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

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 books:

Howard ANTON, Irl BIVENS, Stephen DAVIS - Calculus, 8th edition, Wiley (New Jersey), 2005

ANA ALVES de SÁ, BENTO LOURO, Cálculo Diferencial em Rⁿ ,

 

Other books:.

Courses

• Computer Science and Engineering