1

2019-2020

01001653

Mathematics

Portuguese

Face-to-face

SEMESTRIAL

7.5

Compulsory

1st Cycle Studies

Sequences; Differential and integral calculus of real-valued functions* of one real variable* (Mathematical Analysis I).

Detailed lectures (using occasionally some audio-visual devices) introducing and explaining concepts, principles and theories. Theoretical-practical classes, in which the students with the guidance of the teacher, solve exercises.

The aim of this curricular unit is to o provide the main concepts and techniques of sequences and numerical, power and Fourier series, vectors and the space geometry, and partial derivates, which will be intensively used in the remaining curricular unites.

1. Series

1.1 Sequences

1.2 Numerical series

1.3 The integral test and estimates of sums

1.4 The comparison tests

1.5 Alternating series

1.6 Absolute convergence and the ratio and root tests

1.7 Strategy for testing series

1.8 Power series

1.9 Representations of functions as power series

1.10 Taylor and MacLaurin series

1.11 Binomial series

1.12 Taylor formula

1.13 Fourier series in R

1.14 Fourier series of functions defined in a limited interval

1.15 Cosine and sine series

2 Vectors and the Geometry of Space

2.1 Three-dimensional coordinate systems

2.2 Vectors

2.3 The inner product

2.4 The cross product

2.5 Equations of lines and planes

2.6 Cylinders and quadric surfaces

2.7 Cylindrical and spherical coordinates

3. Parcial Derivatives

3.1 Graphs and level curves

3.2 Limits and continuity

3.3 Parcial derivatives

3.4 Tangent planes and linear approximations

3.5 The chain rule

3.6 Directional derivatives and the gradient vector

3.7 Maximum and minimum values

3.8 Lagrange multipliers

Final

*Exam: 100.0%*

Contínua

*2 frequências: 100.0%*

James Stewart - *Cálculo Vol. II* - 5ª Edição, São Paulo, Pioneira Thomson Learning, 2001.