- 1.1 Todo 3
- 1.2 Problems Not Sorted 5
- 2.1 Introduction 7
- 2.2 Numerical Values 7
- Constants and Other Stuff 7
- Factorial 9
- Significant Figures 9
- Scientific and Engineering Notations 10
- 2.3 Complex Numbers 11
- 2.4 Units and Conversions 12
- How to Use Units 12
- SI Units 13
- A Table 14
- 2.5 Problems 18
- 3.1 The Fundamentals 20
- Basic Operations 20
- Exponents 21
- Basic Polynomials 22
- 3.2 Special Forms 24
- Completing the Square 24
- Newton-Raphson to Find Roots 25
- 3.3 Complex Numbers 26
- 3.4 Equality and Inequality 29
- 3.5 Functions 31
- 3.6 Special Functions 32
- Logarithms 32
- 3.7 Solving Systems of Linear Equations 33
- Substitution 34
- Addition 34
- 3.8 Simplifying Polynomial Expressions 35
- Partial Fractions 35
- Summation and Series 38
- 3.9 Limits 40
- 3.10 Problems 40
- 3.11 Challenge Problems 44
- 4.1 Introduction 46
- Functions 47
- Inverse Functions 50
- Triangles 51
- Relationships 52
- Hyperbolic Functions 54
- Special Relationships 55
- Planes, Lines, etc. 56
- 4.2 Coordinate Systems 58
- Cylindrical Coordinates 58
- Spherical Coordinates 59
- 4.3 Problems 60
- 5.1 Introduction 64
- Dot (Scalar) Product 65
- Cross Product 70
- 5.2 Problems 72
- 6.1 Introduction 73
- Basic Matrix Operations 74
- Determinants 76
- Transpose 77
- Adjoint Matrices 77
- Inverse Matrices 78
- Identity Matrix 79
- Eigenvalues 79
- Eigenvectors 79
- 6.2 Matrix Applications 79
- Solving Linear Equations with Matrices 79
- Gauss-Jordan Row Reduction 82
- Cramer's Rule 83
- Triple Product 85
- Gauss-Siedel 85
- 6.3 Problems 85
- 7.1 Introduction 88
- 7.2 Graphing Functions 89
- 7.3 LOG Plots 90
- 7.4 Multiple Plots 90
- 7.5 Other Items of Interest 91
- 7.6 Problems 91
- 7.7 Challenge Problem 92
- 8.1 Overview 93
- 8.2 Introduction 93
- 8.3 Examples 96
- 8.4 Summary 100
- 8.5 Problems 100
- 8.6 Challenge Problems 100
- 9.1 Introduction 101
- 9.2 Permutations 101
- 9.3 Combinations 102
- 9.4 Probability 103
- 9.5 Problems 105
- 10.1 Introduction 108
- 10.2 Data Distributions 109
- Histograms 110
- 10.3 Discrete Distributions 112
- Normal Distribution 112
- Hypergeometric Distribution 112
- Binomial Distribution 113
- Poisson Distribution 116
- 10.4 Other Distributions 118
- Polynomial Expansions 118
- Discrete and Continuous Probability Distributions 118
- 10.5 Continuous Distributions 119
- Describing Distribution Centers With Numbers 120
- Dispersion As A Measure of Distribution 121
- The Shape of the Distribution 123
- Kurtosis 124
- Generalizing From a Few to Many 125
- The Normal Curve 126
- Probability plots 127
- 10.6 Problems 129
- 10.7 Challenege Problems 130
- 11.1 Introduction 131
- 11.2 Component Failure Rates 132
- 11.3 Serial System Reliabilty 138
- 11.4 Parallel System Reliability 139
- 11.5 Formal Analysis Techniques 141
- Failure Modes and Effects Analysis (FMEA) 141
- 11.6 References and Bibliography 143
- 11.7 Problems 143
- 12.1 Introduction 145
- 12.2 Derivatives 145
- 12.3 Integrals 149
- Integration Examples 154
- 12.4 Vectors 155
- 12.5 Numerical Tools 157
- Approximation of Integrals and Derivatives from Sampled Data 157
