MathCAD Tutorial

This worksheet covers many of the basic operations and functions in MathCAD. It covers simple definitions of constants, variables, and arrays, plotting 2-d and 3-d data and functions, vectors and matrix arithmetic, numerical and symbolic evaluation of integrals and differentials, and animations.

Version 2.0 RLM (20 Jan 2005)

Part 1: Elementary

Literals

Defining variables

Using built-in functions

Display significant digit in result: change to 8 by double-clicking on the answer and changing 'number of decimal places

Using dimensions

a. Example 1

Define some constants

Define custom units in terms of predefined units, express anser in custom units

Angles are normally expressed in radians by default

Replace placeholder with desired angualr unit (deg)

b. Example 2: How long does it take light from the star Vega to reach Earth?

Define constants

c. Example 3: What is the gravitational acceleration on the Earth's surface?

Note mixing of mks,cgs, and English units!

Result is in correct units (MathCAD converts variables to a consistent set of units before evaluation)

d. Example 4: Lost at sea 1 problem (Bennett, p. 109)

At solar transit, the relationship between longitude, UT time of solar transit is

Looking at a world map (e.g. Mapquest, map by coordinates) shows that this location is close to Hawaii

Using Arrays

Use the Insert... matrix to create array X, 3x3 matrix Y

2. Plotting data

Entering and Plotting data

enter by hand using commas

Add a fitting function to the plot

Fitting function (slope and intercept are pre-defined functions)

Function line reports both slope, intercept

Plotting functions: Black body curve

3. Reading and writing data from files

Reading data from a column-based text file

Writing to a data file

Write to a user defined file

4. Vector and matrix arithmetic

define vectors using insert matrix (1 column x n rows))

Dot product

vector addition

Cross product

Length of vector

Suppose we have matrix equation y = M*x. Given M,y, what is x?

5. Numerical integration (definite integrals)

Planck function, suppose:

Since luminosity is proportional to the fourth power of T, we expect luminosity ratio to be:

6. Symbolic evaluation of expression, integrals, differentials

indefinite integrals

select entire integral, choose Symbolics/ evaluate/ symbolically, or simply select and type control . (period), F9

ordinary n-th order differentials, evaluate symbolically:

Definite integral:

Select entire integral, select Symbolics/Evaluate/Symbolically

Evaluation: floating point: note use large finite upper limit

compare with symbolic result

Symbolic calculation of matrix expressions

select matrix, then symbolics/matrix/invert

factoring of algebraic expressions

solve for variable

Solve for y (note: use ctrl-equal for equal sign in symbolic expressions)

Solve for y

8. Solve blocks: single variable

Guess for b

Solving groups of equations

Guesses

9. Solving for roots of an equation using root function

guesses (from inspection of plot)

10. Plotting 3-d curves

Parametric lines

3-d Surface

Function describing graph to be revolved about axis

Interval determining portion of
graph to revolve

set up a grid in i,j

Another example:

11. Animations!

Define a 2-d function to plot, with the variable to be stepped (g) defined by special MathcAD variable FRAME. Then choose Tools/Animations/record. Select the region to be animated (including the FRAME statement), then. Animate button