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

- Lab Average to Instantaneous (lab1summer)
- Lab Local Linearity (lab2summer)
- Graphing and Analysis of Functions (calc1lab5)
- Parametric Eqns 2 Space (parametric2space)
- Riemann Sums Lab (calc2lab1)
- Animation Riemann Sums (YouTube)

*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)

### Calculus 2 Labs

- Polar Coordinates (polarcoordinates)
- Taylor Polynomials (calc2lab5)
- Taylor Series (tlorsrz)

### Numerical Integration

- Rectangular Approximation (calc2lab2)
- Trapezoid Rule (trapzoid)
- Simpson’s Rule (simpsnsrule)

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

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

- Notes – 1D Motion with Air Resistance (1dairresist1)

#### Velocity

#### Position

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

#### Position and Velocity

#### Position First 2 Seconds

#### 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.

- Projectile Motion in the Plane (2dmotion)
- Answer to Projectile Motion Exercise (2dairresistance)

### 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.

- Lion and Antelope-Animation (lionant2)
- Notes – The Lion and the Antelope (lionantlpe)

### Calculus 3 Labs

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

- Basic 3D Graphs (bsc3dgrphs)
- Graphing Contour Diagrams (lab2contourdiag)
- Parametric Equations in 3 Space (lab3paramtetric)

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.

- Contour Gradient Lab (contourgradientlab)
- Cylindrical Coordinates (cylindricalcoordinates)
- Spherical Coordinates (sphericalcoordinates)
- Parametric Surface Plots (parametricsrfpltslctr)

#### Animation1

#### Animation2

#### Animation3

#### Animation4

#### Animation 5

### 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

- Power Functions and Exponentials (pwrexplab)
- Translations and Reflections (rationalfnlab)

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

- Matrix Lab (matricesdemo)
- Linear Regression (linearregress)
- Exponential Regression (expregr)
- Power Function Regression Lab (pwrregrprecalclab)