22.T
Centroids and moments of inertia II <--(READ ME)
Reference: Stewart 13.4, 13.8, 8.4
Keywords: Center of mass, centroid, moment of inertia,
double integrals, polar coordinates,
triple integrals, cylindrical coordinates, symmetry
Learning Objectives: The student will be able to:
- Define the center of mass of a thin lamina, and the centroid of a
planar region
- Express as double integrals the mass of a thin lamina,
its center of mass,
and its moment of inertia with respect to a given axis
- Express a double integral as an iterated integral in polar coordinates
- Decide when polar coordinates are appropriate for
evaluating a double integral
- Express a triple integral in cylindrical coordinates, and
decide when cylindrical coordinates are appropriate for
evaluating a triple integral
- Find the centroid and moments of inertia in simple cases,
using polar and cylindrical coordinates
22.R Differential equations:
Direction fields, Euler's method
Reference: Stewart 8.1, CalcLabs with Maple V Chapter 11 and page
185, Stewart 15.1
Keywords: Ordinary differential equation (ODE),
solution to an ODE, direction field, analytical solution,
numerical solution, graphical solution, direction field, isocline,
Euler's method, numerical methods for ODEs
Learning Objectives: The student will be able to:
- Recognize a first order differential equation
- Verify by direct substitution that a function is a solution to a
differential equation, or to an initial value problem
- Use Maple's dsolve command to find analytical and numerical solutions to
differential equations
- Use Maple to produce a direction field for a first order differential
equation
- Set up initial value problems for simple applications, such as those
leading to exponential growth and decay
- Draw a direction field for a simple differential equation by
plotting points or by using the method of isoclines
- Sketch the solution to
an initial value problem using a direction field
- Use Euler's method
- Explain Euler's method graphically, using a direction field