MA 36600
Ordinary Differential Equations
Fall 2025
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Lecture 1 Introduction and 1.1 Basic Mathematical Models; Direction fields
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Lecture 2 1.1 (continued) and 1.2 Solutions of Some Differential Equations
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Lecture 3 1.2 (continued) and 1.3 Classification of Differential Equations
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Lecture 4 2.1 First Order Linear Equations
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Lecture 5 2.2 Separable Equations
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Lecture 6 2.2 (continued), 2.3 Modeling with First-Order Differential Equations
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Lecture 7 2.3 (continued)
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Lecture 8 2.4 Difference Between Linear and Nonlinear Differential Equations
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Lecture 9 2.4 (continued), 2.5 Autonomous Differential Equations
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Lecture 10 2.5 (continued), 2.6 Exact Differential Equations
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Lecture 11 2.6 (continued)
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Lecture 12 2.7 Euler's Method, 3.1 Linear Homogeneous Diff. Eqs. with Constant Coefficients
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Lecture 13 3.1 (continued), 3.2 Fundamental Solutions of Linear Homogeneous Equations
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Lecture 14 3.2 (continued)
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Lecture 15 3.3 Complex Roots of the Characteristic Eq., 3.4 Repeated Roots and Reduction of Order
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Exam 1 Review
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Lecture 16 3.5 Undetermined Coefficients
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Lecture 17 3.5 (continued)
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Lecture 18 3.6 Variation of Parameters
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Lecture 19 3.6 (continued)
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Lecture 20 3.7 Mechanical Vibrations
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Lecture 21 3.7 (continued)
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Lecture 22 3.8 Forced Periodic Vibrations
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Lecture 23 4.1-4.2 Higher-Order ODEs
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Lecture 24 4.3 Undetermined Coefficients, 6.1 Definition of Laplace Transform
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Lecture 25 6.1 (continued)
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Lecture 26 6.2 Solution of Initial-Value Problems
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Lecture 27 6.3 Step Functions
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Lecture 28 6.4 Differential Equations with Discontinuous Forcing Functions
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Lecture 29 6.4 (continued), 6.5 Impulse Functions
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Lecture 30 6.5 (continued)
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Exam 2 Review
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Lecture 31 6.6 The Convolution Integral
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Lecture 32 7.1-7.3 Systems of 1st-order Equations and Linear Algebra Review
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Lecture 33 7.4 Basic Theory of System of First-Order Equations
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Lecture 34 7.5 Homogeneous Systems with Constant Coefficients
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Lecture 35 7.6 Complex Eigenvalues, 7.8 Repeated Eigenvalues
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Lecture 36 7.8 (continued), 7.7 Fundamental Matrices
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Lecture 37 7.9 Nonhomogeneous Systems
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Lecture 38 5.2 Series Solutions Near Ordinary Points
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Exam 3 Review