Essential Math Skills for Engineers | by Clayton R. Paul | 2009 | ISBN: 9780470405024. Mathematics Books. Math Skills Training. Partial Differential Equations. Fourier Series and Fourier Transform. Mathematics of Vectors. Linear, Constant-Coefficient, Difference Equations

January 6, 2010 by kutenk
Filed under: Engineering Books 

Essential Math Skills for Engineers

by Clayton R. Paul
2009 (231 pages)
ISBN:9780470405024

Logically grouped into categories for easy learning and long-term retention, this book 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 of engineering.

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Essential Math Skills for Engineers







Preface
Chapter 1 – What Do Engineers Do?
Chapter 2 – Miscellaneous Math Skills
OVERVIEW
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
2.8: COMPLEX NUMBERS AND ALGEBRA, AND EULER’S IDENTITY
2.9: COMMON DERIVATIVES AND THEIR INTERPRETATION
2.10: COMMON INTEGRALS AND THEIR INTERPRETATION
2.11: NUMERICAL INTEGRATION




Chapter 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

Chapter 4 – Solution of Linear, Constant-Coefficient, Ordinary Differential Equations
4.1: HOW TO IDENTIFY LINEAR, CONSTANT-COEFFICIENT, ORDINARY DIFFERENTIAL EQUATIONS
4.2: WHERE THEY ARISE: THE MEANING OF A SOLUTION
4.3: SOLUTION OF FIRST-ORDER EQUATIONS
4.4: SOLUTION OF SECOND-ORDER EQUATIONS
4.5: STABILITY OF THE SOLUTION
4.6: SOLUTION OF SIMULTANEOUS SETS OF ORDINARY DIFFERENTIAL EQUATIONS WITH THE DIFFERENTIAL OPERATOR
4.7: NUMERICAL (COMPUTER) SOLUTIONS

Chapter 5 – Solution of Linear, Constant-Coefficient, Difference Equations
5.1: WHERE DIFFERENCE EQUATIONS ARISE
5.2: HOW TO IDENTIFY LINEAR, CONSTANT-COEFFICIENT, DIFFERENCE EQUATIONS
5.3: SOLUTION OF FIRST-ORDER EQUATIONS
5.4: SOLUTION OF SECOND-ORDER EQUATIONS
5.5: STABILITY OF THE SOLUTION
5.6: SOLUTION OF SIMULTANEOUS SETS OF DIFFERENCE EQUATIONS WITH THE DIFFERENCE OPERATOR

Chapter 6 – Solution of Linear, Constant-Coefficient, Partial Differential Equations
6.1: COMMON ENGINEERING PARTIAL DIFFERENTIAL EQUATIONS
6.2: THE LINEAR, CONSTANT-COEFFICIENT, 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

Chapter 7 – The Fourier Series and Fourier Transform
OVERVIEW
7.1: PERIODIC FUNCTIONS
7.2: THE FOURIER SERIES
7.3: THE FOURIER TRANSFORM



Chapter 8 – The Laplace Transform
OVERVIEW
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




Chapter 9 – Mathematics of Vectors
OVERVIEW
9.1: VECTORS AND COORDINATE SYSTEMS
9.2: THE LINE INTEGRAL
9.3: THE SURFACE INTEGRAL
9.4: DIVERGENCE
9.5: CURL
9.6: THE GRADIENT OF A SCALAR FIELD

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