- Centroids and Moments of Inertia 158
- 12.6 Problems 158
- 13.1 Introduction 163
- 13.2 Explicit Solutions 164
- 13.3 Responses 178
- First-order 179
- Second-order 185
- Other Responses 190
- 13.4 Response Analysis 193
- 13.5 Non-Linear Systems 195
- Non-Linear Differential Equations 196
- Non-Linear Equation Terms 200
- Changing Systems 203
- 13.6 Case Study 209
- 13.7 Summary 213
- 13.8 Problems 213
- 13.9 Problems Solutions 218
- 13.10 Challenge Problems 224
- 14.1 Introductions 225
- 14.2 Examples 225
- 14.3 Summary 225
- 14.4 References/Bibliography 225
- 14.5 Problems 226
- 14.6 Challenge Problems 226
- 15.1 Introduction 228
- 15.2 Examples 228
- 15.3 Summary 228
- 15.4 References/Bibliography 228
- 15.5 Problems 228
- 15.6 Challenege Problems 229
- 16.1 Introduction 231
- 16.2 Examples 231
- 16.3 Summary 231
- 16.4 References/Bibliography 231
- 16.5 Problems 231
- 17.1 Introduction 233
- 17.2 Examples 233
- 17.3 Summary 233
- 17.4 References/Bibliography 233
- 17.5 Problems 234
- 17.6 Challenege Problems 234
- 18.1 Introduction 236
- 18.2 Boolean Algebra 236
- 18.3 Logic Design 241
- Boolean Algebra Techniques 247
- 18.4 Common Logic Forms 248
- Complex Gate Forms 248
- Multiplexers 249
- 18.5 Simple Design Cases 250
- Basic Logic Functions 250
- Car Safety System 251
- Motor Forward/Reverse 252
- A Burglar Alarm 252
- 18.6 Summary 256
- 18.7 Problems 257
- 18.8 Problem Solutions 262
- 18.9 Challenge Problems 269
- 19.1 Introduction 270
- 19.2 Numerical Values 271
- Binary 271
- Boolean Operations 274
- Binary Mathematics 275
- Other Base Number Systems 279
- BCD (Binary Coded Decimal) 280
- 19.3 Data Characterization 280
- ASCII (American Standard Code for Information Interchange) 280
- Parity 283
- Checksums 284
- Gray Code 285
- 19.4 Summary 286
- 19.5 Problems 286
- 19.6 Problems Solutions 289
- 19.7 Challenge Problems 292
- 20.1 Laplace Transforms 293
- Laplace Transform Tables 294
- 20.2 z-Transforms 296
- 20.3 Fourier Series 299
- 20.4 Problems 299
- 20.5 Challenge Problems 300
- 21.1 Introduction 301
- Inertia 301
- 21.2 Problems 320
- Challenge Problems 320
- 22.1 Introduction 321
- 22.2 Problems 328
- 22.3 Challenge Problems 329
- 23.1 Introduction 330
- 23.2 System Modeling and Variable Identification 330
- 23.3 Cost Functions and Constraints 331
- 23.4 Single Variable Searches 335
- Example Problem 335
- 23.5 Multivariable Searches 341
- Algorithms 344
- Random Walk 344
- Gradient Decent 345
- Simplex 345
- 23.6 Summary 345
- 23.7 Problems 345
- 23.8 Challenge Problems 345
- 24.1 Introduction 347
- 24.2 Gantt Charts 347
- 24.3 Critical Path Method (CPM) 348
- 24.4 Program Evaluation and Review Technique (PERT) 350
- 24.5 Problems 351
- 24.6 Challenge Problems 352
- 25.1 Introduction 353
- 25.2 Data Structures 354
- 25.3 Applications 358
- Precedence Identification 358
- Graph Searching 359
- 25.4 Other Topics 360
- 25.5 Summary 361
- 25.6 Problems 361
- 25.7 Challenge Problems 361
- 26.1 Introduction 362
- 26.2 Data Structures 363
- 26.3 Applications 365
- Precedence Identification 365
- Tree Searching 366
- 26.4 Summary 368
- 26.5 Problems 368
- 26.6 Challenge Problems 368