Section

Content

Suggested Problems

Section 1.1

 definition of a differential equation
 classification
 notation: Leibnitz vs. Newton
 definition of a solution of an ODE
 explicit vs implicit solutions
 family of solutions
 oneparameter family of solutions

18

Section 1.2

 initialvalue problem (IVP)
 first and second order IVP
 existence and uniqueness
 Theorem 1.1

2, 4, 7, 11,

Section 2.1



Section 2.2

 definition of a separable equation
 method of solution
 initialvalue problem

5, 5, 7, 8, 10, 12, 18, 2426

Section 2.3

 definition of a linear equation
 standard form of a linear equation
 linearity property of solutions of the homogeneous equation
 method of solution
 find integrating factor exp(int(p(x)dx))
 integrate the product of the integrating factor and f(x)
 formualte the general solution of the linear equation
 initialvalue problem
 functions defined by integration

3, 5, 7, 1012, 14, 16, 18, 25, 26, 29

Section 2.4

 definition of an exact equation
 criterion for being exact
 method of solution
 initial value problem
 integrating factors

25, 79, 11, 14, 16, 19, 21, 23

Section 2.5

 homogeneous functions
 homogenous firstorder ODE
 method of solution
 substitution y = ux
 substitution x = vy
 Bernoulli equations
 method of solution
 reduction to separable
 substitution u = Ax + By + C

34, 67, 1012, 1516, 21, 2324, 2728

Section 2.6

 tangent line approximation
 slope from the direction field
 Euler's Method
 y_{n+1} = y_{n} + h f(x_{n},y_{n})
 error estimates
 numerical solvers

None
