Advanced Mathematics

What Students Learn

Building on single-variable calculus, this course studies relationships involving multiple variables. Vectors and three-dimensional geometry describe space, while partial derivatives and multiple integrals extend the analysis of change and accumulation. Vector fields develop spatial thinking and mathematical modeling.

Learning Focus

1. Vectors and spatial geometry: objects and motion in space

2. Multivariable functions and differentiation: partial derivatives and optimization

3. Multiple integration: changes of variables and spatial accumulation

4. Vector calculus: line and surface integrals and integral theorems

Learning Outcomes

Students represent spatial problems mathematically, select appropriate differentiation or integration methods, and explain the geometrical and practical meaning of results. The course develops analytical foundations for university mathematics and related science and engineering study.