Test II Review Sheet--Math 308-511
General Information
The test will be given during our usual class time. It will cover the
following material: from Nagle and Saff, Chapter 4, sections 4.7-4.9,
4.10 (pp. 207-208); Chapter 5, sections 5.1-5.3; Chapter 7, sections
7.1-7.8; from Pratap (MATLAB), section 5.5. You will be allowed to use
MATLAB during the test, but not MAPLE or any program or calculator
that can do symbolic manipulation. You will be provided with a (small)
table of integrals and a table of Laplcae transforms. The test will
have 6 to 8 questions, some with multiple parts. One of the questions
will require you to use MATLAB. Please bring an 8½x11
bluebook.
Methods & Techniques
- Nonlinear or linear equations
- Numerical (Pratap, Section 5.5 & Nagle/Saff, 4.10)
- Linear, nonhomogeneous, constant coefficient equations
- Undetermined coefficients (Section 4.8)
- Variation of parameters (Section 4.9)
- Laplace transforms (Section 7.5)
- Finding Laplace transforms
- Direct calculation (Section 7.2)
- Using properties of the Laplace transforms (Section 7.3)
- Periodic and discontinuous functions (Section 7.6)
- Convolution products (Section 7.7)
- Impulse (delta) functions (Section 7.8)
- Finding inverse Laplace transforms
- Rational functions (Section 7.4)
- Functions of the form F(s)exp(-as) (Sections 7.6 & 7.8)
- Products - F(s)G(s) (Section 7.7)
- L-1[F(s)G(s)]=f*g (Convolution)
Foundations
- Second order nonhomogeneous linear equations
- Superposition & general structure of solutions (Section 4.7)
- Undetermined coefficients - constant coefficient, special right
hand side (Section 4.8)
- Variation of parameters - general method (Section 4.9)
- Laplace transforms and inverse Laplace transforms
- Definition (Section 7.2)
- Properties (Sections 7.3 & 7.4)
Applications
- Spring systems
- Free, damped vibrations (Section 5.1 & 5.2)
- Forced vibrations (Section 5.3)
- Resonance (Section 5.3)
- Linear systems
- Transfer functions (Sections 7.7 & 7.8)
- Impulse forces (Section 7.8)
- Impulse response (Sections 7.7 & 7.8)
Matlab
- odesuite
ode45
- odefile - options