Menü
Positionsanzeige
Inhalt

[ 290MAFSTMAK26 ] KV (*)Tutorium Mathematics for Chemistry
Versionsauswahl
(*) Leider ist diese Information in Deutsch nicht verfügbar.
Workload Ausbildungslevel Studienfachbereich VerantwortlicheR Semesterstunden Anbietende Uni
1,5 ECTS B1 - Bachelor 1. Jahr Mathematik Markus Passenbrunner 1 SSt Johannes Kepler Universität Linz
Detailinformationen
Quellcurriculum Bachelorstudium Chemistry and Chemical Technology 2026W
Lernergebnisse
Kompetenzen
(*)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.
Fertigkeiten Kenntnisse
(*)
  • 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.”
Beurteilungskriterien (*)compulsory attendance, written examination
Lehrinhalte wechselnd? Nein
Sonstige Informationen (*)
  • 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

Äquivalenzen (*)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)

Gilt als absolviert, wenn (*)663MAPHIMAK19: KV Introduction to Mathematics (1.5 ECTS)
Präsenzlehrveranstaltung
Teilungsziffer 35
Zuteilungsverfahren Direktzuteilung