| Code |
5737
|
| Year |
1
|
| Semester |
S1
|
| ECTS Credits |
6
|
| Workload |
TP(60H)
|
| Scientific area |
Mathematics
|
|
Mode of delivery |
Face to face lectures.
|
|
Work placements |
not applicable
|
|
Learning outcomes |
The objectives of this course unit are to apply concepts and methods of differential and integral calculus in the modeling of practical situations and problem solving motivated by research in the field of pharmaceutical sciences.
At the end of the course unit students should be able to apply concepts and methods of differential and integral calculus to solve practical problems.
|
|
Syllabus |
Derivation: calculations with composite and implicit functions, derivatives of higher orders, differential. Mean value theorems (Rolle, Lagrange) and location of the extreme. Calculations with implicit derivatives and differentials. Indefinite integral: primitives, integration by parts, calculation of primitives using substitutions. Defined Integral: existence and properties, methods of calculation (chain rule, use of substitutions). Differential equations. Separable first order equations: properties and applications (autocatalysis, spread of infection). Linear equation of degree 1: Problem solving. Functions with bi-dimensional variables: Limit and continuity, definition and notation of derived functions, Clairaut’s Theorem. Differential function, examples. Differential function. Differentiable function approximation. Chain rule for functions of argument and two-dimensional calculations with functions of bi-dimensional argument (elementary examples).
|
|
Main Bibliography |
• Cálculo com Geometria Analítica, Volume 1. e Volume 2, Louis Leithold;
• Cálculo, vol. 1 e vol. 2, James Stewart, 5ª edição, CENGAGE Learning;
• Cálculo, vol. 2, Howard Anton, Irl Bivens, Stephen Davis, 8ª Edição, 2007, Bookman;
• Notes of Mathematics for Pharmaceutical Sciences, Alberto Simões, UBI.
|
|
Language |
Portuguese. Tutorial support is available in English.
|