Differential Equations and Linear Algebra

by
C. Henry Edwards
David E. Penney

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Select a section: Section 1.1: Differential Equations and Mathematical Models Section 1.2: Integrals as General and Particular Solutions Section 1.3: Direction Fields and Solution Curves Section 1.4: Separable Equations and Applications Section 1.5: Linear First-Order Equations Section 1.6: Substitution Methods and Exact Equations Section 2.1: Population Models Section 2.2: Equilibrium Solutions and Stability Section 2.3: Acceleration-Velocity Models Section 2.4: Numerical Approximation: Euler's Method Section 2.5: A Closer Look at the Euler Method Section 3.1: Introduction to Linear Systems Section 3.2: Matrices and Gaussian Elimination Section 3.3: Reduced Row-Echelon Matrices Section 3.4: Matrix Operations Section 3.5: Inverses of Matrices Section 3.6: Determinants Section 3.7: Linear Equations and Curve Fitting Section 4.1: The Vector Space R3 Section 4.2: The Vector Space Rn and Subspaces Section 4.3: Linear Combination and Independence of Vectors Section 4.4: Bases and Dimensions for Vector Spaces Section 4.5: General Vector Spaces Section 5.1: Introduction to Second-Order Linear Equations Section 5.2: General Solutions of Linear Equations Section 5.3: Homogeneous Equations with Constant Coefficients Section 5.4: Mechanical Vibrations Section 5.5: Undetermined Coefficients and Variation of Parameters Section 5.6: Forced Oscillation and Resonance Section 6.1: Introduction to Eigenvalues Section 6.2: Diagonalization of Matrices Section 6.3: Applications Involving Powers of Matrices Section 7.1: First-Order Systems and Applications Section 7.2: Matrices and Linear Systems Section 7.3: The Eigenvalue Method for Linear Systems Section 7.4: Second-Order Systems and Mechanical Applications Section 7.5: Multiple Eigenvalue Solutions Section 7.6: Numerical Methods of Solutions Section 8.1: Matrix Exponentials and Linear Systems Section 8.2: Nonhomogeneous Linear Systems Section 8.3: Spectral Decomposition Methods Section 9.1: Stability and the Phase Plane Section 9.2: Linear and Almost Linear Systems Section 9.3: Ecological Models: Predators and Competitors Section 9.4: Nonlinear Mechanical Systems Section 10.1: Laplace Transforms and Inverse Transforms Section 10.2: Transformation of Initial Value Problems Section 10.3: Translation and Partial Fractions Section 10.4: Derivatives, Integrals, and Products of Transforms Section 10.5: Periodic and Piecewise Continuous Forcing Functions Section 11.1: Introduction and Review of Power Series Section 11.2: Power Series Solutions Section 11.3: Frobenius Series Solutions Section 11.4: Bessel's Equation