Multivariable Mathematics

764 Pages·1995·55.478 MB·English

by  Richard E. Williamson, Hale F. Trotter

THIRD EDITION
ULT1VAR1ABLE
1VI
IVlATHElVIATlCS
Richard E. Williamson • Hale E. Trotter

MULTIVARIABLE
MATHEMATICS

MULTIVARIABLE
MATHEMATICS
THIRD EDITION
RICHARD E. WILLIAMSON
DartmouthCollege
HALE TROTTER
F.
PrincetonUniversity
PRENTICEHALL,UpperSaddleRiver, NewJersey07458
LibraryofCongressCataloging-in-PublicationData
Williamson,RichardE. —
Multivariablemathematics/RichardE.Williamson.HaleF.Trotter. 3rded.
p. cm.
Includesindex.
ISBN0-13-181645-4(hardcover)
1.Algebras,Linear. 2.Differentialequations. 3.Calculus. I.Trotter,HaleF. II.
Title.
QA184.W54 1996
512'.15—dc20 95-36238
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1
Contents
PREFACE
CHAPTER 1 VECTORS
1 CoordinateVectors 1
2 GeometricVectors 8
A Pointsandvectors,8
B Distanceandlength, 1
C Scalarmultiplication, 12
D Vectoraddition, 13
E Points,arrows,andvectors, 16
3 LinesandPlanes 19
A Lines, 19
B Planes,22
CHAPTER2 DOTPRODUCTSANDCROSSPRODUCTS 28
1 DotProducts 28
A Lengthandangle,28
B Unitvectorsandprojections,30
C Propertiesofx-yandIxl,34
vi Contents
2 EuclideanGeometry 37
A Equationsforlinesandplanes,38
B Distancetoalinein31^oraplanein3P,39
C Thecrossproductin31^,42
CHAPTER3 EQUATIONSANDMATRICES 49
1 SystemsofLinearEquations 49
2 SolvingLinearEquations 55
A Coefficientmatricesandelementaryoperations,55
B Reducedmatrices,61
3 MatrixAlgebra 65
A Sumandscalarmultiple,65
B Matrixmultiplication,66
C Identitymatrices,69
4 InverseMatrices 73
A Invertibility, 73
B Computinginverses, 74
C Specialmatrices, 77
5 Determinants 80
A Definition,80
B Rowandcolumnexpansions,82
C Basicproperties,83
D Computingdeterminants,86
E Invertiblematrices,87
CHAPTER4 DERIVATIVES 93
1 FunctionsofOneVariable 94
A Derivatives,94
B Velocityandspeed,99
C Higher-orderderivatives, 100
D Arclength, 101
E Computerplottingofspacecurves, 105
F Vectorintegration, 106
2 SeveralIndependentVariables 112
A Graphofafunction, 112
B Levelsets, 113
C Computer-generatedgraphs, 115
D Quadricsurfaces, 116