exam 2 fall 2010 outline - Equation of a Plane D. Cross...

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Engineering Math Fall 2010 Exam 2 Outline Chapter 7 Linear Algebra: Matrices, Vectors, Determinants. Linear Systems L. Linear Systems of Equations (7.5) 1. Existence Theorem 2. Uniqueness Theorem 3. Solution Space of a Homogeneous System 4. Rank Theorem 5. Solution Set of a Nonhomogeneous System Chapter 8 Linear Algebra: Matrix Eigenvalue Problems A. Eigenvalues and Eigenvectors (8.1) B. Eigenspaces and Eigenbases (8.4) C. Diagonalization (8.4) Chapter 9 Vector Differential Calculus. Grad, Div, Curl A. Calculus Review 1. Derivatives (9.6) 2. Differentials (9.5) 3. Chain Rule (9.6) 4. Definite Integral B. Vectors (9.1) 1. Addition and Scalar Multiplication 2. Magnitude and Unit Vectors C. Dot Product (9.2) 1. Definition and Properties 2. Angle between Vectors 3. Projections / Components 4. Work 5.
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Unformatted text preview: Equation of a Plane D. Cross Product (9.3) 1. Definition and Properties 2. Normal Vector to a Plane 3. Area of a Parallelogram 4. Torque (Moment of a Force about an Axis) E. Vector and Scalar Functions and Fields (9.4) F. Derivative of a Vector Function (9.4) G. Curves (9.5) 1. Lines 2. Circles / Ellipses 3. Hyperbolas 4. Helices H. Tangent Vectors and Tangent Lines (9.5) I. Tangential and Normal Components of Acceleration (9.5) J. Arc Length (9.5) 1. Arc Length from Point to Point 2. Arc Length Function K. Differentials for a Vector Function (9.5) L. Gradient (9.7) 1. Directional Derivatives 2. Surface Normal Vectors 3. Potentials M. Laplacian and Laplace's Equation (9.7) N. Divergence and Fluid Flow (9.8) O. Curl and Rotating Bodies (9.9)...
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exam 2 fall 2010 outline - Equation of a Plane D. Cross...

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