Mathematics for Earth Science and Geography. Introductory Course with practical Exercises and R/Xcas Resources

Intro......Page 3
Contents......Page 6
Numbers......Page 7
Measurement of Quantities......Page 12
Approximate Values......Page 15
Exercises......Page 19
Solutions......Page 23
Variables & Functions......Page 30
Link Between Variables, Functions......Page 31
Representation of Functions, First Elements......Page 32
Scales and Graphic Representation......Page 35
The Common Functions......Page 38
Evolution and Trends......Page 46
Exercises......Page 50
Solutions......Page 58
Measurements of Angles......Page 72
Plane Geometry (Part 1): Trigonometry, Slope......Page 73
Trigonometric Functions......Page 77
Plane Geometry (Part 2)......Page 80
Geometry of Space......Page 83
Exercises......Page 85
Solutions......Page 91
Scales......Page 102
Measurement of Angles, Geographical Coordinates......Page 103
Spherical Geometry......Page 108
Different Mapping Systems......Page 111
Exercise......Page 112
Solutions......Page 114
Slope and Derivative at One Point......Page 120
Derivative Functions and Common Formulas......Page 123
Variations of a Function and Differentiation......Page 127
Exercises......Page 132
Solutions......Page 137
Integrals: Introduction......Page 150
Notion of Primitive (Antiderivative)......Page 152
Calculation of Integrals......Page 154
Calculating Approximate Values of Integrals by the Rectangle Method......Page 158
Differential Equations......Page 160
Partial Differential Equations......Page 165
Exercise......Page 166
Solutions......Page 172
Appendix A: Free Software R......Page 183
Appendix B: Free Software Xcas......Page 191
Reading......Page 194