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Calculate and Communicate with PTC Mathcad Prime 3.0

VERSION 66  Click to view document history
Created on: Aug 7, 2013 10:41 AM by bedmonds - Last Modified:  Dec 12, 2013 6:32 AM by ptc-5133430

Full list of worksheets

 

Want a free copy of PTC Mathcad Express? Download your copy today.

 

Authors: Hans Wesselingh, Hans de Waard

 

 

This course will help you to learn PTC Mathcad in 25 live lessons of an hour each. These cover worksheets, functions, plotting, programming, units, statistics, calculus, vectors and matrices, linear and non-linear equations and differential equations. Some hundred exercises include examples from applied math, physics, chemistry and physiology.


To begin, download the lessons and exercises from the PTC website. Open the first lesson in Prime 3.0 and work through it. The course consists of read-only Mathcad files, which can be viewed and modified in the free Mathcad Express. The course is also available as a book from Delft Academic Press. This can be ordered via Amazon.

 

What is New: The largest change in Prime 3.0 compared to Prime 2.0 is in the editing of equations. These are handled in lesson 6. You will find the new method of editing to be more natural than the old one: it closely follows that of other Windows programs. There are smaller changes in lesson 1 (the interface), lesson 3 (templates), lessons 7,8 an 9 (plotting) and lessons 10 (labels and global variables). We have partly rewritten lessons 11 and 12 on programming and lessons 13 through 16 on statistics.

 

Worksheets marked with use PTC Mathcad premium features, otherwise they are Express compatible. All worksheets created in PTC Mathcad Prime 3.0.


Chapter
ExerciseDescription

Introducing Mathcad

Mind Map

PTC Mathcad is very useful for problems where you need to be flexible and creative: when you are learning a subject, doing homework, designing, or developing a new product or theory. You can even write a book in it, as this text shows.
Handling of Text

Typing Exercise

PTC Mathcad has one great advantage over other programming languages: it is self-documenting. You will still be able to understand this Mathcad file if you load it in a years time. The program is not a full-fledged text editor, but as you can see in this chapter, text handling is good enough for many purposes.
Worksheet LayoutMy TemplateWhen doing a quick calculation, you may not worry about the layout of your worksheet. However, for a report or a book, the layout needs to be chosen such that it does not distract the reader. For that, PTC Mathcad has integrated lots of features.
Mathcad as Calculator Quick ArithmeticPTC Mathcad is a good calculator, certainly if you have a numerical keypad. It gives a record of calculations which can be easily stored or printed.
Variables and FunctionsDestructive DefinitionsWhen you have mastered the use of variables and functions you will begin to realize the capabilities of Mathcad. This chapter explains how to define and use variables and functions.
Editing of EquationsEdit EquationsTo become a proficient user of PTC Mathcad you must learn to edit equations. For that, check out this chapter!
Ranges and Plots

Great Graphics

Logistics Map and Chaos

Pasting Plots

This chapter explains how a set of counting subscripts is formed using a range variable and how the range variable is applied in plotting of a function.
2D Plots of Functions

Linked Lines

Quadratic Quest

Log Plots

Fun Plots

In this chapter we can explore the many variations in plots. To do that we use the same terms as in lesson 7. Make sure you have the names of the plot elements in your mind.
3D Plots of Functions

Spatial Symmetry

Leaf of Descartes

Donut

Plot of a Spring

3D plots in PTC Mathcad are similar to 2D plots. However, there are differences of which you should be aware of. PTC Mathcad has two kinds of 3D plots: the true 3D plot with three axes as well as the contour plot. Two find out more about them check out this chapter.
Labels and Units

My Template with Labels

Food in the Body

Dissolution of a Tablet

Plate Viscometer

Temperature in a Spray Dryer

Volume of an Ideal Gas

Falling Particle

Flow from a Vessel

Concentration in a Mixture

Vapour Pressure of Water

In practical calculations you often need to use the same letter to describe different entities. For example the letter 'g' might be used to describe a variable, the unit gram, the gravitational acceleration and some function g(x). You can do this in PTC Mathcad without any confusion by giving these entities a different label.
Programming Branches

