Applied Mathematics I

(A) Supply the students with essential mathematical knowledge for their future performance in other subjects of the
course, namely:
– Study of real functions with one real variable
– Computation of the derivative of a function
– Computation of the antiderivative of a function
– Resolution of differential equations
– Computation of the integral of a function with one real variable
(B) Present some practical applications of these subjects in the management field, such as the computation of
rates of variation, the determination of intervals of increase or decrease of a function, the optimization of functions,
the computation of a cost function, being known the marginal cost function model, the computation of plane
regions.
(C) Encourage the implementation of analytical and deductive methods for tackling and solving concrete problems
and stimulate the application of the syllabus contents in other areas, namely those embedded in the corresponding
curricular plan, such as management.

1. Generalities
2. Limits and continuity
3. Exponential and logarithmic functions
4. Derivation of functions
5. Examples of application
II. Integral computation in IR
1. Antiderivative
1.1. Direct integration
1.2. Antiderivative by parts
1.3. Antiderivative of rational functions
1.4. Antiderivative by substitution
1.5. Examples of application
2. Differential equations
2.1. General definitions
2.2. Equations with separable variables
2.3. 1st order linear differential equations
2.4. Examples of application
3. Integrals
3.1 Definition and geometric interpretation of definite integral
3.2 Conditions and properties required of definite integral
3.3 Fundamental theorem for the integral computation
3.4 Trapezoid rule
3.5 Computation of areas of plane regions
3.6 Improper integrals
3.7 Examples of application

NAO

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