Final
1.General Vector Spaces
- Linear independence
- Coordinates and basis
- Dimension
- Geometry of matrix operators on R2
2.Eigenvalues and Eigenvectors
- Eigenvalues and eigenvectors
- Diagonalization
- Gram-Schmidt process
3.Complex Analysis
- Complex numbers
- Division of complex numbers
- Polar form of a complex number
- Power series
- Euler law
- Analytic functions
- Integration of complex functions
1.Systems of LinearEquations and Matrices
- Introduction to systems of linear equations
- Gaussian elimination
- Matrices and matrix operations
- Inverses; Algebraic properties of matrices
- Elementary matrices and a method
- More on linear systems and invertible matrices
- Diagonal, triangular, and symmetric matrices
2.Determinants
- Determinants by cofactor expansion
- Evaluating determinants by row reduction
- Properties of the determinants; Cramer’s rule
3.Euclidean Vector Spaces
- Vectors in 2-space, 3-space, and n-space
- Norm, dot product, and distance in Rn
- Orthogonality
- Geometry of linear systems
- Cross product
1.General Vector Spaces
- Linear independence
- Coordinates and basis
- Dimension
- Geometry of matrix operators on R2
2.Eigenvalues and Eigenvectors
- Eigenvalues and eigenvectors
- Diagonalization
- Gram-Schmidt process
3.Complex Analysis
- Complex numbers
- Division of complex numbers
- Polar form of a complex number
- Power series
- Euler law
- Analytic functions
- Integration of complex functions
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