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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).
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Bring to the Final Exam Math 287 Final Exam Outline
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
o Solving Differential Equations
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