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[ 290MAFSTMAK26 ] KV Tutorium Mathematics for Chemistry
Versionsauswahl
Workload Education level Study areas Responsible person Hours per week Coordinating university
1,5 ECTS B1 - Bachelor's programme 1. year Mathematics Markus Passenbrunner 1 hpw Johannes Kepler University Linz
Detailed information
Original study plan Bachelor's programme Chemistry and Chemical Technology 2026W
Learning Outcomes
Competences
Build clear mathematical arguments in plain language, translate between symbols, graphs, and real-world descriptions, and spot common logical mistakes. Model simple chemical and physical situations with functions, equations, vectors, and matrices; choose suitable analytic or numerical methods; and judge whether results are reasonable. Move comfortably between exact solutions and approximations, quantify error or uncertainty, and communicate assumptions and limitations. Work effectively in groups: explain reasoning, critique solutions constructively, and identify gaps in understanding.
Skills Knowledge
  • Definitions to decisions: read and use definitions (set, function, limit, derivative, integral, vector, basis) and build/check counterexamples. (k1, k2, k3)
  • Single-variable analysis: evaluate limits and continuity; differentiate; use derivatives to optimize and interpret rates of change; estimate with linearization. (k2, k3, k4)
  • Multivariable analysis: compute partial derivatives, gradients, Jacobians, and Hessians; interpret sensitivity and curvature; find and classify extrema (intro to constraints/Lagrange multipliers). (k2, k3, k4)
  • Integration as accumulation: compute definite integrals; apply the Fundamental Theorem of Calculus; use substitutions and basic coordinate changes; interpret areas, masses, totals; do simple line/curve integrals. (k2, k3, k4)
  • Linear systems and matrices: solve systems via Gaussian elimination; understand rank and consistency; compute and interpret determinants, eigenvalues, and eigenvectors in small cases. (k2, k3, k4)
  • Sequences and series for approximation: decide convergence with core tests; use geometric and Taylor series to approximate functions and estimate errors; understand Fourier coefficients for periodic signals. (k2, k3, k4)
  • Differential equations: solve separable and first-order linear ODEs; analyze fixed points and qualitative behavior; connect to kinetics and relaxation processes. (k2, k3, k4)
  • Numerical methods and data: apply bisection and understand Newton’s method conceptually; perform least-squares linear regression; report error bounds and check stability/conditioning. (k3, k4, k5)
  • Coordinate transformations: use polar/cylindrical/spherical changes with the Jacobian to simplify integrals. (k2, k3, k4)
  • Sanity checks and estimation: dimensional analysis, order-of-magnitude estimates, bounding arguments, and limit-case checks. (k2, k3, k4)
  • Core objects and structures: sets and functions; real numbers and completeness (why limits exist); sequences and series; vector spaces, linear independence, bases; norms, inner and cross products.
  • Key theorems and ideas (at an intuitive, usable level): Intermediate Value and Mean Value ideas; Bolzano–Weierstrass (compactness intuition); Fundamental Theorem of Calculus; Taylor’s theorem with remainder; convergence test intuition (geometric, comparison, ratio, alternating/Leibniz); Implicit Function idea for local solvability; Fubini and change of variables with the Jacobian; Schwarz’s theorem for mixed partials.
  • Common formulas and tools worth memorizing or recognizing: binomial and geometric series; basic Taylor expansions (exp, sin, cos, log) and their error terms; small-matrix determinants and eigenpairs; cross product; least-squares normal equations.
  • Problem-solving heuristics: sketch first; pick a simple model; approximate before calculating exactly; check units; test extreme and special cases; compare against bounds or known values; communicate the “why” with the “what.”
Criteria for evaluation compulsory attendance, written examination
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: 663MAPHIMAK19 Introduction to Mathematics

Corresponding lecture 290MAFSMA1U26: UE Exercises for Mathematics in Chemistry I (3 ECTS)
in combination with
290MAFSTMAK26: KV Tutorium Mathematics for Chemistry (1,5 ECTS)
is equivalent to
290MAFSMC1K19: KV Applications of Mathematics in Chemistry with Exercises I (4,5 ECTS)

Is completed if 663MAPHIMAK19: KV Introduction to Mathematics (1.5 ECTS)
On-site course
Maximum number of participants 35
Assignment procedure Direct assignment