Mathematics

Code	13637
Year	1
Semester	S1
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	Do not exist.
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	1 Differential Calculus of Real Functions of Real Variable 1.1 Definition of Derivative 1.2 Higher Order Derivative 1.3 Application of Derivatives 2 Integral Calculus 2.1 Primitives 2.2 Integrals 2.3 Improper Integrals 3 Real Functions of Several Variables 3.1 Introduction 3.2 Functions, Scalar and Vector Fields 3.3 Limits 3.4 Continuity 3.5 Exercises 3.6 1st Order Partial Derivatives 3.7 Differentiability 3.8 Tangent Plane. Linearization 3.9 Directional Derivative 3.10 Higher Order Derivatives. Schwarz theorem 3.11 Derivative of the Composite Function. Implicit Function 3.12 Free and Conditioned Extremes 4 Integral Calculus in Rn 4.1 Double Integral 4.2 Triple Integral 4.3 Variable change 5 Differential Equations 5.1 First notions 5.2 Equations of Separate Variables 5.3 Homogeneous Differential Equations 5.4 Exact Differential Equations 5.5 Integrating Factor Method 5.6 Linear Differential Equations
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.