Essential Math Skills for Engineers

Just the math skills you need to excel in the study or practice of engineeringGood math skills are indispensable for all engineers regardless of their specialty, yet only a relatively small portion of the math that engineering students study in college mathematics courses is used on a frequent basis in the study or practice of engineering. That's why Essential Math Skills for Engineers focuses on only these few critically essential math skills that students need in order to advance in their engineering studies and excel in engineering practice.Essential Math Skills for Engineers features concise, easy-to-follow explanations that quickly bring readers up to speed on all the essential core math skills used in the daily study and practice of engineering. These fundamental and essential skills are logically grouped into categories that make them easy to learn while also promoting their long-term retention. Among the key areas covered are:Algebra, geometry, trigonometry, complex arithmetic, and differential and integral calculusSimultaneous, linear, algebraic equationsLinear, constant-coefficient, ordinary differential equationsLinear, constant-coefficient, difference equationsLinear, constant-coefficient, partial differential equationsFourier series and Fourier transformLaplace transformMathematics of vectorsWith the thorough understanding of essential math skills gained from this text, readers will have mastered a key component of the knowledge needed to become successful students of engineering. In addition, this text is highly recommended for practicing engineers who want to refresh their math skills in order to tackle problems in engineering with confidence.

Clayton R. Paul, PhD, is the Sam Nunn Eminent Professor of Aerospace Systems Engineering in the Department of Electrical and Computer Engineering at Mercer University. He is also Emeritus Professor of Electrical Engineering at the University of Kentucky. Dr. Paul is the author or coauthor of fifteen electrical engineering textbooks and has published more than 200 technical papers. He is a Life Fellow of the Institute of Electrical and Electronics Engineers (IEEE). He was awarded the prestigious 2005 IEEE Electromagnetics Award and the prestigious 2007 IEEE Undergraduate Teaching Award.

Preface	p. xi
What Do Engineers Do?	p. 1
Miscellaneous Math Skills	p. 15
Equations of Lines, Planes, and Circles	p. 15
Areas and Volumes of Common Shapes	p. 21
Roots of a Quadratic Equation	p. 22
Logarithms	p. 23
Reduction of Fractions and Lowest Common Denominators	p. 24
Long Division	p. 26
Trigonometry	p. 27
The Common Trigonometric Functions: Sine, Cosine, and Tangent	p. 27
Areas of Triangles	p. 34
The Hyperbolic Trigonometric Functions: Sinh, Cosh, and Tanh	p. 36
Complex Numbers and Algebra, and Euler's Identity	p. 39
Solution of Differential Equations Having Sinusoidal Forcing Functions	p. 46
Common Derivatives and Their Interpretation	p. 48
Common Integrals and Their Interpretation	p. 51
Numerical Integration	p. 56
Solution of Simultaneous, Linear, Algebraic Equations	p. 59
How to Identify Simultaneous, Linear, Algebraic Equations	p. 59
The Meaning of a Solution	p. 60
Cramer's Rule and Symbolic Equations	p. 61
Gauss Elimination	p. 67
Matrix Algebra	p. 68
Solution of Linear, Constant-Coefficient, Ordinary Differential Equations	p. 83
How to Identify Linear, Constant-Coefficient, Ordinary Differential Equations	p. 83
Where They Arise: The Meaning of a Solution	p. 85
Solution of First-Order Equations	p. 86
The Homogeneous Solution	p. 87
The Forced Solution for "Nice" f(t)	p. 88
The Total Solution	p. 90
A Special Case	p. 94
Solution of Second-Order Equations	p. 96
The Homogeneous Solution	p. 96
The Forced Solution for "Nice" f(t)	p. 99
The Total Solution	p. 99
A Special Case	p. 102
Stability of the Solution	p. 105
Solution of Simultaneous Sets of Ordinary Differential Equations with the Differential Operator	p. 105
Using the Differential Operator to Verify Solutions	p. 110
Numerical (Computer) Solutions	p. 113
Solution of Linear, Constant-Coefficient, Difference Equations	p. 119
Where Difference Equations Arise	p. 119
How to Identify Linear, Constant-Coefficient Difference Equations	p. 122
Solution of First-Order Equations	p. 124
The Homogeneous Solution	p. 125
The Forced Solution for "Nice" f(n)	p. 125
The Total Solution	p. 127
A Special Case	p. 130
Solution of Second-Order Equations	p. 131
The Homogeneous Solution	p. 131
The Forced Solution for "Nice" f(n)	p. 134
The Total Solution	p. 134
A Special Case	p. 138
Stability of the Solution	p. 140
Solution of Simultaneous Sets of Difference Equations with the Difference Operator	p. 141
Using the Difference Operator to Verify Solutions	p. 144
Solution of Linear, Constant-Coefficient, Partial Differential Equations	p. 149
Common Engineering Partial Differential Equations	p. 149
The Linear, Constant-Coefficient, Partial Differential Equation	p. 150
The Method of Separation of Variables	p. 151
Boundary Conditions and Initial Conditions	p. 153
Numerical (Computer) Solutions via Finite Differences: Conversion to Difference Equations	p. 161
The Fourier Series and Fourier Transform	p. 169
Periodic Functions	p. 171
The Fourier Series	p. 174
The Fourier Transform	p. 181
The Laplace Transform	p. 187
Transforms of Important Functions	p. 188
Useful Transform Properties	p. 191
Transforming Differential Equations	p. 194
Obtaining the Inverse Transform Using Partial Fraction Expansions	p. 196
Mathematics of Vectors	p. 207
Vectors and Coordinate Systems	p. 207
The Line Integral	p. 211
The Surface Integral	p. 214
Divergence	p. 216
The Divergence Theorem	p. 218
Curl	p. 220
Stokes' Theorem	p. 223
The Gradient of a Scalar Field	p. 225
Index	p. 229
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Essential Math Skills for Engineers

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