- Exam 1 is next Thursday (Feb. 25)
- Material since start of semester (e.g., 3D coordinates and surfaces, vectors
and their products, lines, planes, vector-valued functions, their derivatives,
limits, integrals, arc length, muPad)
- Maybe curvature, maybe not
- Whole class period
- 4 - 6 short-answer questions
- Open references (book, notes, computer), closed person
- Can use calculators, CASes, etc.
- Material since start of semester (e.g., 3D coordinates and surfaces, vectors
and their products, lines, planes, vector-valued functions, their derivatives,
limits, integrals, arc length, muPad)
- How to get multiple lines on one plot in muPad?
- List multiple plot objects in
plotcommand
- List multiple plot objects in
- Section 13.2
- Integrate each component
- Fundamental theorem applies: definite integral from a to b = difference of anti-derivatives at b and a
- Projectile motion
- Integrate each component
- Integration in muPad
- Examples
- How fast do I launch a ball up a ruler?
- Range = 32.5 inches
- Angle = 60 degrees
- Could derive time in terms of range and angle as an initial value problem
- Or could take advantage of the fact that the book already did that, use its formula
- If that ball is launched at an upward angle of 60 degrees from the origin
with horizontal component parallel to <1,1,0>, what is the equation for its
position?
- 3D version of projectile motion analysis book does for 2 dimensions
- Do work this one out from first principles, i.e., by integrating from acceleration
- v0 = 120 in/sec
- We’ll finish this tomorrow
- See if you can figure out how non-zero horizontal velocities get in
- How fast do I launch a ball up a ruler?
- Problem Set
- Finish 3D projectile derivation
- Then arc length and vector-valued functions
- Read section 13.3