# Labs for Math 3354 and Math 3355

Here are some of the labs for Math 3354 and Math 3355. Each of these labs will be worked through and completed in a two week period.
Lab 1: Maple for Vector Calculus
This lab is an introduction to visualizing and computing mathematics using the Computer Algebra System Maple.
Lab 2: Visualization of Planes
The goal of this lab is to use technology to visualize planes in space, and understand how they can be defined in terms of vectors.
Lab 3: Visualization of Surfaces
The goal of Lab 3 is to understand the geometry of surfaces, and discover the meaning of a tangent plane with respect to a surface.
Lab 4: Matlab for Gradient Vector Fields
This lab is an introduction to gradient vector fields using the Matlab Numerical software package.
Lab 5: Newton's Equations and Gradient Vector Fields
This lab explores the gradient vector fields that represent Newton's laws of gravitaion.
Lab 6: Limits, Continuity, and Differentiability of multivariable functions
Lab 6 explores the behaviour of some ``wacky'' functions at certain points of interest.
Lab 7: Vector Fields and Linear Vector Fields
This Lab explores how general vector fields near an equilibrium point can be approximated by linear vector fields.
Lab 8: Phase Portraits of Vector Fields
Everything you wanted to know about the local behavior of phase portraits in the neighborhood of a equilibrium point but were afraid to ask is in this lab.
Lab 9: Eigenvalues, Eigenvectors and the Determinant
As the title suggests, this lab studies the relationships between eigenvalues, eigenvectors and the determinant.
Lab 10: Forced Oscillators
This lab studies the ODEs that model forced oscillators and makes a comparison between linear and nonlinear models.
Lab 11: Polar Coordinates and Differential Equations
This lab studies how a polar change of coordinates affects vector fields and trajectories to a vector field.
Lab 12: Computing Area and Volumes
In this lab we study integration in two dimensions by computing the surface area and volume of the HHH Metrodome.