Labs for Math 3354 and Math 3355

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.