Index of Example Topics

Working with PTC Mathcad Prime
Display of Integer Decimal Results	Editing an Excel Component	Predefining the Input and Output Expressions Cell Range
Display of Non-Integer Decimal Results	Formatting an Excel Component

Operators
Boolean Operators	Interleaving of Local and Global Definitions	Understanding the Define-Evaluate Operation
Complex Numbers, Polar Notation	Numerical Double Integrals	Using the try-on-error Programming Operator
Differentiation and Integration of Data Vectors	Row, Column, and Index Operators	Using the Element Of Operator
Effects of TOL and Method on Definite Integration	Summation and Product Operators	Using the Limit Operator

Vectors, Matrices, and Tables
Elementary Row Operations on Matrices	Seeded Iteration and Difference Equations	Vector Algebra
Matrix Algebra	Special Characteristics of Matrices
Nested Arrays	Special Types of Matrices

Solve Blocks
Adding Units to Solve Blocks	Solve Block with Multiple Guesses	Using minerr for Nonlinear Least Squares Fitting
Optimizing a Function	Solve Blocks with Inequality Constraints
Optimization Functions	Solving Nonlinear Systems of Equations

Plots
XY Plots	Contour Plots with Singularities	3D Plots and Waterfall
Arc Length and Surface Area	Using Polar Plots to Plot Data	Plotting 3D Curves
Column, Normal Probability, and Box Plots	Plotting Large Data Sets Using Polar Plots	Creating Waterfall Plots
Pareto and Effects Plots	General	Plotting a Function and a Matrix in 3D
Plotting a Function and Its Derivatives	Converting Units in Plots	Plotting a Vector-Valued Function
Plotting Inequalities and Piecewise Functions	Plotting Complex Valued Functions or Data	Plotting Large Data Sets Using 3D Plots
Polar Plots and Contour Plots	Using Range Variables in Plots
Contour Plots or Level Curves

Programs		Units
Finding Local Min/Max of Vectors	Recursive Functions	Using Money Units
Fourier Polynomial	Strict Boolean Comparison
Looping and Control

Symbolics
Comparing the Hypergeom, Mhyper, and Fhyper Symbolic Functions	Factoring and Expanding Expressions	Symbolic Elliptic Integral Functions
Example: Dirac Delta (Unit Impulse) and LambertW Functions	Fourier Transform Pairs	Symbolic Integral Functions
Demonstrating Symbolic Functions	Simplifying and Rewriting Expressions	Symbolic Solutions of Equations
Displaying Explicit Values	Symbolic Calculus I	Symbolic Transforms
Explicit Calculation	Symbolic Calculus II	Working with Sine and Cosine Integral Symbolic Functions

Functions

Data Analysis
Curve Fitting	Interpolation and Prediction	Outliers and NaN
Exponential Regression	Cubic Spline Interpolation	Grubbs' Method for Detecting Outliers
Fitting a Model Function to Data	Least-Square Spline	Interquartile Range Method for Detecting Outliers
Linear Combination of Functions	Linear Interpolation	NaN Detection and Removal
Linear Regression	Linear Prediction 1	Outlier Detection
Logarithmic Regression	Linear Prediction 2	Outlier Removal
Logistic Regression	Polynomial Interpolation	Smoothing
Median-Median Regression	Thiele Interpolation	Adaptive Smoothing
Nonlinear Regression 1	Using Units with the Polynomial Interpolation Functions	Data Smoothing
Nonlinear Regression 2	Principal Component Analysis	Kernel Smoothing
Piecewise Quadratic Fitting	Principal Component Analysis 1	Median Smoothing
Power Regression	Principal Component Analysis 2	Smoothing of X-Y Data
Rational Function Regression 1		Smoothing Time Series
Rational Function Regression 2
Sinusoidal Regression
Thiele Interpolation and Regression

Design of Experiments
Factor Screening	Regression Analysis	Monte Carlo Simulation
1 Factor ANOVA	Identifying Influential Observations	Monte Carlo Simulation
ANOVA and Blocking	Multiple Regression Predictor Retention Analysis
ANOVA for Unreplicated Factorials	Quality of Fit
Calculating Effects	Residual Analysis
De-aliasing Factors	Second-Order Response Surface
Determining Optimal Conditions
Interactions

Finance	Graphing
Finance Functions	Converting a Spherical Data Set into Cartesian Coordinates	Using CreateSpace and CreateMesh
	Converting Rectangular Coordinates to Polar Coordinates	Working with Polar Angles
	Parametric Curves in 2D Plots

Image Processing
Understanding the Packed Image Matrices
Image Color Tools	Image Manipulation	Combinations of Images
Grayscale and Color in Images	Addition and Measurement of Noise	Blending and Masking
HLS and HSV Color Systems	Binarization and Quantization	Boolean Operations
Television Image Color Standards	Equalization	Replacing a Part of an Image
Tools for Packed Matrices	Function and Level Mapping	Convolution and Filters
Geometric Transforms	One-Dimensional and Two-Dimensional Histograms	Median and Quantile Filtering
Flipping Images	Scaling and Clipping	Smoothing
Rotating Images	Thresholding and Inversion	Wiener Filtering
Translating Images	Transform Domain	Edge Finders
Zooming and Scaling	Centering a Transformed Image	Canny Edge Detector
Morphological Processing	Discrete Cosine Transform	Convolution and Comparison Edge Finders
Grayscale Morphology	Filtering in the Fourier Transform Domain	Convolution Edge Finders
Thinning and Skeletonization	Wavelet Transform Filtering	Row and Column Gradients
Feature Extraction	Segmentation
Connected Component Labeling	Region Growing
Convex Hull
Euclidean Distance Transform
Moment Invariants
Shape Features

