URL study guide
https://tue.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=2WBB0&collegejaar=2025&taal=enDescription
- 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 I(C3a)
Differentiable functions; interpretation of derivatives in terms of tangent line; computation of derivatives using the product, quotient, and chain rules; implicit differentiation. - Differentiation II (C3b)
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. - First-Order Differential Equations(C6a)
Simple first-order differential equations (separable differential equations) and linear first-order differential equations. - Vectors in the Plane and in Space(L1a)
Equations and parametric (vector) equations for lines in the plane and in space, for planes in space; dot products and cross products; lengths of vectors, distances and angles between vectors.
A detailed description of the modules C1, C2, C3, C4, C5, C6a, C10a en L1a can be found here .
Objectives
- 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)
Understanding the conceptual definition of limits; able to compute various types of limits; able to determine whether a function is continuous, or can be extended to a continuous function. - Differentiation I(C3a)
Understanding the notion of differentiable functions; able to interpret derivatives in terms of tangent line; able to compute derivatives using the product, quotient, and chain rules; able to use implicit differentiation. - Differentation II (C3b)
Higher order derivatives; linear approximations of a function; Taylor polynomials; l'Hopital's rule and Taylor polynomials as tools to determine limits. - Transcendental functions(C4)
Able to determine inverse functions of one-to-one (injective) functions; in particular, knowing the main properties of the natural logarithm (as inverse of the exponential function) and of the inverse trigonometric functions. - Integration(C5)
Able to compute definite and improper integrals using various techniques such as integration by substitution, integration by parts, and partial fractions;
understanding sums and Sigma notation, Riemann sums. - First-Order Differential Equations(C6a)
Able to solve simple first-order differential equations (separable differential equations) and linear first-order differential equations. - Vectors in the Plane and in Space(L1a)
Able to find equations and parametric (vector) equations for lines in the plane and in space, for planes in space;
able to interpret and compute with dot products and cross products;
able to determine lengths of vectors, distances and angles between vectors.