Clayton R. Paul

Essential Math Skills for Engineers

• Broschiertes Buch

Produktbeschreibung

Review of Essential Math Skills is based on the idea that in order to be a good engineer, one must also be a very good applied mathematician. This book offers the solid and basic math skills that all engineers and students of engineering need to have at their fingertips for immediate and day-to-day use. Topics covered include: solution of simultaneous, linear, algebraic equations, solution of linear, constant coefficient ordinary differential equations, solution of linear, constant coefficient difference equations, solution of linear, and constant coefficient partial differential equations.

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Just the math skills you need to excel in the study or practice of engineering

Good 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 calculus
Simultaneous, linear, algebraic equations
Linear, constant-coefficient, ordinary differential equations
Linear, constant-coefficient, difference equations
Linear, constant-coefficient, partial differential equations
Fourier series and Fourier transform
Laplace transform
Mathematics of vectors

With 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.

Produktdetails

• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 248
• Erscheinungstermin: 3. April 2009
• Englisch
• Abmessung: 234mm x 156mm x 14mm
• Gewicht: 412g
• ISBN-13: 9780470405024
• ISBN-10: 0470405023
• Artikelnr.: 26010035

Autorenporträt

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.

Inhaltsangabe

Preface. 1 What Do Engineers Do? 2 Miscellaneous Math Skills. 2.1 Equations
of Lines, Planes, and Circles. 2.2 Areas and Volumes of Common Shapes. 2.3
Roots of a Quadratic Equation. 2.4 Logarithms. 2.5 Reduction of Fractions
and Lowest Common Denominators. 2.6 Long Division. 2.7 Trigonometry. 2.7.1
The Common Trigonometric Functions: Sine, Cosine, and Tangent. 2.7.2 Areas
of Triangles. 2.7.3 The Hyperbolic Trigonometric Functions: Sinh, Cosh, and
Tanh. 2.8 Complex Numbers and Algebra, and Euler's Identity. 2.8.1 Solution
of Differential Equations Having Sinusoidal Forcing Functions. 2.9 Common
Derivatives and Their Interpretation. 2.10 Common Integrals and Their
Interpretation. 2.11 Numerical Integration. 3 Solution of Simultaneous,
Linear, Algebraic Equations. 3.1 How to Identify Simultaneous, Linear,
Algebraic Equations. 3.2 The Meaning of a Solution. 3.3 Cramer's Rule and
Symbolic Equations. 3.4 Gauss Elimination. 3.5 Matrix Algebra. 4 Solution
of Linear, Constant-Coeffi cient, Ordinary Differential Equations. 4.1 How
to Identify Linear, Constant-Coeffi cient, Ordinary Differential Equations.
4.2 Where They Arise: The Meaning of a Solution. 4.3 Solution of
First-Order Equations. 4.3.1 The Homogeneous Solution. 4.3.2 The Forced
Solution for "Nice" f(t). 4.3.3 The Total Solution. 4.3.4 A Special Case.
4.4 Solution of Second-Order Equations. 4.4.1 The Homogeneous Solution.
4.4.2 The Forced Solution for "Nice" f(t). 4.4.3 The Total Solution. 4.4.4
A Special Case. 4.5 Stability of the Solution. 4.6 Solution of Simultaneous
Sets of Ordinary Differential Equations with the Differential Operator.
4.6.1 Using the Differential Operator to Verify Solutions. 4.7 Numerical
(Computer) Solutions. 5 Solution of Linear, Constant-Coeffi cient,
Difference Equations. 5.1 Where Difference Equations Arise. 5.2 How to
Identify Linear, Constant-Coeffi cient Difference Equations. 5.3 Solution
of First-Order Equations. 5.3.1 The Homogeneous Solution. 5.3.2 The Forced
Solution for "Nice" f(n). 5.3.3 The Total Solution. 5.3.4 A Special Case.
5.4 Solution of Second-Order Equations. 5.4.1 The Homogeneous Solution.
5.4.2 The Forced Solution for "Nice" f(n). 5.4.3 The Total Solution. 5.4.4
A Special Case. 5.5 Stability of the Solution. 5.6 Solution of Simultaneous
Sets of Difference Equations with the Difference Operator. 5.6.1 Using the
Difference Operator to Verify Solutions. 6 Solution of Linear,
Constant-Coeffi cient, Partial Differential Equations. 6.1 Common
Engineering Partial Differential Equations. 6.2 The Linear, Constant-Coeffi
cient, Partial Differential Equation. 6.3 The Method of Separation of
Variables. 6.4 Boundary Conditions and Initial Conditions. 6.5 Numerical
(Computer) Solutions via Finite Differences: Conversion to Difference
Equations. 7 The Fourier Series and Fourier Transform. 7.1 Periodic
Functions. 7.2 The Fourier Series. 7.3 The Fourier Transform. 8 The Laplace
Transform. 8.1 Transforms of Important Functions. 8.2 Useful Transform
Properties. 8.3 Transforming Differential Equations. 8.4 Obtaining the
Inverse Transform Using Partial Fraction Expansions. 9 Mathematics of
Vectors. 9.1 Vectors and Coordinate Systems. 9.2 The Line Integral. 9.3 The
Surface Integral. 9.4 Divergence. 9.4.1 The Divergence Theorem. 9.5 Curl.
9.5.1 Stokes' Theorem. 9.6 The Gradient of a Scalar Field. Index.