# CLEAR Calculus

## 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 Rn, 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.