Curricular Unit:			Code:
Biomathematics			297BMAT
Year:	Level:	Course:	Credits:
1	Master	Pharmaceutical Sciences	4 ects
Learning Period:		Language of Instruction:	Total Hours:
		Portuguese	52
Learning Outcomes of the Curricular Unit:
To teach the set of mathematical tools from polynomial algebra to Laplace transforms, that the student, future professional of pharmaceutical sciences, need to solve all types of mathematical problems that arise in the field of Pharmaceutical Sciences.
Syllabus:
1. Rules of algebraic calculation 2. Algebraic equations systems of equations and inequalities 3. Matrices 4. Logarithms exponential and logarithmic equations 5. Graphs 6. Functions 7. Derivation 8. Primitives 9. Integrals 10. Differential equations 11. Laplace transforms 12. Systems of nonlinear equations
Demonstration of the Syllabus Coherence with the Curricular Unit's Objectives:
The operating rules of algebraic calculus and algebraic equations are essential to solve any mathematical problem. The matrix algebra taught in Chap. 3 aims to provide students with new methods of resolution to handle systems of equations. In addition to the algebraic equations in the field of Pharmaceutical Sciences often arise problems of exponential and logarithmic equations (chap. 4). The drawing and interpreting graphs (ch. 5) is a fundamental mathematical tool in mathematical modeling from experimental data. After understanding the concept of limit of a function (Ch.6) the student is ready to learn derivatives, primitives and integrals, which will be done in chapters 7, 8 and 9 respectively. These tools are fundamental in formulating and solving differential equations studied in Ch.10. The resolution of differential equations that model the administration of multiple doses, is facilitated by using Laplace transforms (ch.11).
Teaching Methodologies (Including Evaluation):
The teaching will be expository and demonstrative in the theoretical classes. The theoretical-practical lessons are devoted to solving exercises. The time in the classroom is supplemented by attendance in office. It will also be proposed, such as group work, projects of mathematical modeling in the field of pharmacokinetics. The evaluation will be done through two individual written tests and two mathematical modeling projects (group work). The final grade of the course is calculated as follows: 70% (average of tests) + 30% (classification obtained in the projects).
Demonstration of the Coherence between the Teaching Methodologies and the Learning Outcomes:
The difficulty expressed by the majority of students in the area of mathematics combined with the complexity of the subjects discussed require lectures to explain, justify and demonstrate each of the discussed mathematical tools. Classes of problem solving are essential for the student to become familiar and materialize what he learned from a theoretical standpoint. Obviously preference will be given to solving examples applied to Pharmaceutical Sciences. The project of mathematical modeling in the area of pharmacokinetics is a fundamental problem in the area of pharmaceutical sciences but since this is a complex mathematical problem is proposed to a group of students and solved outside the classroom.
Reading:
[1] - Barreira, S, Matemática Aplicada às Ciências Farmacêuticas, com Excel vol. 1, Escolar Editora, 2013. [2] - Barreira, S, Matemática Aplicada às Ciências Farmacêuticas, com Excel vol. 2, Escolar Editora, 2014. [3] - Neuhauser C., Calculus for Biology and Medicine 2nd Ed. Prentice Hall, 2004. [4] - Farlow, S. An Introduction to Differential Equations and their Applications, McGraw-Hill, 1994.