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1. PREFACE 3
1.1 Todo 3
1.2 Problems Not Sorted 5
2. NUMERICAL VALUES AND UNITS 7
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. ALGEBRA 20
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. TRIGONOMETRY 46
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. VECTORS 64
5.1 Introduction 64
Dot (Scalar) Product 65
Cross Product 70
5.2 Problems 72
6. MATRICES 73
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. GRAPHING 88
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. PROGRAMMING 93
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. PERMUTATIONS AND COMBINATIONS 101
9.1 Introduction 101
9.2 Permutations 101
9.3 Combinations 102
9.4 Probability 103
9.5 Problems 105
10. STATISTICS 108
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. RELIABILITY 131
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. CALCULUS 145
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. ANALYSIS OF DIFFERENTIAL EQUATIONS 163
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. ELECTRICAL AND COMPUTER ENGINEERING REVIEW 225
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. MECHANICAL ENGINEERING REVIEW 228
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. INDUSTRIAL ENGINEERING OVERVIEW 231
16.1 Introduction 231
16.2 Examples 231
16.3 Summary 231
16.4 References/Bibliography 231
16.5 Problems 231
17. PRODUCT DESIGN AND MANUFACTURING REVIEW 233
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. BOOLEAN LOGIC DESIGN 236
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. NUMBERS AND DATA 270
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. TRANSFORMS 293
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. GEOMETRY 301
21.1 Introduction 301
Inertia 301
21.2 Problems 320
Challenge Problems 320
22. FINANCIAL 321
22.1 Introduction 321
22.2 Problems 328
22.3 Challenge Problems 329
23. OPTIMIZATION 330
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. PROJECT SCHEDULING 347
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. DIRECTED GRAPHS 353
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. TREE DATA STRUCTURES 362
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
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