G5301 Mathematical Geology

Faculty of Science
Spring 2006
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: graded credit.
Teacher(s)
doc. Ing. Jiří Faimon, Dr. (lecturer)
Guaranteed by
doc. RNDr. Rostislav Melichar, Dr.
Department of Geological Sciences – Earth Sciences Section – Faculty of Science
Contact Person: Běla Hrbková
Timetable
Wed 12:00–13:50 Bp1,01007, Wed 14:00–14:50 Bp1,01007
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.

The capacity limit for the course is 32 student(s).
Current registration and enrolment status: enrolled: 0/32, only registered: 0/32
fields of study / plans the course is directly associated with
there are 51 fields of study the course is directly associated with, display
Course objectives
The course should persuade students about usefulness of mathematical methods in geology. Traditionally, many geologists keep off mathematics. Thus, the aim of the course is demonstrating simplicity, elegance, and beauty of mathematical procedures at solving of geological problems. Besides "philosophical" considerations, there are summarized and strengthened the knowledges of functions, inverse methods, linear algebra, differential calculus, integral calculus, and differential equations. In addition, vector analysis and numeric methods are demonstrated on geological examples. Majority of the applications is practiced in MS Excel.
Syllabus
  • Mathematics in geology: History and present, 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
  • MUSTOE, L.R. and M.D.J. BARRY. Foundation Mathematics. Wiley., 1998, 668 pp. ISBN 0-471-97092-1. info
  • MUSTOE, L.R. and M.D.J. BARRY. Mathematics in Engineering and Science. Wiley, 1998, 768 pp. ISBN 0-471-97093-X. info
  • ALBARÉDE, Francis. Introduction to geochemical modeling. 1st pub. Cambridge: Cambridge University Press, 1995, 543 s. ISBN 0-521-45451-4. info
  • ATKINSON, Kendall E. An Introduction to Numerical Analysis. Wiley., 1989, 712 pp. ISBN 0-471-62489-6. info
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
Information on the per-term frequency of the course: Výuka bude probíhat v jarním semestru 2005/2006.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2003, Spring 2004, Spring 2008, Spring 2010, Spring 2012, spring 2012 - acreditation, Spring 2014, Spring 2015, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2023, Spring 2025.
  • Enrolment Statistics (Spring 2006, recent)
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