Mathematics: A Simple Tool For Geologists

Mathematics Simple Tools For Geologists CoverWith an increasing use of computers and quantitative methods in all aspects of geology it is vital that geologists should be seen to be as numerate as their colleagues in other physical sciences. This book is for students who did not follow mathematics through to the end of their school careers and for graduates and professionals whose mathematics have become rusty and who are looking for a refresher course. The book aims to teach simple mathematics using geological examples to illustrate mathematical ideas. This approach emphasises the relevance of mathematics to geology, helps to motivate the reader and gives examples of mathematical concepts in a context familiar to the reader.

The book begins by discussing basic tools such as the use of symbols to represent geological quantities and the use of scientific notation for expressing very large and very small numbers. Simple functional relationships between geological variables are then covered (for example, straight lines, polynomials, logarithms) followed by chapters on algebraic manipulations. The mid–part of the book is devoted to trigonometry (including an introduction to vectors), data plotting and statistics. The last two chapters give an introduction to differential and integral calculus.

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The book is prepared with a large number of worked examples and problems for the students to attempt themselves. The latest edition contains many new problems and also has associated spreadsheets designed to improve student′s understanding. These spreadsheets can also be used to solve many of the problems student′s are likely to encounter during the remainder of their geological careers. Answers to all the questions are given at the end of the book.

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Contents

  • Preface.
  • 1. Mathematics as a tool for solving geological problems.
  • 2. Common relationships between geological variables.
  • 3. Equations and how to manipulate them.
  • 4. More advanced equation manipulation.
  • 5. Trigonometry.
  • 6. More about graphs.
  • 7. Statistics.
  • 8. Differential calculus.
  • 9. Integral calculus.
  • Appendix A – useful equations.
  • Appendix B – answers to problems.
  • Index

Spreadsheets

Available for you to download, here is a list of spreadsheets that illustrate examples in the book.

Spreadsheet Section in the Book Description
Intro.xls 1.5 & 1.8 Introductory sheet showing scientific notation and graphing.
S_Line.xls 2.2 Plots straight line given m & c.
Quadrat.xls 2.3 Plots quadratic function given a, b & c.
Poly.xls 2.4 Plots polynomial function up to n=5.
Exp.xls 2.7 Plots exponential function for any values of a, b or c.
Log.xls 2.8 & 2.9 Plots common, natural and user-defined-base log functions.
Roots.xls 3.5 Calculate roots of quadratic eqn given a, b & c.
Simul.xls 4.3 Solve 2×2, 3×3, 4×4 or 5×5 system of simultaneous linear equations.
Trig.xls 5.3 Solve triangle given 3 pieces of information.
Vsum.xls 5.6 Calculate vector sums.
Triangle.xls 6.3 Plot data on a triangular diagram.
Polar.xls 6.5 Plot data on equal interval, equal angle and equal area plots.
Gauss.xls 7.5 Calculate and plot a normal distribution and give area under curve between 2 points.
Bfit.xls 7.6 Calculate and plot best fit lines given 2 columns of data.
Sterr.xls 7.8 Calculate standard error given a standard deviation and number of data points.
Differentiate.xls 8.4 Comparison of gradient between two separated points and gradient of tangent.
Integ.xls 9.2 – 9.4 Comparison of discrete area under curve to integral solution.