PEA702 Applied Mathematical Methods

SUBJECT: Applied Mathmatical Methods

CODE: PEA702 

WORKLOAD: 45 class hours

PROFESSOR: José Luiz de Medeiros

SUMMARY: 

1. Algebraic Equations (AE) : 
   Linear Algebra; Matrices and Determinants; General Linear System; Inverses and Pseudo-inverses. Nonlinear Systems; Numerical Resolution Methods; Homogeneous Square Linear System; Eigenvalues ​​and Eigenvectors; Quadratic Forms; Diagonalization of Quadratic Forms; Classification of Quadratic Forms; Equivalence, Congruence, Similarity and Orthogonal Transformations; Factorization of Matrices with Eigenvalues ​​and Eigenvectors. Applications in Optimization. 
2. Ordinary Differential Equations (ODE): 
   Classification; Analytical Methods; General Linear ODE of O(N); Matrix Exponential; ODE Systems of O(1); Stability of ODE Solutions; Characteristic Equation; Parameter Variation Method in Non-Homogeneous Linear ODE of O(N); Orthogonal Functions; Fourier Series; Sturm-Liouville Problem. 
3. Partial Differential Equations (PDE): 
   Classification of PDEs. O(2) PDEs in Conservation Principles with Transport Phenomena; Homogeneous and Non-Homogeneous Linear PDEs; Principle of Superposition of Solutions; PDE Solution by Separation of Variables; PDE Solution via Laplace Transform and Fourier Transform. Numerical Solutions and Approximate Methods. 

BIBLIOGRAPHY: 

Textbook 1: Advanced Engineering Mathematics, 10^thEd., Kreyszig, 2011 Livro Texto 2: Advanced Engineering Mathematics, 6^thEd., Wylie & Barret, 2017. 

Textbook 3: Applied Mathematics and Modeling for Chemical Engineers. 2^ndEd., Rice & Do, 2012. 

Textbook 4: Programação em MATLAB para Engenheiros, S.J. Chapman, Ed.Thompson, 2002.