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Math 287 Final: Linear Eqns, Diff Eqns, Linear Alg, & Transformations - Prof. Robert A. Sc, Exams of Linear Algebra

An outline for the final exam of math 287, covering topics such as linear equations (homogeneous and nonhomogeneous), differential equations (verifying solutions, direction fields, and numerical methods), and linear algebra (matrix algebra, determinants, inverses, vector spaces, and linear transformations).

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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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

Partial preview of the text

Download Math 287 Final: Linear Eqns, Diff Eqns, Linear Alg, & Transformations - Prof. Robert A. Sc and more Exams Linear Algebra in PDF only on Docsity!

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 ƒ Homogeneous ƒ Nonhomogeneous ƒ 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