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Premaster Calculus and Probability

Cursus

URL study guide

https://tue.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=2DL10&collegejaar=2025&taal=en

Omschrijving

  • Algebraic Skills, Functions(C1)
  • Recapitulation of elementary algebra and high school mathematics with emphasis on algebraic skills (such solving inequalities), Cartesian coordinates, and functions; in particular, algebraic manipulation of trigonometric, exponential and logarithmic functions.
  • Limits(C2)
  • Conceptual definition of limits; various types of limits; concept of continuity.
  • Differentiation (C3)
  • Differentiable functions; interpretation of derivatives in terms of tangent line; computation of derivatives using the product, quotient, and chain rules; implicit differentiation. Taylor polynomials of functions; l'Hopital's rule for computing limits.
  • Transcendental functions(C4)
  • Inverse functions of one-to-one (injective) functions; in particular, the main properties of the natural logarithm (as inverse of the exponential function) and of the inverse trigonometric functions.
  • Integration(C5)
  • Computation of definite and improper integrals using various techniques such as integration by substitution, integration by parts, and partial fractions; sums and Sigma notation, Riemann sums.
  • Sequences and series(C8)
  • Sequences, their properties and limit. Series, geometric series. Convergence of series, various tests for convergence, absolute convergence. Power series, Taylor series.
  • Probability theory(S1 and S2)
  • Sample space, events, probability, axioms. Probability rules, conditional probability, independence, Bayes' theorem, random variabele. Discrete distributions, cumulative distribution function, expectation and variance. Uniform distribution, binomial distribution. Geometric, and Poisson distribution; connection of binomial and Poisson distributions


Students following one of the HBO-TOP/premaster programs follow Calculus courses as follows:
Avans students:
2DL10 - HBO-TOP Computer Science and Engineering, HBO-TOP Data Science in Engineering
2WBB0 - HBO-TOP Embedded Systems

Fontys:
2DL10 - 4 year program
2WBB0 - 3 year program (from 2020-2021)

Premaster:
2DL10 - Data Science in Engineering, Embedded Systems (2 semesters)
2WBB0 - Computer Science and Engineering, Information Security Technology, Embedded Systems (1 semester

Doelstellingen

 After this course, students are able to:
  1. Apply basic operations on and properties of equations and functions.
  2. Apply the rules of differentiation to determine slopes of a graph, find extreme values and construct Taylor polynomials.
  3. Evaluate integrals using their properties and the methods of substitution, rewriting fractions and integration by parts.
  4. Determine whether a series converges using convergence tests, and compute its limit.
  5. Apply the fundamental definitions and rules of probability.
  6. Apply the properties of discrete random variables, including the binomial, geometric, hypergeometric and Poisson random variable.
  7. Write well-structured and correct mathematical arguments using full sentences.

Beoordelingsmethode

Written examination
Cursusperiode1/09/1331/08/26
CursusformaatCursus