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Fundamental Engineering Mathematics: A Student-Friendly Workbook

Fundamental Engineering Mathematics: A Student-Friendly Workbook

          
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About the Book

This student friendly workbook addresses mathematical topics using SONG - a combination of Symbolic, Oral, Numerical and Graphical approaches. The text helps to develop key skills, communication both written and oral, the use of information technology, problem solving and mathematical modelling. The overall structure aims to help students take responsibility for their own learning, by emphasizing the use of self-assessment, thereby enabling them to become critical, reflective and continuing learners – an essential skill in this fast-changing world. The material in this book has been successfully used by the authors over many years of teaching the subject at Sheffield Hallam University. Their SONG approach is somewhat broader than the traditionally symbolic based approach and readers will find it more in the same vein as the Calculus Reform movement in the USA.

Table of Contents:
About the Authors Foreword 1: Numbers, Graphics and Algebra 1.1 NUMBERS, GRAPHICS AND ALGEBRA 1.2 WHAT NUMBERS ARE 1.3 HOW NUMBERS (AND LETTERS) BEHAVE 1.4 FRACTIONS, DECIMALS AND SCIENTIFIC NOTATION 1.5 POWERS OR INDICES 1.6 ANGLE AND LENGTH - GEOMETRY AND TRIGONOMETRY END OF CHAPTER 1 - CALCULATOR ACTIVITIES – DO THESE NOW! 2: Linking Algebra and Graphics 1 2.1 ALGEBRA AND PICTURES 2.2 NUMBERS, LETTERS AND BRACKETS 2.3 “SPEAKING” ALGEBRA 2.4 ALGEBRAIC FRACTIONS 2.5 SOLVING SIMPLE EQUATIONS 2.6 CONNECTING STRAIGHT LINES AND LINEAR EXPRESSIONS 2.7 SOLVING LINEAR EQUATIONS GRAPHICALLY 2.8 TRANSPOSING FORMULAE 2.9 STRAIGHT LINES IN ENGINEERING 2.10 STRATEGIES FOR HANDLING LINEAR EQUATIONS AND GRAPHS END OF CHAPTER 2 - MIXED ACTIVITIES – DO THESE NOW! 3: Linking Algebra and Graphics 2 3.1 MORE ON CONNECTING ALGEBRA TO GRAPHS 3.2 QUADRATIC FUNCTIONS 3.3 SOLVING QUADRATIC EQUATIONS 3.4 AN ALGEBRAIC TRICK - COMPLETING THE SQUARE 3.5 A DIVERSION - MATCH THE GRAPHS WITH THE FUNCTIONS 3.6 STRATEGIES FOR HANDLING QUADRATIC FUNCTIONS 3.7 WHERE NEXT WITH POLYNOMIALS? END OF CHAPTER 3 ACTIVITY - DO THIS NOW! 4: Other Essential Functions 4.1 ESSENTIAL ENGINEERING FUNCTIONS 4.2 THE BASICS OF EXPONENTIALS AND LOGARITHMS 4.3 HOW THE EXPONENTIAL FUNCTION BERAYES 4.4 HOW THE LOGARITHM FUNCTION BEHAVES 4.5 THE BASICS OF TRIGONOMETRIC FUNCTIONS 4.6 INVERSE FUNCTIONS AND TRIGONOMETRIC EQUATIONS END OF CHAPTER 4 - MIXED ACTIVITIES! 