Higher mathematics for bachelors of geoinformatics
The aim of the course is to create an idea of the application of mathematical methods in earth sciences and allow creative application of mathematics in the specialty, and facilitate studies in other study-related and multidisciplinary sciences that use mathematical semantics and students' logical and abstract thinking. The objectives of the course are to promote basic knowledge in certain branches of mathematics, which can be used to mathematically correctly describe and solve practical problems, as well as to acquire basic skills in solving various standard mathematics problems.
The course will be taught in English and Latvian.
Knowledge 1. understands the elements of set theory: operations with sets, set equality and equivalence, basic concepts of mathematical logic: construction of expressions, their truth’s values, logical operations, denial of expression, as well as proof of the contrary; 2. understands the methodology of solving systems of linear equations, operations with determinants and matrices, their applications in solving systems of linear equations; 3. understands the definition of a function, elementary functions and their properties, the definition of a function limit, properties and calculation techniques, the continuity of a function, the definition of derivatives and differentials, their calculation techniques and applications in extreme problems and approximate calculations. 4. understand the definition and calculation techniques of indefinite integral and definite integral, as well as applications; 5. understands the definition of binary function, the definitions of their partial derivatives and differentials, calculation techniques and their applications in extreme problems and approximations, definition of double integral, calculation techniques and applications; 6. understands the concept of scalar field, examples, curves of levels, surfaces of levels, derivative in a given direction and scalar field gradient definitions, their properties and applications, vector field definition and examples. Skills 7. independently solve standard tasks on operations with sets, set equality and equivalence, determine the truth values of the expressions by performing logical operations with the expressions, constructing the denial of the expressions, as well as perform proof of the contrary; 8. independently solve standard tasks on systems of linear equations, determinants and matrices and their applications in solving systems of linear equations; 9. independently solves standard tasks on determination of elementary function definition set and value set, property research, limit calculation, continuity research, derivatives, differentials and their applications in finding extremes and approximate calculations; 10. independently solves standard tasks regarding finding an indefinite integral, calculation of a definite integral and applications; 11. independently solves standard tasks on partial derivatives of binary functions, differentials and their applications in extreme problems and approximations, double integrals and their applications; 12. independently solves standard tasks regarding scalar field level curves, level surfaces, derivatives in a given direction, scalar field gradient and its applications. Competencies 13. independently formulates the basic results on set theory: operations with sets, set equality and equivalence, expressions, their truth values, logical operations, construction of denial of expression, as well as proof of the contrary, apply them to standard and practical problems and explain results; 14. independently formulates basic results on systems of linear equations, determinants and matrices, applies them to solve standard and practical problems and explains the obtained results; 15. independently formulate basic results on the properties of elementary functions, properties and calculation of function limits, continuity of functions, derivatives, differentials, apply them to solve standard and practical problems and explain the obtained results; 16. independently formulates the basic results regarding the indefinite integral and the definite integral, the technique of their calculation, applies them to solve standard and practical tasks and explains the obtained results; 17. independently formulates basic results on binary functions, their partial derivatives, differentials, double integrals, applies them to solve standard and practical problems and explains the obtained results; 18. independently formulates the basic results of scalar field level curves, level surfaces, derivative in a given direction, scalar field gradient, its properties, applies them to solve standard and practical problems and explains the obtained results.
Presential
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Higher mathematics for bachelors of geoinformatics
Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or HaDEA. Neither the European Union nor the granting authority can be held responsible for them. The statements made herein do not necessarily have the consent or agreement of the ASTRAIOS Consortium. These represent the opinion and findings of the author(s).
