Bring to the Final Exam Math 287 Final Exam Outline
• Pencil or Pen
• 8 1/2 x 11 inch page of notes
• Scientific Calculator
Linear Equations: Entire Class
o Linear Equations
Homogeneous
Nonhomogeneous
Structure of solution sets
o Homogeneous Superposition Principle
o Nonhomogeneous Superposition Principle
o Nonhomogeneous Principle
Differential Equations: Chapters 1, 2, 4, 8
o Verifying Solutions
o Direction Fields and Phase Portraits
o Numerical Solutions
• Euler’s Method
• Runge-Kutta
• Richardson’s Extrapolation
o Solving Differential Equations
• Separation of Variables
• Integrating Factor
• Variation of Parameters (for first order
and second order)
• Characteristic Equation
• Undetermined Coefficients
• Laplace Transform
o Modeling and Applications
Systems of Differential Equations Section 2.6 and
Chapter 6
o Verifying Solutions
o Phase Plane
o Isoclines
o Solving Systems of Differential Equations
o Homogeneous Constant Coefficients
o Nonhomogeneous Constant
Coefficients
o Decoupling
o Variation of Parameters
o Undetermined Coefficients
o Classifying Equilibriums
o Modeling Radioactive Decay and Tank
Problems
Linear Algebra and Linear Transformations
Chapters 3 and 5
o Matrix Algebra
o Addition, Subtraction,
Multiplication
o Determinants
o Inverses
o Row Equivalent Matrices
o Reduced Row Echelon
Form
o Solving Systems of Linear Equations
o Gauss-Jordan Reduction
o Cramer’s Rule
o Matrix Inverses
o Vector Spaces
o Definition and
Common/Prominent
Spaces
o Subspaces
o Basis and Dimension
o Lines and Cosets
o Linear Independent/Linear
Dependent sets
o Span of a set
o Column Space of a Matrix
o Linear Transformations
o Definition and Common
examples
o Kernel, Image, Nullity,
and Rank
o Similar Matrices
o Change of Basis
o Characteristic Equation
o Eigenvalues and
Eigenvectors
o Eigenspaces
o Diagonalizable Matrix