Differential Equations and Linear Algebra
First Edition

by Jerry Farlow
James E. Hall
Jean Marie McDill
Beverly H. West

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Select a section: Book Resources Section 1.1: Dynamical Systems: Modeling Section 1.2: Solutions and Direction Fields Section 1.3: Separation of Variables: Quantitative Analysis Section 1.4: Euler's Method: Numerical Analysis Section 1.5: Picard's Theorem: Theoretical Analysis Section 2.1: Linear Equations: The Nature of Their Solutions Section 2.2: Solving the First-Order Linear Differential Equation Section 2.3: Growth and Decay Phenomena Section 2.4: Linear Models: Mixing and Cooling Section 2.5: Nonlinear Models, Logistic Equation Section 2.6: Systems of DEs: A First Look Section 3.1: Matrices: Sums and Products Section 3.2: Systems of Linear Equations Section 3.3: The Inverse of a Matrix Section 3.4: Determinants and Cramer's Rule Section 3.5: Vector Spaces and Subspaces Section 3.6 Objectives Section 4.1: The Harmonic Oscillator Section 4.2: Real Characteristic Roots Section 4.3: Complex Characteristic Roots Section 4.4: Undetermined Coefficients Section 4.5: Forced Oscillations Section 4.6: Conservation and Conversion Section 5.1: Linear Transformation Section 5.2: Properties of Linear Transformations Section 5.3: Eigenvalues and Eigenvectors Section 5.4: Coordinates and Diagonalization Section 6.1: Theory of Linear DE Systems Section 6.2: Linear Systems with Real Eigenvalues Section 6.3: Linear Systems with Nonreal Eigenvalues Section 6.4: Decoupling a Linear DE System Section 6.5: Stability and Linear Classification Section 7.1: Nonlinear Systems Section 7.2: Linearization Section 7.3: Numerical Solutions Section 7.4: Chaos, Strange Attractors and Period Doubling Section 8.1: Linear Nonhomogeneous Problems Section 8.2: Variation of Parameters Section 8.3: Laplace Transform I Section 8.4: Laplace Transform II Section 8.5: Forced Osciallations Section 9.1: Iterative Equations Section 9.2: Linear Iterative Systems Section 9.3: Nonlinear Iterative Equations: Chaos Again Section 10.1: Feedback Controls Section 10.2: Introduction to Optimal Control Section 10.3: Pontryagin Maximum Principle