Contact Information

Yantong XIE, Ph.D. candidate

School of Mathematical Science, Peking Univertsity

No. 5 Yiheyuan Road Haidian District, Beijing, P.R.China 100871

Office Location: Room 84106, Building JIAYIBING, Peking University

Email:darkoxie at pku dot edu dot cn

Breif CV

Education

Middle school, 2009-2015, at the Experimental High School Attached to Beijing Normal University

B.S. in Computational Mathematics, 2015-2019, at Peking University.

Ph.D. candidate in Mathematics, 2019-NOW, at Peking University. Advisor: Prof. Zhennan ZHOU.

Research interest

Semiclassical Schrödinger Equations: Analysis and computations

Computaional problems arised in quantum mechanics or condensed matter physics

Computation of Leak-and-fire model in neuroscience

Research Papers

2021

Y Xie, Z Zhou, Frozen Gaussian Sampling: A Mesh-free Monte Carlo Method For Approximating Semiclassical Schrödinger Equations, preprint.

2020

J-G Liu, Z Wang, Y Xie, Y Zhang, Z Zhou, Investigating the integrate and fire model as the limit of a random discharge model: a stochastic analysis perspective, published on Mathematical Neuroscience and Applications (MNA).

2019

J Hu, J-G Liu, Y Xie, Z Zhou, A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: numerical analysis and exploration, published on JCP.

Notes

Advanced Mathematics B, Volume 1 (高等数学B1)

Thanks for choosing my Advanced Mathematics lecture notes. If you want to read my notes, make sure you have read this. If you perfer learning advanced mathematics from a more modern perspective, these notes may also be a good choice.

Lecture 1: Preparation(预备知识)

Lecture 2: Sequence limit theory(序列极限)

Lecture 3: Function limit theory(函数极限)

Lecture 4: Continuous functions(连续函数)

Lecture 5: Derivative and differential(导数)

Lecture 6: Indefinite integral(不定积分)

Lecture 7: Definite integral(定积分)

Lecture 8: Differential mean value theorem(微分中值定理)

Lecture 9: L'Hospital's rule and Taylor's expansion(洛必达法则和泰勒公式)

Lecture 10: Advanced topics in derivative(函数性质和作图)

Lecture 11: Analytic geometry (解析几何)

Lecture 12: Multivariable differential calculus(多元函数微分学)

Lecture 13: Advanced topics in multivariable differential calculus(多元函数微分学的应用)

Advanced Mathematics B, Volume 2 (高等数学B2)

Lecture 1: Review

Lecture 2: Double integral(二重积分)

Lecture 3: Triple integral(三重积分)

Lecture 4: Advanced topics in multiple integral (重积分的应用)

Lecture 5: Curvilinear integral(曲线积分)

Lecture 6: Surface integral(曲面积分)

Lecture 7: Solutions to ODE(常微分方程的解法)

Lecture 8: Advanced topics in ODE(常微分方程一般理论)

Lecture 9: Sequence series(数项级数)

Lecture 10: Function series(函数项级数)

Lecture 11: Power series (幂级数)

Lecture 12: Improper integral(无穷积分和瑕积分)

Lecture 13: Integrals with parameters(含参变量积分)

Lecture 14: Fourier series(傅里叶级数)

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