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Table of Contents
Part I Systems of linear equations
1 Introduction
2 Systems with two equations and two unknowns
3 Gaussian elimination
Part II Matrices and related topics
4 Basic operations
5 Linear dependence, bases, coordinates
6 Determinants
Part III Complex numbers
7 Complex numbers: definition and operations
8 The Fundamental Theorem of Algebra
9 Linear systems with complex coefficients
Part IV Vector spaces and linear maps
10 Vector spaces and their linear subspaces
11 Linear maps
12 Inner products on K-vector spaces
Part V Eigenvalues and eigenvectors
13 Eigenvalues and eigenvectors of Clinear maps
14 Eigenvalues and eigenvectors of R-linear maps
15 Quadratic forms on Rn
Part VI Differential equations
16 Introduction
17 Linear ODEs with constant coefficients of first order
18 Linear ODEs with constant coefficients of higher order
Appendix A Solutions.
1 Introduction
2 Systems with two equations and two unknowns
3 Gaussian elimination
Part II Matrices and related topics
4 Basic operations
5 Linear dependence, bases, coordinates
6 Determinants
Part III Complex numbers
7 Complex numbers: definition and operations
8 The Fundamental Theorem of Algebra
9 Linear systems with complex coefficients
Part IV Vector spaces and linear maps
10 Vector spaces and their linear subspaces
11 Linear maps
12 Inner products on K-vector spaces
Part V Eigenvalues and eigenvectors
13 Eigenvalues and eigenvectors of Clinear maps
14 Eigenvalues and eigenvectors of R-linear maps
15 Quadratic forms on Rn
Part VI Differential equations
16 Introduction
17 Linear ODEs with constant coefficients of first order
18 Linear ODEs with constant coefficients of higher order
Appendix A Solutions.