Essential PTC Mathcad Prime 3.0 : a guide for new and … · · 2015-01-28PTC® Mathcad Prime ®...

Essential

PTC® Mathcad

Prime® 3.0A Guide for New and

Current Users

Brent Maxfield, P.E.

AMSTERDAM • BOSTON • HEIDELBERG • LONDON

NEW YORK • OXFORD • PARIS • SAN DIEGO

SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO

Academic Press is an imprint of Elsevier

@

Contents

Preface xvii

Acknowledgements xix

PART I BUILDING YOUR PTC MATHCAD TOOLBOX

CHAPTER 1 An Introduction to PTC® Mathcad Prime® 3.0 3

Before You Begin 3

PTC Mathcad Basics 4

Creating Simple Math Expressions 5

Grouping 6

Editing Expressions 9

Selecting Characters 9

Deleting Characters 9

Deleting and Replacing Operators 9

Modifying Expressions 10

PTC Mathcad Workspace 11

PTC Mathcad Button 12

Quick Access Toolbar 12

Open Worksheets Bar 12

Status Bar 12

Ribbon Bar 12

Math Tab 12

Operators 12

Symbols 13

Constants 14

Summary of Equal Signs 14

Regions 14

Math Regions 15

Text Regions 15

Plot Regions 15

Functions 16

Built-in Functions 16

User-defined Functions 17

Units 17

Assigning Units to Numbers 17

Evaluating and Displaying Units 19

Arrays and Subscripts 20

Creating Arrays 20

ORIGIN 21

vi Contents

Subscripts 22

Range Variables 26

Plotting - X-Y Plots 26

Plots Tab 26

Setting Plotting Ranges 28

Programming, Symbolic Calculations, Solving and Calculus 29

Getting Started Tab 32

Summary 32

Practice 33

CHAPTER 2 PTC® Mathcad Prime® 3.0 for Current

Mathcad 15 Users 35

Differences to Become Accustomed to 35

Tab Key 35

Extra Spacebar 36

Editing Expressions 36

Creating Text Boxes 36

Literal Subscripts 36

Page Breaks 37

Regions to the Right of the Right Margin Do Not Print 37

Units 37

Creating a Range Variable 38

Single Quote Does Not Add Parentheses 38

Highlighting Regions 38

Exciting New Features in PTC Mathcad Prime 39

Labels 39

Ribbon Bar 39

Open Worksheets Bar 39

Status Bar 40

Ability to "pin" a Worksheet on the RecentlyUsed Worksheets List 40

Remove Empty Space 40

Mixed Units in Arrays 40

Operators 40

Features from Mathcad 15 that Are Not in Mathcad

Prime 3.0 40

Summary 41

CHAPTER 3 Variables and Regions 43

Variables 43

Types of Variables 43

Rules for Naming Variables 43

Case and Font 43

Characters That Can Be Used in Variable Names 45

Contents

Literal Subscripts 45

Special Text Mode 46

String Variables 47

Why Use Variables 48

Regions 50

Understanding the Difference Between "activate" and

"select" 50

Selecting and Moving Regions 51

Separating Regions 51

Text Regions 51

Changing Font Characteristics 52

Controlling the Width of a Text Box 53

Paragraph Properties 53

Areas 53

Additional Information About Math Regions 54

Math Regions in Text Regions 54

Math Regions That Do Not Calculate 54

Find and Replace 55

Find 55

Replace 56

Inserting and Deleting Lines ..58

Page View and Page Breaks 58

View 59

Gridlines 60

Page Breaks 60

Summary 61

Practice 61

CHAPTER 4 Simple Functions 63

Built-in Functions 63

Labels 67


Assigning the "Function" Label to User-defined

Functions 68

Why Use User-defined Functions? 70

Using Multiple Arguments 71

Variables in User-defined Functions 71

Examples of User-defined Functions 75

Passing a Function to a Function 76

Warnings 77

Engineering Examples 81

Engineering Example 4.1: Column Buckling 81

Engineering Example 4.2: Torsional Shear Stress 82

Summary 83

Practice 83

viii Contents

CHAPTER 5 Units! 85

Introduction 86

Definitions 86

Changing the Default Unit System 87

Using and Displaying Units 87

Derived Units 90

Custom Default Unit System 91

Units of Force and Units of Mass 92

Creating Custom Units 93

Units in Equations 95

Using Labels to Distinguish Between Variables

and Units 97

Units in User-defined Functions 99

Units in Empirical Formulas 100

SIUnitsOf(x) 101

Unit Scaling Functions 105

Fahrenheit and Celsius 105

Change in Temperature 106

Degrees Minutes Seconds (DMS) 109

Hours Minutes Seconds {hhmmss) 110

Feet Inch Fraction (FIF) 113

Money 114

Dimensionless Units 114

Using the Unit Placeholder for Scaling 117

Summary 118

Practice 118

PART II HAND TOOLS FOR YOUR PTC MATHCAD TOOLBOX

CHAPTER 6 Arrays, Vectors, and Matrices 123Review of Chapter 1 123

