Mathematics for Earth Science and Geography: Introductory Course with Practical Exercises and R/Xcas Resources

201 Pages·2019·6.357 MB·English

by  Cyril Fleurant, Sandrine Bodin-Fleurant

Cyril Fleurant · Sandrine Bodin-Fleurant
Mathematics
for Earth Science
and Geography
Introductory Course with
Practical Exercises and R/Xcas Resources
Springer Textbooks in Earth Sciences,
Geography and Environment
The Springer Textbooks series publishes a broad portfolio of textbooks on
Earth Sciences, Geography and Environmental Science. Springer textbooks
provide comprehensive introductions as well as in-depth knowledge for
advanced studies. A clear, reader-friendly layout and features such as end-
of-chapter summaries, work examples, exercises, and glossaries help the
reader to access the subject. Springer textbooks are essential for students,
researchersandappliedscientists.
Moreinformationaboutthisseriesathttp://www.springer.com/series/15201
(cid:129)
Cyril Fleurant
Sandrine Bodin-Fleurant
Mathematics for Earth
Science and Geography
Introductory Course with Practical
Exercises and R/Xcas Resources
CyrilFleurant SandrineBodin-Fleurant
DepartmentofGeography InspectionacadémiqueduRhône
UniversityofAngers Lyon,France
Angers,France
Additionalmaterialtothisbookcanbedownloadedfromhttp://extras.springer.com.
ISSN2510-1307 ISSN2510-1315 (eBook)
SpringerTextbooksinEarthSciences,GeographyandEnvironment
ISBN978-3-319-69241-8 ISBN978-3-319-69242-5(eBook)
https://doi.org/10.1007/978-3-319-69242-5
LibraryofCongressControlNumber:2018940145
TranslationfromtheFrenchlanguageedition:Basesdemathematiquespourlage´ologieetla
ge´ographie.Coursetexercisescorrige´sbySandrineFleurant&CyrilFleurant,#Dunod2015.
AllRightsReserved.
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Sandrine Bodin-Fleurant and Cyril Fleurant
Angers, August 2018
To Victor, Abel, Martin and Jeanne our beloved children
Acknowledgement
ThisbookwastranslatedandadaptedfromFrenchbytheauthors.Thiscould
not have been possible without the invaluable help of Sarah Pope, MSc
graduate,Geography,SwanseaUniversity,U.K.Shehasthoroughlyreviewed
the entire content of the book and made numerous useful comments. Many
thankstoher.
vii
Introduction
Geography(whetherphysical,humanorsocial)andearthsciencearecomplex
sciences that require elaborate quantification tools to understand their
foundationsandtheirprocesses.
Thistextbookincludesexercisestoacquireandconsolidatethemathemat-
ical basics necessary to practice physical geography and earth science. The
aim of this textbook is to be of use in real geographical and earth science
situations, and to illustrate how mathematical tools can be used to enhance
thesedisciplines.
Thetextbookisorganizedaroundissuesingeographyandinearthscience
that will motivate the need for theoretical contributions and mathematical
practice. The text is illustrated with examples developed and derived from
them.Thistextbookisbasedontheauthors’experiencesandneedsofstudents
in their construction of mathematical tools. Mathematical theoretical
contributions will be those that are actually useful for the construction of a
solidgeographicalorearthscienceculture.
Priority is also given to digital applications and computing. The authors
want the links between geography, earth science and mathematics to be as
completeaspossible,socomputertools(freewareRandXcas)willbeused.
Who Is This Book For?
Thistextbookismainlyintendedforbachelor’sdegreestudentsingeography
andearthscienceandtheirteachers—and,ofcourse,alsobeyond(forinstance
master’sstudentswishingtoupgradetheirmathematicalknowledge).
Thesestudentsaredividedintotwomaingroups:
(cid:129) Studentswithadvancedmathematicstrainingwhohavetakenasecondary
science course. These students need to consolidate their mathematical
knowledge, and especially to learn to use this knowledge in
non-mathematicalcontexts,comingfromthedisciplinesstudied.
(cid:129) Studentswhohavenotstudiedadvancedmathematicsatschoolforwhich
it is necessary to start with the basics of mathematics. These basics are
givenheredirectlyinthecontextofgeographyandearthscience.
ix
x Introduction
Thistextbookisalsointendedforteachersinsecondaryschools(whether
inearthscience,geographyormathematics),whowillfindinitmanyideasfor
interdisciplinaryteaching.
Why This Book?
Theauthorsareusedtoworkingwithpupils,studentsandtheirteachers.An
observationwasmadeonthedifficultiesthatmanystudentsfacewhenusing
