Essential PTC Mathcad Prime 3.0 A 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 Acknowledgements xvii 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
X-Y vi Contents Subscripts 22 Range Variables 26 - Plotting 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 Recently Used 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 Why Use Variables 48 Variables 47 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 User-defined Functions 68 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 123 Review 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 Ending Values 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 Examples 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 Range Variables 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 Mapping Functions 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 Examples 253 Engineering Example 8.1 253 Engineering Example 8.2 254 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 Display Conclusions 287 Engineering Examples 289 Engineering Example 9.1 289 Engineering Example 9.2 292 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 Examples 353 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 Engineering Example 12.1 383 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 Engineering Examples 417 Engineering Example 13.1 417 Engineering Example 13.2 423 Practice 433 PART IV CREATING AND ORGANIZING YOUR ENGINEERING CALCULATIONS WITH PTC MATHCAD CHAPTER 14 Putting It All Together 437 Introduction 437 Guidelines for Naming Variables 437 Naming Guideline 1 438 Naming Guideline 2 438 Naming Guideline 3 439
Contents xiii Naming Guideline 4 439 Naming Guideline 5 440 PTC Mathcad Toolbox 440 Variables 440 Editing 440 User-defined Functions 441 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 Creating New 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 507 Introduction 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