Math 246 Syllabus

BD indicates sections from the textbook (Boyce & DiPrima), M indicates sections from Differential Equations with Matlab.

BD 1.1-1.3: Motivation and Classification of differential equations
BD 2.1: Linear equations
BD 2.2: Separable equations.
Note: the separable ODE y'(t) = f(t) g(y) has two types of solutions: Those found by separation of variables, and constant solutions y(t) = a where a satisfies g(a) = 0.
BD 2.3: Modeling with First Order Equations
BD 2.4: Differences Between Linear and Nonlinear Equations
BD 2.5: Population Dynamics and Related Problems
M 5: Solution of Differential Equations
M 6: A qualitative approach to differential equations
BD 2.6: Exact Equations and Integrating Factors
BD 8.1: Euler Method, Errors (backward Euler method is not done)
BD 8.2, 8.3: Improved Euler, Runge-Kutta methods (three-term Taylor formula is not done)
M 7: Numerical Methods
BD 3.1, 3.4, 3.5: Homogeneous Equations with Constant Coefficients
(reduction of order in 3.5 is skipped)
Summary of all cases is on p. 165
BD 3.6: Nonhomogeneous Equations; Method of Undetermined Coefficients
BD 3.7: Variation of Parameters
M 9: 2nd Order Equations. Read only introduction, section ``Second Order Equations with Matlab''.
BD 3.2, 3.3
BD 3.8, 3.9
BD 6.1-6.2; M 11
BD 7.4, 7.5, 7.6, M 12
BD 9.1-9.3, M 13

There is an error in Boyce/diPrima in table 9.3.1 on page 484 about types of critical points of almost linear systems:

r₁ = r₂ > 0 or r₁ = r₂ < 0: the type of the almost linear system should be more general types of N, SpP (which can look different from the nodes and spiral points for linear systems) . In this case the statement below the table (that the slopes are the same as for the linear equation) is not always true.
r₁ = i , r₂ = -i with nonzero: the type of the almost linear system should be C, SpP or other.

In these cases even very near the critical point the trajectories of the nonlinear system can be very different from those of the linear system.

Here is a correct table. One can construct examples where ``other'' types than the ones in table 9.3.1 occur.