## G5301 Mathematical Geology

Faculty of Science
Spring 2022
Extent and Intensity
1/2/0. 5 credit(s). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
Mgr. Pavel Pracný, Ph.D. (lecturer)
Mgr. Marek Lang, Ph.D. (lecturer)
Guaranteed by
Mgr. Pavel Pracný, Ph.D.
Department of Geological Sciences - Earth Sciences Section - Faculty of Science
Contact Person: doc. Mgr. Martin Ivanov, Dr.
Supplier department: Department of Geological Sciences - Earth Sciences Section - Faculty of Science
Prerequisites (in Czech)
! G5300 Mathematical geology
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 62 fields of study the course is directly associated with, display
Course objectives
The course should demonstrate usefulness of mathematical methods in geology. Traditionally, many geologists keep off mathematics. Thus, the aim of the course is to demonstrate simplicity, elegance, and beauty of mathematical procedures when solving geological problems. Besides the course is aimed on strengthening of necessary mathematical skills.
Learning outcomes
After the course, students are able to:
understand basic mathematical principles;
apply mathematical methods on problems and models regarding earth systems;
use fundamental mathematical tools;
explain original mathematical solution to other concerned parties.
Syllabus
• Mathematics in geology: History and presence, role of mathematics, quantitative sciences.

Functions: Constants, symbols, variable. Function of a single variable. Dependent and independent variable. Explicit and implicit functions. Elementary functions: Linear function, equation of straight line, power functions, exponential function, logarithmic functions. Inverse functions. Functions of more variables. Error function.

Inverse methods: Regress of experimental data by chosen function (choice of polynomial order), trend-lines in MS Excel. Least square method, minimization, solver in MS Excel. Multiple regresses.

Matrix algebra: Matrix. Elementary operations for matrices, matrix multiplication. Identity matrix, determinant and inverse of matrices. Special matrices: Triangular, symmetric, diagonal. Transpose operation. System of homogenous linear equations. Calculation of equilibrium pH in carbonate system. Calculation of steady states of dynamic system.

Vectors, vector spaces: Mineral composition as vector. Rock composition in vector space. Transformation of coordinates. Founding of mineral composition of granite rock.

Differential calculus: Limits, basic equation for the derivative. Tangents and normal slope. Derivation of the basic functions. Table of derivatives. Differentials. Physical meaning (process rate, increments, decrements, gradients). Calculation of mineral dissolution rate. Higher order derivatives and differentials. Geometrical meaning (maximums and minimums, points of inflection).

Partial derivatives: Derivatives of function of more variables. Total differential. Total differential of Gibbs' energy. Gradient of scalar function.

Integral calculus: Integral. Some properties of the indefinite integral. Definite Integral. Integrals and Area. The length of a curve. Volumes of revolution. Area of surface of revolution.

Differential equations: Separable equations. Linear first order differential equations. Homogeneous linear equations. Solution of rock dissolution dynamic model.

Numeric methods: Algorithms, iteration methods. Nonlinear equation solving. Newton's method. Solution of carbonate system. Solving of nonlinear differential equation system, Euler's method. Solution of nonlinear dynamic model.

Literature
recommended literature
• DOŠLÁ, Zuzana and Petr LIŠKA. Matematika pro nematematické obory : s aplikacemi v přírodních a technických vědách. 1. vyd. Praha: Grada, 2014. 304 s. ISBN 9788024753225. info
• PALMER, Paul I. Essential maths for geoscientists : an introduction. Hoboken, NJ, USA: Wiley Blackwell, 2014. xii, 204. ISBN 9780470971949. info
• HRADILEK, Ludvík and Eduard STEHLÍK. Matematika pro geology. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990. 426 s. ISBN 8003003849. info
not specified
• ALBARÉDE, Francis. Introduction to geochemical modeling. 1st pub. Cambridge: Cambridge University Press, 1995. 543 s. ISBN 0-521-45451-4. info
• MUSTOE, L.R. and M.D.J. BARRY. Foundation Mathematics. Wiley., 1998. 668 pp. ISBN 0-471-97092-1. info
• ATKINSON, Kendall E. An Introduction to Numerical Analysis. Wiley., 1989. 712 pp. ISBN 0-471-62489-6. info
Teaching methods
Lectures, class excercises, homework, discussions, presentation
Assessment methods
Final grade is given by score gained from problem solving in lectures and tests (at least 60%, it is possible to repeat tests)
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught once in two years.
Information on the per-term frequency of the course: Bude otevřeno v jarním semestru 2019/2020.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2003, Spring 2004, Spring 2006, Spring 2008, Spring 2010, Spring 2012, spring 2012 - acreditation, Spring 2014, Spring 2015, Spring 2016, spring 2018, Spring 2020.
• Enrolment Statistics (Spring 2022, recent)