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Lecture 25, 10/26/2022. This page is for Section 1 only.
ACMS 20550: Applied Mathematics Method I
Instructor: Bei Hu, b1hu@nd.edu, Hurley 174A

Chapter 6: Vector Analysis

  1. Applications.
    1. Work = Force$\cdot$ Displacement = $\vec F\cdot \vec d$
    2. Torque = $\vec r\times \vec F$

    3. Angular Velocity = $\vec \omega\times \vec r$


  2. Jacobian - recovery of formula from Chapter 5.

  3. Differentiation of Vectors
    1. Differentiate a vector term by term.
    2. Product rules apply.
      (a)
      $\frac{d}{dt} \Big(a \vec A\Big) = \frac{da}{dt} \vec A + a \frac{d \vec A}{dt}$.
      $\m$ (b)
      $\frac{d}{dt} \Big( \vec A \cdot \vec B\Big) = \vec A \cdot \frac{d\vec B}{dt} + \frac{d \vec A}{dt} \cdot \vec B$.
      $\m$ (c)
      $\frac{d}{dt} \Big( \vec A \times \vec B\Big) = \vec A \times \frac{d\vec B}{dt} + \frac{d \vec A}{dt} \times \vec B$.


    Example: a particle that moves on a circle.