Math 325 - Fall 2004 - Course Outline

All section numbers refer to W. E. Boyce's and R. C. DiPrima's "Elementary Differential Equations and Boundary Value Problems", 8th edition.

 Week Reading Topics 1   (9/2) 1.2       1.3 Solutions to some differential equations Classification of Differential Equations 2   (9/7 - 9/9) 1.3       2.1       2.2 Classification of Differential Equations Linear Equations: Method of Integrating Factors Separable Equations. 3   (9/14 - 9/16) 2.4       2.5       2.6 Differences Between Linear and Nonlinear Equations Autonomous Equations and Population Dynamics Exact Equations and Integrating Factors 4   (9/21 - 9/23) 2.8       * The Existence and Uniqueness Theorem Prelim 1, September 23 5   (9/28 - 9/30) 3.1       3.2       3.3 Homogeneous Equations with Constant Coefficients Fundamental Solutions of Linear Homogeneous Equations Linear Independence and the Wronskian 6   (10/5 - 10/7) 3.4       3.5       3.6 Complex Roots of the Characteristic Equation Repeated Roots; Reduction of Order Nonhomogeneous Equations; Method of Undetermined Coefficients 7   (10/12 - 10/14) *       3.7       4.1 Reading Holiday, October 12 Variation of Parameters General Theory of n-th Order Linear Equations 8   (10/19 - 10/21) 4.2       4.3       4.4 Homogeneous Equations with Constant Coefficients The Method of Undetermined Coefficients The Method of Variation of Parameters 9   (10/26 - 10/28) *       7.1       7.2 Prelim II, October 26 Systems of First Order Linear Equations; Introduction Review of Matrices 10   (11/2 - 11/4) 7.3       7.4       7.5 Linear Algebraic Equations; Linear Independence; Eigenvalues, Eigenvectors Basic Theory of Systems of First Order Linear Equations Homogeneous Linear Systems with Constant Coefficients 11   (11/9 - 11/11) 7.6       7.7       7.8 Complex Eigenvalues Fundamental Matrices Repeated Eigenvalues 12   (11/16 - 11/18) 5.1       * Review of Power Series Prelim III, November 18 13   (11/23 - 11/25) 5.2       5.3       * Series Solutions Near an Ordinary Point Series Solutions Near an Ordinary Point Thanksgiving, November 25 14   (11/30 - 12/2) 10.1       10.2       10.3 Two-Point Boundary Value Problems Fourier Series The Fourier Series Convergence Theorem 15   (12/7 - 12/9) 10.4       10.5 Even and Odd Functions Separation of Variables