Review for the FINAL EXAM (12/16/05, 10:30-12:30PM).
CHAPTER 2 Differential Equations. Sections 2.2, 2.3, 2.4
-First Order Linear Equations 
-Separation of Variables  Method. 
Review problems:
2.2 # 2a-f, 5, 9, 10
2.4 # 1a-d, i-n, 6, 7

CHAPTER 9  Vector Space. Sections: 9.2-9.5 and 9.6-9.9
-Geometrical representation
-Angle, Dot product
- n-Space
- Dot (inner)  product   norm and angle  properties in n-Spaces. 
- Cauchy-Schwarz inequality
- Orthogonal and  Orthonormal sets. 
-Span and Subspace
-Bases, Expansions, Dimension
Review problems:
9.2 # 1, 2, 9
9.3 # 1, 3, 5, 6
9.4 # 2a, 2b
9.5 # 1ab, 7, 8, 9ab, 14. 
9.7 # 1 ae, 3, 5ab.
9.8 # 3 acd, 4, 5. 
9.9 # 1 ad, 2a, 4bh, 8ah, 9h.
    
 CHAPTER 10: Matrices and Linear  Equations. Sections 102-10.6 
-Matrices and Matrices Algebra, Transposes: properties
-Special type of matrices: symmetric, skew symmetric, identity matrix,
-Determinants: cofactor expansion, properties, row operation method. 
-Rank, REF of a matrix, applications to linear dependence and existence and  uniqueness of linear systems.   
Review problems: 
10.2 # 8ab, 11a, 12a, 21ac. 
10.3 #  4a, 6, 7a, 9.
10.4 # 2a, 3a, 4a, 7, 9a, 10. 
10.5 # 1 cde, 6a, 8ac,  15. 
10.6 # 1agq, 2g, 5bd.

CHAPTER  11: Eigenvalue Problem. Sections 11.2-11.4
-Know to find eigenvalues, eigenvectors, eigenspaces for square matrices of dimension two and three. 
-Eigenvalues/eigenvectors properties for symmetric matrices
-Diagonalization 
 
11.2 # 3bjk, 5acd, 6b, 9, 10, 11, 14. 
11.3 #1 abc
11.4 # 1bf

CHAPTER 3: Linear DE of Second Order and Higher
-Linear dependence/independence of functions 
-Wronskian Condition for LI/LD
-Homogeneous Equations. General solution for:
    constant coefficients
    Cauchy-Euler Equations
 -Non-homogeneous Equations. 
  Undetermined Coefficients   
  Variation of Parameters
  Review problems:
3.2 # 2b, 4a
3.4 # 4 a-h q r, 6 a-e.
3.6 # 1egk 
3.7 # 2bckps, 4gms