### Calculus 3 Labs

## Calculus 3 Labs

**Lab 1: Dirac's belt trick** [pdf]

This lab develops vector representations of rotations in 3-space.

**Lab 2: Vector-valued functions** [pdf]

This lab develops the meaning of vector valuyed functions, from **R** to **R**^{n}, and derivatives and integrals of these functions.

**Lab 3: The physics of rotation** [pdf]

This lab uses vector-valued functions to represent physical quantities in the rotation of rigid bodies, establishing relationships between torque and angular momentum.

**Lab 4: The precessing top** [pdf]

This lab continues the development of vector-valued functions to represent physical quantities in the rotation of rigid bodies, ultimately deriving the phenomenon of precession.

**Lab 5: Just what is the x-direction anyway?** [pdf]

This lab explores the dependence of partial derivatives on the entire system of coordinates and develops the idea of the partial derivative as a directional derivative in a direction along which all other coordinates remain constant.

**Lab 6: Applications of multivariable integrals - part 1** [pdf]

This lab develops interpretation and modeling of multivariable integrals.

**Lab 7: Applications of multivariable integrals - part 2** [pdf]

This lab asks for a written explanation of the models developed in Lab 6 and extends the work to a new context.