Tables 124

Range Variables 127

Range Variables vs. Vectors 127

Converting a Range Variable to a Vector 128

Using Range Variables to Create Arrays 128

Using Units in Range Variables 132

Calculating Increments from the Beginning and EndingValues 134

Displaying Arrays 134

Displaying and Resizing a Large Matrix 137

Show/Hide Indices 139

Using Units with Arrays 141

Contents ix

Calculating with Arrays 144

Addition and Subtraction 144

Multiplication 144

Division 148

Array Functions 149

Creating Array Functions 149

Size Functions 151

Lookup Functions 151

Extracting Functions and Operators 154

Sorting Functions 156

PTC Mathcad Calculation Summary 156


Engineering Example 6.1: Using Vectors

in a User-defined Function 157

Engineering Example 6.2: Using Vectors in Expressions... 158

Engineering Example 6.3: Using Matrices in Functions

and Expressions 159

Engineering Example 6.4: Comparison of Using RangeVariables and Vectors 160

Summary 161

Practice 161

CHAPTER 7 Selected PTC Mathcad Functions 163

Review of Built-in Functions 164

Selected Functions 164

max and min Functions 164

mean and median Functions 166

Truncation and Rounding Functions 168

Summation Operator 178

(/"Function 185

linterp Function 186

Miscellaneous Categories of Functions 190

Curve Fitting, Regression, and Data Analysis 190

Error Function 190

String Functions 191

Picture Functions and Image Processing 191

Complex Numbers, Polar Coordinates, and MappingFunctions 191

Mapping Functions 192

Polar Notation 192

Angle Functions 192

Reading from and Writing to Files 192

Summary 195

Practice 196

X Contents

CHAPTER 8 Plotting 199

Plots Tab 199

Creating a Simple XY Plot 200

Creating a Simple Polar Plot 201

XY Plot Range and Tick Marks 204

Number of Points Plotted 207

Showing Only Points 207

Using Range Variables to Set Plot Domain 209

Polar Plot Range and Tick Marks 212

Graphing with Units 213

Formatting Plots 216

Axis Location 216

Location of Axis Placeholders 216

Markers 217

Formatting Plot Values 217

Logarithmic Scaling 218

Trace Styles 218

Labels 221

Graphing Multiple Functions 221

Scale Factors 224

Plotting Data Points 224

Range Variables 224

Data Vectors 230

Error Plots 233

Parametric Plotting 234

Trace and Zoom 235

Plotting over a Log Scale 236

Plotting a Family of Curves 238

3D Plots and Contour Plots 240

3D Plots 240

Contour Plots 250


Engineering Example 8.1 253


Summary 259

Practice 259

CHAPTER 9 Simple Logic Programming 263

Introduction to the Programming Toolbar 263

Creating a Simple Program 264

Use of else j/and also if Operators 268

Local Assignment 276

Return Operator 277

Boolean Operators 279

Contents xi

Adding Lines to a Program 284

Using Conditional Programs to Make and DisplayConclusions 287




Summary 294

Practice 294

PART III POWER TOOLS FOR YOUR PTC MATHCAD

TOOLBOX

CHAPTER 10 Introduction to Symbolic Calculations 297

Getting Started with Symbolic Calculations 297

Keywords and Modifiers 298

Float 303

Solve 305

Explicit 309

Assume 311

Fully 311

Using 315

Solving a System of Equations 316

Expand, Simplify, and Factor 318

Coeffsand Collect 320

Substitute 322

Combine and Rewrite 322

Series 326

Explicit 327

Using More than One Keyword 330

Units with Symbolic Calculations 332

Additional Topics to Study 336

Summary 336

Practice 336

CHAPTER 11 Solving Engineering Equations 339

Root Function 340

Polyroots Function 343

Solve Blocks 345

Isolve Function 349

Solve Blocks using Maximize and Minimize 351

TOL, CTOL, and Minerr 351

Using Units 353

xii Contents


Engineering Example 11.1: Object in Motion 354

Engineering Example 11.2: Electrical Network 357

Engineering Example 11.3: Pipe Network 358

Engineering Example 11.4: Chemistry 361

Engineering Example 11.5: Determining the Flow

Properties of a Circular Pipe Flowing Partially Full 364

Engineering Example 11.6: Box Volume 365

Engineering Example 11.7: Maximize Profit 366

Summary 368

Practice 368

CHAPTER 12 Advanced Programming 369

Local Definition 369

Looping 371

For Loops 371

While Loops 375

Break and Continue Operators 379

Return Operator 380

Try-On Error Operator 381


