You may bring a notecard to the exam with review information you have prepared for the exam.
Section
|
Content
|
Suggested Problems
|
Section 5.1
|
- Linear Dynamical Systems
- Hooke's Law
- Newton's Second Law
- Spring/Mass
- Equilibrium Position
- Coordinate System Orientation
- Free Undamped Motion
- mx" + kx = 0
- x" + ω2x = 0
- Alternative Form of Solution
- Free Damped Motion
- mx" + βx' + kx = 0
- x" + 2λx' + ω2x = 0
- Overdamped, Critically Damped, Underdamped
- Driven or Forced Motion
- mx" + βx' + kx = f(t)
- x" + 2λx' + ω2x = F(t)
- Transient vs Steady-State Solutions
|
3, 6, 9, 10, 21, 22, 26, 29
|
Section 7.1.1
|
- Definition of Improper Integral
- Basic Definition of Laplace Transform
- Transforms of Basic Functions (Theorem 7.1)
- Exponential Order
- Theorem 7.1.2 Sufficient Condition for Existence
- Laplace Transform of Piece-wise Continuous Function
|
3, 5, 9, 13, 21, 24, 27, 31,
|
Section 7.2
|
- Inverse Transforms
- Theorem 7.2.1
- Partial Fraction Expansions and Linearity
- Transforms of Derivatives
- Solving linear initial-value problems
- Solve First Order Linear IVPs
- Solve Second Order Linear IVPs
|
3, 4, 8, 15, 17, 20, 23, 26, 27, 32, 34, 36
|
Section 7.3
|
- Translation on the s-axis
- First translation/shifting theorem (Theorem 7.3.1)
- Unit step function
- Piece-wise Defined Functions
- Translation on the t-axis
- Second translation/shifting theorem (Theorem 7.3.2)
- Alternative Version of Theorem 7.3.2
- Solving linear initial-value problems
|
3, 6, 9, 10, 11, 14, 16, 18, 19, 22, 24, 26, 29, 37, 41, 43, 44, 47, 63, 65, 68
|
Section 7.4
|
- Derivatives of Transforms (Theorem 7.4.1)
- Convolution Theorem (Theorem 7.4.2)
- Transform of a Period Function (Theorem 7.4.3)
- Solving linear initial-value problems
|
3, 6, 9, 11, 13, 21, 23, 50, 51
|
Section 7.5
|
- Unit Impulse Function
- Dirac Delta Function
- Solving linear initial-value problems
|
1, 3, 6, 9
|