OSAKA UNIV. CBCMP

OSAKA UNIVERSITY CHEMISTRY - BIOLOGY COMBINED MAJOR PROGRAM

Mathematics 3

Outline

In this class, the students will learn the basic concept on linear algebra

and techniques on matrices and their applications. We learn basic operations

on matrices, computation of determinants and inverse matrices, Gaussian

elimination, the reduced echelon forms, eigenvalue problems, diagonalization,

matrix rank and independence of vectors. Further, computation of matrix power,

the way to solve a linear recurrences and ordinary linear differential equations

will also be covered.

 

1. Operations on Matrices
2. Determinants and Minors
3. Elementary operations on matrices
4. Rank and Nullity
5. Formulas in geometry involving determinants
6. Linear systems
7. Geometry of Linear maps
8. Span and linear independence
9. Basis and Dimension
10. Eigenvalues and Eigenvectors 1
11. Eigenvalues and Eigenvectors 2
12. Exercise Session
13. Diagonalization of Matrix
14. Applications of Diagonalization
15. Abstract linear spaces

Textbook

Reference:

Thomas S. Shores/Applied linear algebra and matrix analysis/Springer/ISBN13: 978-0-387-33195-9

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Grading

Attendance 10 percents

Assignments  20 percents

Mid Examination 35 Percents

Final Examination  35 percents

Instructor

Associate Professor, International College

Kentaro Ihara

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