Section
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Content
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Suggested Problems
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Section 1.1
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- definition of a differential equation
- classification
- notation: Leibnitz vs. Newton
- definition of a solution of an ODE
- explicit vs implicit solutions
- family of solutions
- one-parameter family of solutions
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1-8
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Section 1.2
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- initial-value problem (IVP)
- first and second order IVP
- existence and uniqueness
- Theorem 1.1
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2, 4, 7, 11,
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Section 2.1
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Section 2.2
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- definition of a separable equation
- method of solution
- initial-value problem
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5, 5, 7, 8, 10, 12, 18, 24-26
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Section 2.3
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- 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
- initial-value problem
- functions defined by integration
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3, 5, 7, 10-12, 14, 16, 18, 25, 26, 29
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Section 2.4
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- definition of an exact equation
- criterion for being exact
- method of solution
- initial value problem
- integrating factors
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2-5, 7-9, 11, 14, 16, 19, 21, 23
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Section 2.5
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- homogeneous functions
- homogenous first-order ODE
- method of solution
- substitution y = ux
- substitution x = vy
- Bernoulli equations
- method of solution
- reduction to separable
- substitution u = Ax + By + C
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3-4, 6-7, 10-12, 15-16, 21, 23-24, 27-28
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Section 2.6
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- tangent line approximation
- slope from the direction field
- Euler's Method
- error estimates
- numerical solvers
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None
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Section 2.7
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- growth/decay linear models
- Newton's Law of Cooling/Heating
- dT/dt = k(T-Tm)
- ambient temperature
- Mixtures
- dx/dt = (input rate of salt) - (output rate of salt)
- inflow volume equals outflow volume
- inflow volume does not equal the outflow volume
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3, 5, 11, 14-15, 21, 25
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Section 2.8
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- population dynamics
- logistic equation
- solution of logistic equation
- modifications of the logistic equation
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None
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