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)

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