simple mathematical knowledge in different contexts (drawing regression
lines, manipulating units, using derivatives). We felt it was necessary to
emphasizetheseneedsinordertocomplementuniversitylecturesandexisting
works.
Thetextbookvoluntarilytakesovermanynotionsandgivesmethodologi-
cal advice (e.g. about making conversions or plotting functions). Useful
mathematical functions are discussed with contextualized examples. The
textbookalsoaddresses(alwaysinaverycontextualizedway)moreadvanced
notions,suchasintegrals,differentialequationsandpartialderivatives.
Please note that we chose not to deal with statistics, for which there are
already many references. For example, the interested reader may refer to
DadsonS.J.,2017,Statisticalanalysisofgeographicaldata:anintroduction,
Wiley.
Another aim of this text is to help readers acquire an understanding of
ordersofmagnitudeandunitscommonlyusedinuniversitycourses,aswellas
agreaterconfidenceintheresolutionmethodandencrypteddata.
Contents
The book is divided into six chapters that progressively lead to ever more
advancednotions.
Chapter1,“QuantitiesandMeasures”,treats decimal andsexagesimal
numerationsystems.Itpresentsthenotionsofsymbol,measurement,unitand
approximatevalue (rounded,significantdigits,uncertainty,error),aswellas
conversion units, percentages and rates. It also discusses scientific notation
andthepowersoften.
Chapter2,“VariablesandFunctions”,discussesthevariablesandtheir
valuesandlinksthemtogethertodefinethenotionoffunction.Wealsoshow
the interest of the representation of these functions to illustrate natural phe-
nomena.Somecommonfunctionsingeographyandearthsciencearedevel-
oped, as are the notions of increasing, decreasing, minimum and maximum,
usefulforthestudyoftheirevolutionandtrends.
Chapter 3, “Trigonometry, Geometry of Plane and Space”, develops
2Dtrigonometry,trigonometricfunctionsand2Dand3Dgeometry.
Chapter 4, “Cartography”, provides mathematical foundations for
understanding a mapping system, in particular concerning the identification
ofitemsonaglobe,projectionsandsphericaltrigonometry.
Introduction xi
Chapter 5, “Derivation”, shows the use of derivatives in the study of
common functions. It will shed light on the advantages of derivation for the
study of function variations. The elements of computational techniques are
provided,andthemoreintensivecalculationscanbecarriedoutusingformal
calculationsoftware.
Chapter 6, “Integration and Differential Equations”, presents two
fundamental tools related to functions: integration and the concept of differ-
entialequations.Theconceptofpartialdifferentialequationsisalsopresented.
Eachchapterofferstwotypesofexercises:
(cid:129) Mathematical application exercises, which allow students to take into
account the main elements of the text and help them to memorize them.
Theyarenotcontextualizedbutarenonethelessfocusedontheknowledge
and know-how that will be useful for students in earth science and
geography;
(cid:129) Exercisesinearth scienceandgeographyinwhichproblemsituationsare
identified. These exercises aim to contextualize mathematical tools in
concreteproblemsencounteredbystudents.
Half of these exercises are contextualized and all (over 110 in total) are
fullycorrected.
How to Use This Manual
Each series of exercises in each chapter begins with three series of flash
questions.Thesequestionsallowreaderstodeterminewhetherthecontentof
the chapter is familiar to them. First try to answer the questions without
looking at the content and then use it to check or reinforce the methods and
calculations.Donotworkonallthreeseriesatatime.
Dependingontheirknowledgeandgoals,studentscan:
(cid:129) Startdirectlywithaseriesofflashquestions(asadiagnostictest)andthen
workon(ornot)thecontentofthetextaccordingtotheresult;
(cid:129) Begin by reading the key points at the end of the chapter to assess their
familiarity with the contentsand then decide whether towork first on the
textortheexercises;
(cid:129) First workonthe text andthen check its level of familiarity based on the
variousexercises;
(cid:129) Start directly with the geography or geology exercises and refer to the
textandthemathematicalexercisesasrequired.
General Advice When performing the calculations, first seek an order of
magnitude of the result. Then carry out the calculations without the use of a
calculator, and finally finish by checking your answers with a calculator or
withR(calculationsoftware).