# Computer Lab Assignments

If you are unfamiliar with or are just learning Mathcad you may want to consider the Intro lab on basic graphs in Mathcad.

## Introduction to Basic Graphs

### Calculus 1 Labs

For more examples of Riemann Sums see Riemann Sum Page

The following 2 labs use the tangent line approximation to solve Physics problems.

The first deals with the motion of a mass on a spring.

The second is based on a discussion of planetray motion in the Feynman Lectures and uses the tangent line approximation to plot the trajectory of the earth around the sun.

Mass-Spring and the Tangent Line Approx (lab6springpossible)

Trajectory of the Earth and the Tangent Line Approx (lab6earthtrajectory)

### Numerical Integration

A lab on parametric equations in 2 space is included in my Calculus 1 Labs

In some cases parametric equations are taught in Calc1 sometimes Calc2, personally I think it is such a good application of the derivative as instantaneous rate of change I include it in Calc 1.
Differential Equations

The following 2 labs deal with numerical solutions to 1st order differential equations.

1. The first deals with IVPs of the form where dy/dx = f(x)   and dy/dx = f(y)

2. The second deals with the general IVP where dy/dx = f(x,y) This is called Euler’s method

• dy/dx = f(x) dy/dx =f(y) (project1)
• dy/dx = f(x.y) –Euler’s Method (project4)

For a computer lab on projectile motion in the plane click the link below

Projectile Motion

## 1st order Diff Eqs -Motion

On this page are the lecture notes and animation which discuss one-dimensional motion with air resistance

#### Position

In this animation note that as terminal velocity is approached the trajectory becomes linear

#### Entire Trajectory

The following is an extra credit assignment which extends the ideas discussed to projectile motion in the plane. It also describes how to graph parametric eqns in Mathcad. The extension to 3-D is then obvious.

### The Lion and the Antelope

The following is an example which combines parametric equations and 1st order differential equations which gives the trajectroy of a lion chasing down an antelope.

### Calculus 3 Labs

Make sure you are familiar with the Basic 3D Graph  Lab first

The Contour Gradient Lab describes how to create Vector Field PLots and How to use contour diagrams and gradient fields to locate and classify local extrema for functions of 2 variables.

### PreCalculus Labs

Before doing the following labs make sure you are familiar with the Basic Graphs in Mathcad  Lab at the top of the page

The following Lab deals with solving systems of equations using the method of Matrix Inverses