to either Fudan University or East China Normal University. In 1956, most part of SJTU moved w...
Functional Analysis is the core course for the modern analysis. It is about the analysis on infinitely dimensional linear spaces. It is natural continuation for both mathematical analysis and linear algebra. Functional analysis plays an important role in the study for the partial differential equations and mathematical foundation for quantum mechanics.
Mathematical analysis, in which ideas and skills are diversified and plentiful, is a fundamental course of modern mathematical science. It is one of the most comprehensively used subjects in science and technology. Mathematical analysis is an indispensable basic course for any student who majors in science and engineering.
The main content of mathematical analysis is divide...
Calculus is one of the greatest achievements of the human intellect. Calculus is the foundation of modern mathematics and almost all other branches of modern science.
Inspired by problems in astronomy, Newton and Leibniz developed the ideas of calculus three hundred years ago. Since then, each century has demonstrated the power of calculus to illuminate questions in mathema...
The course is introduction to the theory of Fourier series and transform as well as to the theory of Lebesque integration. Fundamental ideas and rigorous proof will be presented. Topics of the course to be covered include Fourier series, their convergence and applications, Poisson kernel, Cesaro and Abel summability, Plancherel formula, Poisson summation formula, measures, meas...
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