5: Combining and Applying Mathematical Tools 5.1 USING YOUR TOOLBOX 5.2 THE MOST BASIC FUNCTION – THE STRAIGHT LINE 5.3 TRANSFORMATIONS OF GRAPHS 5.4 DECAYING OSCILLATIONS 5.5 A FOGGY FUNCTION 5.6 HEAT LOSS IN BUILDINGS – A MATHEMATICAL MODEL 6: Complex Numbers 6.1 THE NEED FOR COMPLEX NUMBERS 6.2 THE j NOTATION AND COMPLEX NUMBERS 6.3 ARITHMETIC WITH COMPLEX NUMBERS 6.4 GEOMETRY WITH COMPLEX NUMBERS: THE ARGAND DIAGRAM 6.5 CARTESIAN AND POLAR FORM, MODULUS AND ARGUMENT 6.6 EULER’S RELATIONSHIP AND EXPONENTIAL FORM 6.7 SOME USES OF POLAR AND EXPONENTIAL FORM 6.8 COMPLEX ALGEBRA 6.9 ROOTS OF COMPLEX NUMBERS 6.10 MINI CASE STUDY END OF CHAPTER 6 – MIXED EXERCISES – DO ALL THESE NOW! 7: Differential Calculus 1 7.1 THE NEED FOR DIFFERENTIAL CALCULUS 7.2 DIFFERENTIAL CALCULUS IN USE 7.3 WHAT DIFFERENTIATION MEANS GRAPHICALLY 7.4 VARIOUS WAYS OF FINDING DERIVATIVES 7.5 NUMERICAL DIFFERENTIATION 7.6 PAPER AND PENCIL APPROACHES TO DIFFERENTIATION 7.7 COMPUTER ALGEBRA SYSTEMS OR SYMBOL MANIPULATORS 8: Differential Calculus 2 8.1 DIFFERENTIAL CALCULUS: TAKING THE IDEAS FURTHER 8.2 SOLVING THE EXAMPLES FROM CHAPTER 7 8.3 HIGHER ORDER DERIVATIVES AND THEIR MEANING 8.4 FINDING MAXIMUM AND MINIMUM POINTS 8.5 PARAMETRIC DIFFERENTIATION 8.6 IMPLICIT DIFFERENTIATION 8.7 PARTIAL DIFFERENTIATION 8.8 AN ENGINEERING CASE STUDY END OF CHAPTER 8 EXERCISES – DO ALL THESE NOW! 9: Integral Calculus 1 9.1 THE NEED FOR INTEGRAL CALCULUS 9.2 INDEFINITE INTEGRATION AND THE ARBITRARY CONSTANT 9.3 USING A COMPUTER ALGEBRA SYSTEM TO MAKE A TABLE OF INTEGRALS 9.4 DEFINITE INTEGRATION AND AREAS 9.5 USING AREAS TO ESTIMATE INTEGRALS 9.6 APPROXIMATE INTEGRATION - THE TRAPEZIUM RULE AND SIMPSON’S RULE 9.7 PAPER AND PENCIL APPROACHES TO INTEGRATION END OF CHAPTER 9 - MIXED EXERCISES – DO ALL THESE NOW! 10: Integral Calculus 2 10.1 INTRODUCTION 10.2 INTEGRATION AS SUMMATION: MEAN AND RMS 10.3 INTEGRATION AS SUMMATION: CHARGE ACCUMULATION 10.4 INTEGRATION AS SUMMATION: VOLUME AND SURFACE AREA 10.5 A FIRST LOOK AT DIFFERENTIAL EQUATIONS END OF CHAPTER 10 EXERCISES - DO ALL OF THESE NOW! 11: Linear Simultaneous Equations 11.1 THE NEED FOR LINEAR SIMULTANEOUS EQUATIONS 11.2 WHERE SIMULTANEOUS EQUATIONS OCCUR – TWO EXAMPLES 11.3 SOLVING SIMULTANEOUS EQUATIONS GRAPHICALLY 11.4 SOLVING SIMULTANEOUS EQUATIONS WITH SIMPLE NUMBERS 11.5 SOLVING SIMULTANEOUS EQUATIONS ALGEBRAICALLY 11.6 SOLVING SIMULTANEOUS EQUATIONS USING TECHNOLOGY 11.7 EQUATIONS WITH NO UNIQUE SOLUTION - SINGULAR EQUATIONS 11.8 ILL CONDITIONED EQUATIONS 11.9 SOLVING THE “REAL” PROBLEMS END OF CHAPTER 11 - MIXED EXERCISES – DO THESE NOW! 12: Matrices 12.1 MATRICES: WHAT ARE THEY, AND WHY DO YOU NEED THEM? 12.2 ARITHMETIC AND ALGEBRAIC OPERATIONS WITH MATRICES 12.3 MATRICES AND TECHNOLOGY 12.4 MATRICES AND SIMULTANEOUS EQUATIONS – THE MATRIX INVERSE 12.5 MATRICES AND GEOMETRICAL TRANSFORMATIONS END OF CHAPTER 12 - MIXED EXERCISES - DO ALL THESE NOW! 13: More Linear Simultaneous Equations 13.1 LARGER SETS OF SIMULTANEOUS EQUATIONS 13.2 ELIMINATION METHODS: GAUSSIAN ELIMINATION 13.3 ITERATIVE METHODS 13.4 THE