Reading and Writing Files
Data	Images	Sound
Read and Write CSV Files	Separating and Combining Red, Green, and Blue from an Image	Explaining Overlap When Converting Vector to Matrix
Reading and Writing Data Files	Using READRGB and READBMP	Working with WAV Files and Creating Spectrograms
Working with PRN Files	Using HLS and HSV Color Systems File Access Functions	Signal Generation

Signal Processing
Signals and Systems	Digital Filtering	Additional Transforms
Elementwise Phase	Filter Gain	The Hartley Transform
Noise Generators	FIR Filter Design	The Hilbert Transform
Quantizing a Signal	FIR Filters by Remez Exchange	Time Series Analysis
Signals and Classification of Signals	IIR Filter Design	Correlation and Partial Autocorrelation
Spectral Analysis	Interpolation and Sampling	Linear Detrending
Cepstrum and Complex Cepstrum	Time Response of Digital Filters	Linear Prediction Methods
Chirp z-Transform	Zero-Phase Filtering
Signal Windowing	Joint Time-Frequency Analysis
Spectral Analysis	The Short-Time Fourier Transform

Solving and Optimization
Parametrizing Solutions	Damped Harmonic Oscillation in Circuits	Root and Linear System Solvers
Solving a First-Order ODE Initial Value Problem	Heat Flow on a Square Plate - I	Finding the Roots of a Polynomial
Solving a Linear System of Equations	Heat Flow on a Square Plate - II	Solving an Equation in a Single Unknown
Differential Equation Solvers	State Space Solver	Solve Block Functions
Augmented Jacobian for Stiffb and Stiffr	The Jacob Function	Solving a First-Order System of ODEs

Special
Bessel
Airy Functions	Kelvin Functions	Gamma Functions
Bessel Functions	Modified Bessel Functions of the First Kind	Polynomial Functions
Bessel Functions of the First Kind	Modified Bessel Functions of the Second Kind	Using the Kronecker Built-in Function
Bessel Functions of the Second Kind	Other Special Functions	Piecewise Functions
Hankel Functions of the First and Second Kind	Error Functions	Piecewise Functions

Statistics
Descriptive Statistics	Probability Distributions
Location Estimators	Binomial and Negative Binomial Distributions	Seed for Random Number Generation
Confidence Interval for the Mean	Cauchy Distribution	T-Score of a Vector of Data
Hypothesis Test of a Normal Mean	Chi-Square Test for Goodness of Fit	T-Test on Normal Means
Variance and Standard Deviation	Gamma Distribution Functions	Z-Score of a Vector of Data
Computing Standard Errors	Geometric and Hypergeometric Distribution Functions	Graphical Statistics
Kurtosis and Skewness	Generating Random Numbers	Histograms
F-Test	Log Normal Distribution Functions	Quantile-Quantile Plots
Covariance and Correlation Coefficient	Monte Carlo Probability Estimation	Combinatorial Analysis
Correlation and Contingency Tables	Probability Density and Cumulative Probability Distribution	Finding Digits and Improving Result Precision
	Probability Distributions	Combinations and Permutations

Transforms and Filters
dft and idft of a Matrix	Filtering in the Frequency Domain	Local Cosine Transform
dft and idft of a Vector	Filtering Versus Exponential Smoothing	Lowpass Filtering Using dftr
DFT of Complex Functions	Forward Transform dft	The Inverse Transformation idft
Filtering an Image	Introduction to FFTs	Wavelet Transforms

Trigonometric, Log and Exponential	Utility
Inverse Trigonometric Functions	Explaining the SIUnitsOf(x) Function	Truncation and Roundoff Functions
Trigonometric Identities	Finding Minima and Maxima of an Array	Unit Conversion Using SIUnitsOf
Hyperbolic and Inverse Hyperbolic Functions	String Variable Manipulation	Using Complex Number Functions

Miscellaneous Functions
Converting Feet-Inches-Fractions to Length	Converting Radians to Deg-Min-Sec
Converting hhmmss to Time	Working with Temperatures

Vector and Matrix
Array Characteristics	Creating and Subdividing Arrays	Other Array Functions
Covariance and Principal Component Analysis	Creating Logarithmically Spaced Points Vectors	2D Correlation and Prototype Matching
Downsampling a Vector	Inserting and Extracting Subarrays	Lookup Functions
Eigenvectors and Eigenvalues	Matrix Decomposition	Effect of TOL on Lookup Functions
Finding the Left and Right Eigenvectors	Cholesky Factorization of Complex Matrices	Ranking and Ordering Vectors
Using genvals and genvecs Built-in Functions	Cholesky Factorization of Real Matrices	Sorting Functions
Matrix Norm and Determinant Functions	LU Matrix Factorization	Deconvolution and Cross Correlation between Matrices
Combo Box	QR Matrix Factorization	Using the Comparison Option with the Lookup Functions
Using Combo Box	SVD Matrix Factorization	Effect of ORIGIN on Lookup Functions
		Effect of ORIGIN on non-Lookup Functions