Summary 397

Practice 397

CHAPTER 13 Calculus and Differential Equations 399

Differentiation 399

Integration 407

Differential Equations 411

Ordinary Differential Equations (ODEs) 411

Partial Differential Equations (PDEs) 417




Practice 433

PART IV CREATING AND ORGANIZING YOUR ENGINEERINGCALCULATIONS WITH PTC MATHCAD

CHAPTER 14 Putting It All Together 437Introduction 437

Guidelines for Naming Variables 437

Naming Guideline 1 438



Contents xiii



PTC Mathcad Toolbox 440

Variables 440

Editing 440


Units! 441

PTC Mathcad Settings 441

Customizing PTC Mathcad with Templates 441

Hand Tools 441

Power Tools 442

Let's Start Building 442

What is Ahead 442

Summary 443

Practice 443

CHAPTER 15 PTC Mathcad Settings 445

PTC Mathcad Options 445

Enable Getting Started Tab 445

Enable PTC Places 447

Set the Path for Accessing Help at an Alternate

Location 447

Disable Quality Agent Reporting 447

Show PTC Mathcad News and Information 447

Specify an Alternate Folder for My Templates 447

Specify an Alternate Folder for Shared Templates 447

Use an Alternate Template When CreatingNew Worksheets 447

Ribbon Bar Settings 448

Math Tab 448

Matrices/Tables Tab 449

Plots Tab 450

Math Formatting Tab 450

Results Format 451

Show Trailing Zeros 452

Display Precision 453

Complex Values 455

Calculation Tab 455

Controls 456

Worksheet Settings 456

Document Tab 459

Page 459

View 460

Summary 461

Practice 461

xiv Contents

CHAPTER 16 Customizing PTC Mathcad 463

Styles 463

Math Formatting and Label Styles 464

Differentiating Between Variables with the Same Name....466

Applying Labels to User-defined Functions 468

Changing Label Styles 468

Math Font Changes: Region Specific Verses Global

Changes 470

Text Formatting 472

Headers and Footers 472

Creating Headers and Footers 473

Information to Include in Headers and Footers 474

Examples 475

Margins 476

Quick Access Toolbar Customization 476

Summary 477

Practice 477

CHAPTER 17 Templates 479

Information Saved in a Template 479

PTC Mathcad Templates 480

Review of Chapters 5, 15, and 16 481

Creating Templates 481

Where Are Templates Stored? 482

Creating Your Customized Template 483

EM Metric 483

Document Tab 483

Math Tab 485

Math Formatting Tab '. 485

Text Formatting Tab 486

Calculation Tab 487

EM US 489

Alternate Default Template 489

Summary 490

Practice 490

CHAPTER 18 Assembling Calculations from Standard

Calculation Worksheets 491

Copying Regions from Other PTC Mathcad Worksheets 492

Creating Standard Calculation Worksheets 492

Protecting Information 493

Potential Problems with Inserting Standard Calculation

Worksheets and Recommended Solutions 493

Guidelines 494

How to Use Redefined Variables in Project Calculations 495

Contents

Resetting Variables 499

Using User-defined Functions in Standard Calculation

Worksheets 502

Using the Include Feature 504

When to Separate Project Calculation Files 505

Summary 505

Practice 506

CHAPTER 19 Microsoft® Excel Component 507Introduction 507

Excel Component Block 508

Input Context 509

Excel Component Table 509

Output Context 509

Simple Example 510

Inputs and Outputs 511

Inputs 511

Outputs 511

Hiding Inputs and Outputs 516

Important Concepts 517

Opening, Closing, and Saving Excel 517

Input Values Have Precedence 517

What Displays in the Component Table 517

Dealing with Empty Cells 519

Inputs and Outputs Do Not Track Excel Changes 519

Existing Spreadsheets 523

Using Units with Excel 523

Input 523

Printing the Excel Component 526

Summary 527

Practice 527

CHAPTER 20 Conclusion 529

Advantages of PTC Mathcad 529

Creating Project Calculations 529

Additional Resources 530

Conclusion 530

Appendix 1: PTC® Mathcad Prime® 3.0 Keyboard Shortcuts 533

Appendix 2: Keyboard Shortcuts for Editing and Worksheet Management 541

Appendix 3: Greek Letters 543

Appendix 4: Built-in Constants and Variables 545

Appendix 5: Reference Tables 549

Index .' 553

Essential PTC Mathcad Prime 3.0 : a guide for new and … · · 2015-01-28PTC® Mathcad Prime ®...

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Transcript of Essential PTC Mathcad Prime 3.0 : a guide for new and … · · 2015-01-28PTC® Mathcad Prime ®...