URL study guide
https://tue.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=2DL10&collegejaar=2025&taal=enOmschrijving
- 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:- Apply basic operations on and properties of equations and functions.
- Apply the rules of differentiation to determine slopes of a graph, find extreme values and construct Taylor polynomials.
- Evaluate integrals using their properties and the methods of substitution, rewriting fractions and integration by parts.
- Determine whether a series converges using convergence tests, and compute its limit.
- Apply the fundamental definitions and rules of probability.
- Apply the properties of discrete random variables, including the binomial, geometric, hypergeometric and Poisson random variable.
- Write well-structured and correct mathematical arguments using full sentences.