Doctor of Philosophy in Mathematics - Partial Differential Equations
加州大学圣塔芭芭拉分校
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国际学生入学条件
To be considered for admission to UCSB, applicants must have received a bachelor's degree or its equivalent (with a cumulative grade point average of 3.0 or better) from an accredited university prior to the quarter for which admission is sought.
completed an undergraduate or graduate degree at an institution whose primary language of instruction is English. The minimum score for consideration is 550 when taking the paper-based TOEFL, or 80 when taking the internet-based test, some departments require a higher score. Applicants must make arrangements to take the TOEFL directly with ETS (www.ets.org). Scores should be reported to UCSB using institution code 4835. TOEFL scores must be no more than two years old at the time of application submission. UCSB also considers a minimal score of 7 on the IELTS as an alternative to the TOEFL. IELTS scores must be no more than two years old at the time of application submission
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雅思考试总分
7.0
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- 雅思总分:7
- 托福网考总分:80
- 托福笔试总分:550
- 其他语言考试:NA
课程简介
Our understanding of the fundamental processes of the natural word is based to a large extent on partial differential equations (PDE). For example, the Einstein equations describe the geometry of space-time and its interaction with matter. The dynamics of fluids and elastic solids are governed by partial differential equations that go back to Euler and Cauchy. Electro-magnetic waves including the propagation of light in various media are modeled by Maxwell's equations. More recently, PDE's are gaining importance in the social and life sciences. The Black-Sholes PDE underpins the theory of option pricing in financial mathematics. Reaction-diffusion models are used in neurophysics and population dynamics.<br><br>The analysis of PDE's has given rise to new mathematical ideas. For example, the study of the equation thermal diffusion lead to the discovery of Fourier series and ultimately the field of Fourier analysis. Hilbert's investigations into eigenvalue problems arising in the PDE's for vibrating strings and Schrodinger's equation in quantum mechanics evolved into to modern theory of functional analysis and operator theory.
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