Dave's Web Corner

MTH-261 Week 4 (September 15-21)

recommended exercises
- 8, 11, 13, 17, 25, 28, 39, 41
learning objectives
- describe the velocity and acceleration vectors of a particle moving in space
- explain the tangential and normal components of acceleration
- state Kepler’s laws of planetary motion
additional notes
- tangential and normal components of acceleration
  - in terms of speed, curvature, and linear acceleration
  - in terms of velocity and acceleration
- projectile motion (neglecting rotational dynamics and drag)
  - two-dimensional:
    - initial position \( \langle x_{0},y_{0} \rangle \), initial speed \( \|\vec{v}_{0}\| \), angle of elevation \( \alpha \), constant acceleration due to gravity \( \langle 0,-g \rangle \)
    - \( \displaystyle{ \vec{r}(t) = \left\langle x_{0}+t\|\vec{v}_{0}\|\cos\alpha,y_{0}+t\|\vec{v}_{0}\|\sin\alpha -\frac{1}{2}gt^{2} \right\rangle } \)
  - in general:
    - initial position \( \vec{r}_{0} \), initial velocity \( \vec{v}_{0} \), acceleration \( \vec{a}(t) \)
    - integrate and incorporate initial values

recommended exercises
- 3, 7, 9, 11, 15, 17, 19, 27, 31, 32, 33, 37, 45, 50, 53, 57, 59-64, 68, 71, 73
learning objectives
- recognize a function of two variables and identify its domain and range
- sketch a graph of a function of two variables
- sketch several traces or level curves of a function of two variables
- recognize a function of three or more variables and identify its level surfaces
additional notes

Deadlines
- All homework is due at the beginning of class on the date indicated.
- All exams are given in class on the date indicated.
- Late homework is not accepted and there are no make-ups for missed exams. Contact me before the deadline if you have a conflict with a deadline and we will find a mutually agreeable solution.
- Solutions are posted under these links after the deadline.
Homework
- due Thursday, September 19:
  - 12, 13, 14, 15, 16
- due Thursday, September 26:
  - 17, 18, 19, 20, 21
- due Tuesday, October 1:
  - 22, 23
Exams
- Thursday, October 3: Exam 1
  - Exam 1 (solutions)
  - Exam 1 covers sections 12.1-12.6, 13.1-13.4, and 14.1-14.3