This course is designed to learn how to solve real problems using mathematical knowledge, scientific computing methods, mathematics modeling tools, and modern computers. Practical applications and mathematical modeling will be emphasized throughout the entire course.

"Scientific Computing and Mathematical Modeling" is a fundamental course designed for all science and engineering majors in Central South University, with 64 credit hours and 4 credits.

Mathematical modeling ideas and methods will be introduced with balanced discussion of the related theory and scientific computing in this course.

This is a new course designed for learning new materials in mathematical modeling, scientific computing as well as research explorations in practical problem-solving process with applications. The teaching materials cover mathematical modeling skills, numerical analysis and scientific computing. We will start from some problems in daily life to explain how to establish mathematical models step by step; followed by theoretical analysis of the models and analysis; analytic solution techniques if available; numerical methods and justifications; validation of numerical results, and feedback for improving the models.

The course topics include: introduction of mathematical modeling and scientific computing and their connections with traditional mathematics; computer number system and error analysis, polynomial and other interpolation and fitting methods, numerical integration, equation solving techniques, AHP modeling, comprehensive evaluation, time series analysis, statistical analysis and prediction methods, and a number of case studies, etc.

Emphasis of the "Scientific Computing and Mathematical Modeling" course curriculum include practical applications; students interests orientated; class learning and experimental activities; campus learning and extracurricular practicing; group study and independent learning abilities.  Instructors of the course will take full consideration of students’ backgrounds and their particularly needs and adjust course materials accordingly.

One of the important goals of the course teaching is to improve students' ability to apply mathematical knowledge to solve practical problems, comprehensively train students to use mathematical tools to build mathematical models, and apply scientific calculation methods to solve practical problems. The scientific computing ability, mathematical modeling ability and scientific research paper writing ability, cultivate the ability to engage in modern scientific research activities and related qualities.

Calculus

Linear algebra

Textbook:

Zheng Zhoushun, Zhang Hongyan, etc., Scientific Computing and Mathematical Modeling, Shanghai: Fudan University Press, 2011

Jiang Qiyuan, Xie Jinxing, Ye Jun. Mathematical Model (Third Edition), Beijing: Tsinghua University Press, 2007

Li Qingyang, Wang Nengchao, Yi Dayi. Numerical Analysis, Beijing: Tsinghua University Press, 2008