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| Detailed information |
| Original study plan |
Bachelor's programme Chemistry and Chemical Technology 2026W |
| Learning Outcomes |
Competences |
| Students can extend univariate mathematical principles to multivariate systems, enabling them to analyze higher-dimensional vector spaces, matrices, and multi-variable functions rigorously. They determine the convergence and evaluate the limit of numerical series, formulate multi-variable models, and implement both exact algebraic and numerical approximation methods to solve complex engineering and scientific problems.
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| Skills |
Knowledge |
- Analyze the convergence and absolute convergence of infinite series, power series, and Fourier expansions using structural convergence tests. (k1, k2, k3)
- Determine partial derivatives, gradients, Jacobian matrices, and Hessian matrices for scalar and vector fields of several variables. (k1, k2, k3)
- Explain structural algebraic and geometric concepts including vector spaces, linear independence, bases, norms, and inner or cross products. (k1, k2, k3)
- Evaluate the unique local solvability of non-linear multi-variable equation systems using the implicit function theorem. (k2, k3, k4)
- Calculate determinants, eigenvalues, eigenvectors, and integrals over geometric regions using coordinate transformations. (k2, k3, k4)
- Apply Gaussian elimination for linear systems and linear regression techniques to analyze noisy measurement data using mean-square error minimization. (k3, k4, k5)
- Solve simple differential equations. (k2, k3, k4)
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- Definitions of infinite series, partial sums, vector spaces, standard bases, regular or singular matrices, partial or Fréchet differentiability, and smooth curves.
- Theorems including the Leibniz criterion, Cauchy's condensation test, Taylor's series theorem, Fubini's theorem, the implicit function theorem, and Schwarz's theorem.
- Formulas for geometric series sums, Taylor series expansions of elementary functions, Fourier coefficients, cross products, and principal minors.
- Integration techniques, specifically the rule of substitution and integrals over curves in space
- Axioms defining algebraic vector space operations, vector norms, and inner products.
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| Criteria for evaluation |
written examination, homework, attendance
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| Changing subject? |
No |
| Further information |
- The Chemistry Maths Book, Erich Steiner, Oxford University Press, 1996, ISBN 0-19-855913-5
- Mathematics for Physical Chemistry, Robert G. Mortimer, Elsevier, 2005, ISBN 0-12-508347-5
- Maths for Chemistry: A chemist's toolkit of calculations, Paul Monk and Lindsey J. Munro, Oxford University Press, 2010, ISBN 0-19-954129-9
- Mathematics for Chemists, .G. Francis, Springer, 1984, ISBN 978-94-010-8950-0
Until termin 2026S known as: 663MAPHMA2U18 Applications of Mathematics for Biological Chemistry 2
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| Is completed if |
663MAPHMA2U18: UE Applications of Mathematics for Biological Chemistry 2 (3 ECTS)
or
290MAFSMC2U19: UE Applications of Mathematics in Chemistry with Exercises II (3 ECTS)
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