| Code |
10234
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| Year |
1
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
T(30H)/TP(30H)
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| Scientific area |
Mathematics
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Entry requirements |
Do not exist.
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Mode of delivery |
Classroom
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Learning outcomes |
In this course we will explore the key ideas of differential and integral calculus relevant to the Life Sciences
The student will work examples, analytic and graphically, and it is hoped that he will be able to communicate orally, discuss and write in a clear and organized way.
-Apply the basics of differential calculus.
-Calculate the mean values ??of functions.
-Apply the concept of partial derivatives to solve optimization problems and linear approximation of functions of several variables.
-Identify and solve Ordinary Differential Equations and interpret the solutions.
-Demonstrate skills of effective oral and written communication, presenting ideas in a clear, logical and organized, supported by the correct use of notations.
-Using new technologies to show computational capacity to solve problems.
-Demonstrate resourcefulness in self-study, showing ability to study independently.
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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
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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;
• Notas de Matemática para Ciências Farmacêuticas, Alberto Simões, UBI.
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Language |
Portuguese. Tutorial support is available in English.
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