Fundamentals of Mathematics for Environmental Science (250554) – Course 2025/26 PDF
Contents
- Manipulation of algebraic expressions with parameters. - Trigonometric functions: sine, cosine and tangent. - Logarithms.
Dedication
1h 30m Large group + 1h 30m Medium group + 4h 30m Self Study- Graphical representation and main features of elementary functions: polynomial, rational, logarithmic, exponential, trigonometric, piecewise functions. - Operations with functions and transformations f(x)+a, f(x+a). - Composition of functions. - Limits for x tending to infinity. Solution of indeterminations infinity/infinity, infinity-infinity: orders of magnitude. - Limits for x tending to a real value. Lateral limits. Vertical asymptotes. Solution of indeterminations 0/0: simplification and equivalent infinitesimals. - Continuity of functions.
Dedication
4h 30m Large group + 4h 30m Medium group + 13h 30m Self Study- Definition of derivative an its application to compute derivatives of simple functions. - Interpretation of the derivative as the slope of the tangent line. - Computation of the derivative of elementary functions: ax, x^p, sin(x), cos(x), ln(x), exp(x). - Derivative of the sum, the product and the quocient of functions: (f+g)’, (fg)’, (f/g)’. - Chain rule. - Relation between the sign of the derivative and the increase/decrease of a function. Determination of critical points and classification of extrema. Optimisation problems.
Dedication
7h 30m Large group + 7h 30m Medium group + 22h 30m Self Study- Computation of primitives of elementary functions: polynomials, exp(x), sin(x), cos(x), 1/x, and those obtained as the compoistion of functions (f’(g(x))*g’(x)). - Computation of integrals by integration by parts. - Definite integral and Barrow’s rule. - Applications of the definite integral: computation of areas and volumes of revolution bodies; problems in mathematical modelling.
Dedication
7h 30m Large group + 7h 30m Medium group + 22h 30m Self Study- Matrices: definition and operations with matrices. - Determinants of 2x2 and 3x3 matrices. - Planar linear transformations: rotations, axial symmetries, translations, homotheties, affine transformations. - Spatial linear transformations. - Space geometry: definition of straight lines and planes, relative position of two lines, plane intersection. - Gauss method for the solution of systems of equations. Relation between the solution of a 3x3 system and the intersection of three planes.
Dedication
9h Large group + 9h Medium group + 27h Self Study