Mathematical Analysis II E
Code
7996
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Jorge Manuel Leocádio André
Weekly hours
6
Total hours
84
Teaching language
Português
Objectives
Learn the basic topics of R2 and R3, and differential equations of Mathematical Analysis. It is intended that the students acquire elementary techniques of calculus for Physics, Chemistry and Engineering. Moreover, they should develop solid methods of logical reasoning.
Subject matter
1. Differential equations
1.1. First order equations
1.2. Euler’s method
2. Finite dimension linear spaces
2.1. Quadric surfaces
2.2. Polar, cylindrical and spherical coordinates
3. Vector-valued functions
3.1. Continuity, differentiability and integral
4. Functions of several variables: differential calculus
4.1. Topological notions
4.2. Limits and continuity
4.3. Partial derivatives; differentiability
4.4. Chain rule
4.5. Directional derivative
4.6. Tangent plane
4.7. Extrema
4.8. Lagrange multipliers
5. Multiple integrals
5.1 Double integrals
5.2 Triple integrals
5.3 Change of variables in multiple integrals
Bibliography
Main book:
Howard ANTON, Irl BIVENS, Stephen DAVIS - Calculus, 8th edition, Wiley (New Jersey), 2005
Other books:
- EARL W. SWOKOWSKI, Cálculo com geometria analítica, Vol. 2, MacGraw-Hill,1983.
- SALAS, HILLE, Calculus, one and several variables, John Wiley Sons, Inc, 1995.
- APOSTOL, T., Calculo, Vol.2, Reverté, 1993.
- STEWART, J., Calculus, 3ª edição, Brooks/Cole Publishing Company, 1995.
- ANA ALVES de SÁ, BENTO LOURO, Cálculo Diferencial em Rn , FCT/UNL, 2010
- ANA ALVES de SÁ, Cálculo Diferencial em Rn Exercícios resolvidos, FCT/UNL, 2010