P1_1130 - MATH 415.01 Review Sheet CHAPTER 7: you should...

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MATH 415.01 Review Sheet CHAPTER 7: you should know: transpose , conjugate, adjoint of a matrix singular (non-invertible) , nonsingular (invertible) matrix. Gaussian Elimination Matrix A is singular if det ( A ) = 0. Matrix A is nonsingular if det ( A ) 6 = 0. Then it has an inverse A - 1 Solution of Ax=b if A is nonsingular , there is unique solution x = A - 1 b if A is singular, the solution either do not exist or do exist, but not unique. Also you should know these IMPORTANT notions: linear dependence and linear independence eigenvalues and eigenvectors CHAPTER 1: you should know: Direction Fields Equilibrium points order of a differential equation Classification of Differential Equations.( linear/nonlinear - ordinary/partial) CHAPTER 2: 2.1 Method of Integrating Factors: General linear first order equation: dy dt + p ( t ) y = g ( t ) Define μ ( t ) = e R p ( t ) dt . The solution is: y = 1 μ ( t ) ±Z μ ( t ) g ( t ) dt + c ² 2.2 Separable Equations:
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P1_1130 - MATH 415.01 Review Sheet CHAPTER 7: you should...

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