HOME 学部前期課程 全学自由研究ゼミナール（PEAK）Mathematics II②(PEAK)

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# 全学自由研究ゼミナール（PEAK）Mathematics II②(PEAK)

Introductory course in linear algebra, continued
Phenomena in natural and social sciences are usually complicated, and seldom described by linear equations. However, Linear Algebra is still powerful and effective in describing essential parts of the phenomena by linear approximation. Thus Linear Algebra has vast applications.

Linear Algebra will further provide basics for considering linear spaces that appear in quantum mechanics or Fourier analysis. The ideas in Linear Algebra are broadly utilized in sciences and engineering, including agriculture, medicine, and economy, as well as in mathematics and physics.

Although Linear Algebra is simple and clear in theory, one needs to be familiar with abstract concepts in mathematics to properly deal with it in practice. It is important for students to keep on deepening their understanding by working with exercise and related problems.

コース名

30737
CAS-TC1200S1

S1 S2

2

NO

The topics listed below will be covered in the course. The items 1-4 and their applications will be treated in Mathematics II (1) in 2022 A semester and 5-10 in Mathematics II (2) in 2023 S semester. The latter will be heavily based on the the former. 1. Geometry of plane and space 2. Matrices and linear maps 3. Systems of linear equations 4. Bases of linear spaces 5. Change of bases 6. Inner products and orthogonality 7. Signature of quadratic forms 8. Determinants of square matrices 9. Eigenvalues and eigenvectors 10. Jordan form of square matrices The classes will be conducted for 105 minutes.

Lectures by blackboard and projector.

この科目は、PEAK理科生向けの英語による線型代数学の講義「数学II(PEAK)」に参加して、英語で線型代数を学ぶというものです。 通年の授業内容の前半部分をAセメスターで扱い、後半部分は引き続くSセメスターで扱います。 後半部分に相当する本科目の授業は、前半部分の授業内容を前提として行いますので、Aセメスターに開講される前半部分を先に履修することを薦めます。