GAUSS-JORDAN METHOD 13.5 FINDING A MATRIX INVERSE BY THE GAUSS-JORDAN METHOD 13.6 ENGINEERING CASE STUDY: HEATING AND COOLING 14: Vectors 14.1 INTRODUCTION 14.2 REPRESENTING VECTORS 14.3 THE ALGEBRA OF VECTORS 14.4 PRODUCTS OF VECTORS END OF CHAPTER 14 EXERCISES – DO ALL OF THESE NOW! 15: First Order Ordinary Differential Equations 15.1 INTRODUCTION 15.2 OVERVIEW 15.3 DIRECT INTEGRATION REVISITED 15.4 SOLUTION BY SEPARATION OF VARIABLES 15.5 ENGINEERING CASE STUDIES 15.6 NUMERICAL SOLUTION METHODS – THE EULER METHOD 15.7 EXPLORING THE PARAMETERS END OF CHAPTER 15 MIXED EXERCISES – DO ALL OF THESE NOW! 16: Second Order Ordinary Differential Equations 16.1 INTRODUCTION 16.2 SECOND ORDER DIFFERENTIAL EQUATIONS 16.3 CASE STUDY: A SUSPENSION SYSTEM 16.4 THE SOLUTION OF LINEAR SECOND ORDER O.D.E.S 16.5 THE COMPLEMENTARY FUNCTION/PARTICULAR INTEGRAL APPROACH 16.6 THE CF - FINDING OUT ABOUT UNFORCED CHANGE 16.7 FINDING THE ARBITRARY CONSTANTS BY USING INITIAL CONDITIONS 16.8 FINDING THE P.I. - THE EFFECT OF FORCING CHANGE 16.9 TECHNOLOGICAL SOLVERS 16.10 SOME FINAL EXAMPLES END OF CHAPTER 16 MIXED EXERCISES - DO ALL OF THESE NOW! 17: Laplace Transforms And Ordinary Differential Equations 17.1 THE USEFULNESS OF THE LAPLACE TRANSFORM 17.2 WHAT IS THE LAPLACE TRANSFORM? 17.3 THE LAPLACE TRANSFORM IN ACTION: FIRST ORDER ODES 17.4 USING THE LAPLACE TRANSFORM WITH SECOND ORDER ODEs 17.5 A FINAL SPECIAL CASE – RESONANCE END OF CHAPTER 17 EXERCISES – DO ALL THESE NOW! 18: Taylor Series 18.1 THE ESSENTIAL ROLE OF TAYLOR SERIES 18.2 LINEARISATION 18.3 MACLAURIN SERIES 18.4 GETTING AWAY FROM x = 0: TAYLOR SERIES 18.5 USES OF TAYLOR AND MACLAURIN SERIES END OF CHAPTER 18 PROBLEMS – DO ALL THESE NOW! 19: Statistics And Data Handling 19.1 WHY ENGINEERS NEED DATA HANDLING SKILLS 19.2 PRESENTING DATA IN PICTURES 19.3 SUMMARISING DATA SETS IN A FEW NUMBERS 19.4 FITTING LAWS TO EXPERIMENTAL DATA 20: Probability 20.1 WHAT IS PROBABILITY? 20.2 SIMPLE EXAMPLES – COMPLETE ENUMERATION 20.3 MORE COMPLEX SITVATIONS – THE LAWS OF PROBABILITY 20.4 TREE DIAGRAMS 20.5 SOME MORE PROBABILITY PROBLEMS 20.6 WHERE NEXT WITH PROBABILITY? Glossary G1 GREEK ALPHABET G2 SI UNITS G3 COMMON GRAPHS TO NOTE G4 POWER SERIES G5 COMMON NOTATION G6 TABLE OF TRIGONOMETRIC FUNCTION FORMULAE


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Product Details
  • ISBN-13: 9781898563655
  • Publisher: Elsevier Science & Technology
  • Publisher Imprint: Horwood Publishing Ltd
  • Depth: 19
  • Height: 25 mm
  • No of Pages: 288
  • Series Title: English
  • Sub Title: A Student-Friendly Workbook
  • Width: 25 mm
  • ISBN-10: 1898563659
  • Publisher Date: 01 Jan 2008
  • Binding: Paperback
  • Edition: WKB STU
  • Language: English
  • Returnable: N
  • Spine Width: 25 mm
  • Weight: 440 gr


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