Math 431 Outline - Last Updated 6/2/99
Check class log to see when the various sections are covered
(Note: IT stands for Important Topics/Ideas)

Review
  Classification of ODEs (1.1)
     IT: Order, Linear vs. Non-linear, Meaning of Solution, Direction Field
     HW 1.1 #2, 5, 9, 12, 16, 19
  First Order ODEs (Chapter 2)
     Direct Integration
     Integrating Factor (2.1,2.2)
        IT: Integrating Factor, Constant of Integration
        HW 2.1 #2, 10, 15, 32, 33
        HW 2.2 #6, 10, 17, 23, 35
     Bernoulli's Equation (2.2, ex. 37-41)
        IT: Tranformation by substitution
        HW 2.2 #37, 38
     Separable & Separable w/Substitution (2.3)
        IT: Recognition of Separable, Implicit solution
        HW 2.3 #3, 6, 11, 18
     Exact & Exact w/Integrating Factor (2.8)
        IT: Recognition of Exact, 'partial' integration
        HW 2.8 #2, 5, 7, 13, 25
     Homogeneous (2.9)
        IT: Recognition of Homogeneous
        HW 2.9 #1, 12
     Picard's Iteration (2.11)
        IT: Integral form of ODE, Approximation
        HW 2.11 #4, 9
  2nd Order Linear ODEs (Chapter 3)
     Linearity, Superposition Principle, Wronskian (3.2, 3.3)
        IT: General solution, linear independence & Wronskian
        HW 3.2 #2, 13, 25, 3.3 #1, 5, 10
     Homogeneous Equation, Characteristic Equation (3.1, 3.4, 3.5)
        IT: Classification by roots, asymptotic behavior
        HW 3.1 #1, 5, 9, 30, 37, 3.4 #9, 19, 3.5 #1, 12, 24
     Non-homogeneous Equations
        IT: form of solution (homogeneous + particular)
        Method of Undetermined Coefficients (3.6)
           IT: Guess plus modify by checking homogeneous soln.
           HW: 3.6 #1, 7, 13
        Variation of Parameters (3.7)
           IT: Initial form plus assumption, Final formula
           HW: 3.7 #5, 11, 14
  Higher Order Linear ODEs (Chapter 4)
           IT: Repeat of topics from Chapter 3, generalized
           HW 4.1 #8,12,15 4.2 #11,19,26 4.3 #2,4,14  4.4 #1,8

New
  Series Solution of 2nd Order Linear ODEs (Chapter 5)
     Power Series, Radius of Convergence, Algebra (5.1)
        IT: 11 Properties of Power Series
	HW: 5.1 #1, 4, 8, 12, 16, 21, 26
     Around Ordinary Points (5.2, 5.3)
        IT: index manipulation, recursive relation
        HW: 5.2 #1, 5, 8, 13,  5.3 #2, 6, 7, 12
     Around Regular Singular Points (5.4, 5.5, 5.6, 5.7, 5.8)
        Euler's Equation, Bessel's Equation
	HW: 5.4 #2, 4, 15, 5.5 #1, 5, 10, 5.6 #1, 7, 10, 5.7 #3, 5, 12, 5.8 #1,5
  Systems of 1st Order Linear ODEs (Chapter 7)
     Formulation, Linear Algebra Basics (7.2, 7.3, 7.4)
     Homogeneous, Constant Coefficient (7.5, 7.6, 7.7)
     Fundamental Matrices (7.8)
     Non-Homogeneous (7.9)
        Diagonalization
        Variation of Parameter
        Method of Undetermined Coefficients
  Nonlinear ODEs and Stability (Chapter 9)
     Phase Plane for Linear Systems (9.1)
     Autonomous Systems, Stability (9.2)
     Almost Linear Systems (9.3)