final exam outline - Engineering Math Spring 2009 Final...

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Engineering Math Spring 2009 Final Exam Outline Chapter 6. Laplace Transforms A. Definition (6.1) B. Laplace Transform Formulas (6.1) C. Linearity (6.1) D. -shifting (6.1) = E. Inverting Transforms (6.1) 1. Partial Fractions 2. Completing the Square F. Transforms of Derivatives (6.2) G. Solving Initial Value Problems (6.2) H. Unit Step Function (6.3) I. -shifting (6.3) > J. Dirac Delta Function (6.4) K. Periodic Functions (6.4 exercises) L. Convolution (6.5) 1. Definition 2. Convolution Theorem 3. Using Convolution to Find Inverse Laplace Transforms 4. Using Convolution to Solve Integral Equations M. Differentiation of Transforms (6.6) N. Systems of ODEs (6.7) Chapter 7 Linear Algebra: Matrices, Vectors, Determinants. Linear Systems A. Basic Definitions and Concepts (7.1) B. Matrix Addition and Scalar Multiplication (7.1) C. Matrix Multiplication (7.2) D. Determinants and Cofactors (7.6 and 7.7) E. Matrix Inverses (7.8) F. Singularity and Nonsingularity (7.8) G. Vector Spaces (7.9) 1. Defining Properties 2. Subspaces 3. Spanning 4. Linear Dependence and Independence 5. Basis 6. Dimension H. Elementary Row Operations and Gauss Elimination (7.3) I. Solving Systems of Linear Equations (7.3) J. Row Space and Column Space of a Matrix (7.4) K. Rank of a Matrix (7.4) L. Linear Systems of Equations 1. Existence Theorem (7.5) 2. Uniqueness Theorem (7.5) 3. Solution Space of a Homogeneous System (7.5) 4. Solution Set of a Nonhomogeneous System (7.5)
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Chapter 8 Linear Algebra: Matrix Eigenvalue Problems A. Eigenvalues and Eigenvectors (8.1) B. Stochastic Matrices (8.2) C. Markov Processes and Limits of Markov Chains
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final exam outline - Engineering Math Spring 2009 Final...

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