URL study guide
https://tue.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=6BBR03&collegejaar=2025&taal=enDescription
This course covers the basics in the field of calculus, including algebraic skills, functions, limits,differentiation, transcendental functions, integration, first-order differential equations, and vectors in plane and space.
Extra information about the assessment
The results of the digital tests are only valid in the academic year in which they were taken.
The final course grade will be the weighted average, which should by at least a 5.5 to pass the course.
The digital tests for this course will take place every afternoon (3 sessions per afternoon, with a maximal capacity of 36 students per session, during week 1 till week 7 of quartile 1, and every morning and afternoon (3 sessions per morning and 3 sessions per afternoon, with a maximal capacity of 36 students per session in week 8 of quartile 1. Each student has the right to have at least 1 resit for each digital test within the course, as long as the student distributed the attempts for the digital tests evenly over the quartile.
Objectives
- The student is able to apply algebra and high school mathematics with emphasis on algebraic skills (such as solving inequalities), Cartesian coordinates, and functions, with in particular, algebraic manipulation of trigonometric, exponential and logarithmic functions.
- The student is able to compute various types of limits and determine whether a function is continuous or can be extended to a continuous function.
- The student is able to define the notion of differentiable functions, interpret derivatives in terms of tangent line, is able to compute derivatives using the product, quotient, and chain rules, and use implicit differentiation.
- The student is able to compute and use higher order derivatives, linear approximations of a function, Taylor polynomials, l'Hôpital's rule and Taylor polynomials as tools to determine limits.
- The student is able to determine inverse functions of one-to-one (injective) functions, with in particular, knowing the main properties of the natural logarithm (as inverse of the exponential function) and of the inverse trigonometric functions.
- The student is able to compute definite and improper integrals using various techniques such as integration by substitution, integration by parts, and partial fractions, and is able to understand sums, Sigma notation, and Riemann sums.
- The student is able to solve simple first-order differential equations (separable differential equations) and linear first-order differential equations.
- The student is able to find equations and parametric (vector) equations for lines in the plane and in space, and for planes in space.
- The student is able to interpret and compute with dot products and cross products.
- The student is able to determine lengths of vectors, distances and angles between vectors.