Cylinder Modified

Truncated Sine

Black or White

Specifications of a Tablet

Singular Singularities

PTC Mathcad contains a programming environment that greatly extends its capabilities. Despite the small number of commands you can construct the three main elements of any programming language: actions, branches and loops. That combined with the many other parts of Mathcad that you have learned in the previous chapters gives you humongous possibilities.
Programming Loops

Filling a Vector

Filling a Matrix

Counting Exam Scores

Timing

Sum of a Series

While versus For

In this second lesson on programming the focus is on 'loops'. These repeat calculations in different ways - often many times.
Statistics

Start Simply

Books per Student

stdev Uniform Distribution

Central Limit Theorem

stdev of Means

In this lesson (and the following ones) we look at data which will be regarded as two vectors of equal length. We will show how to summarize the behaviour of data by the mean and the standard deviation. Further we discuss two of the random number generators in PTC Mathcad.
Distributions

Tossing a Coin

Dice and Cards

False Positives

Standard Normal Distribution

Binomial and Normal

Packs of Sugar

In this chapter we look at a few probability distributions. The two main ones are discrete distributions and continuous distributions. To find out more about those, read this chapter!
Testing

Simple Samples

New Machine for Tablets

Jam and Bottle

New Machine Again

The t-Distribution

Small Samples

This chapter considers sampling and testing of data.
Data Analysis

Response to Glucose

Fitting a Quadratic

Drug in the Body

Different Lines

In this chapter we look at how to handle data, specifically how to find relations between variables from experiments. We will look at two techniques for handling experimental data: Data fitting (regression analysis) and interpolation between data points.
Input Output

Sunspots

Excel Ellipse

You can use variables and functions from other Mathcad files in your worksheet. Further PTC Mathcad also allows you to read data from Excel and use Excel tables in your worksheets.
Symbolic Calculus

Some Derivatives

Indefinite Integrals

Slope Area and Average

Limits

Function with a Hole

The Cannon Ball

Fractal Lung

PTC Mathcad is a layout program in which you can place text and math regions. In the previous chapters, the math regions have been numerical. However, you can also use these to do 'symbolic' calculations. These will allow you to redo classic 'calculus' on the computer: differentiation, integration, limits, series... and all these operation with equations as you would write them.
Solve and Series

Linear Equations

Cubic Equations

More Problems

Some Series

Same Series

In this chapter we explore variations of symbolic evaluation using keywords and modifiers. We apply these to get a symbolic solution of equations, and to approximate a function as a series of polynomials.
Shapping Equations

Expand and Factor

Evaluate and Simplify

Partial Fractions

Float and Assume

Exponential Equations

Equations are often not in the form that you would like them to be. PTC Mathcad has several tools to help you shape equations by rearranging or substituting them.
Vectors and Matrices

Manipulating Matrices

Symmetric and Skew-symmetric

Dot Multiplication

Simple Inverses

Linear Equations

Inverse of a 3x3 Matrix

You may know a lot about this subject without having realized. Calculations in Excel are vector and matrix operations. You can do these in PTC Mathcad with the advantage that calculations are much easier to follow and you are less likely to make any mistakes.
Linear Equations

Linear Equations A

Linear Equations B

Blood Circulation Short

Plane Transformations

In these chapter we look at applications of vector and matrix algebra. These applications often require the solution of sets of linear equations.
Nonlinear Equations

Non-linear Equation

Three Linear Equations

Dissociation of a Weak Acid

PTC Mathcad can solve implicit sets of linear and non-linear equations. It does this with a clever multi-variable interation technique. If you provide an approximate solution, then the program will improve your estimate. Because of that you must understand the behavior of the functions that you are studying.
Solving with Functions

Guess Values

Two Nonlinear Equations

Solving of equations is important for practical problems. For that PTC Mathcad has the function 'solve block' which you learn how to use in this chapter. .
Differential Equations

Differential Equations

Absorption in the Intestines

Cat and Mouse Equations

Body and Drug

Ordinary differential equations contain two kinds of variable: dependent and independent. In this chapter you learn how to solve these in a solve block.
EndingEndingWe like to end with two bits of advice. Firstly that real problems take longer and secondly there is a lot more in PTC Mathcad that you have seen in these chapters. For more details, check out this chapter.