Curricular Unit:Code:
Numerical Analysis831ANUM
Year:Level:Course:Credits:
2UndergraduateComputer Systems Engineering5 ects
Learning Period:Language of Instruction:Total Hours:
Winter SemesterPortuguese/English65
Learning Outcomes of the Curricular Unit:
The main objective of Numerical Analysis is to determine approximate solutions to complex mathematical problems using only the simple operations of arithmetic. This course present different methodology applied to solve engineering problems. It seeks to develop in students the ability of analysis in order to establish the degree of confidence in the results.
Syllabus:
Errors: Rounding Error, Truncation Error, Propagation of Error. Non-linear Equations: Bisection Method, False Position Method, Fixed-Point Iteration, Newton’s Method, Secant Method. Systems of Equations: Gauss’s Method, Gauss-Jordan, Gauss-Seidel, Decomposition LU (Doolittle, Crout, Cholesky). Polynomial Approximation and Interpolation: Least Squares Approximations, Newton Polynomials, Lagrange Polynomials, Spline. Numerical Integration. Numerical Differentiation. Numerical Solution of Differential Equations: Euler’s Method, Runge-Kutta Method.
Demonstration of the Syllabus Coherence with the Curricular Unit's Objectives:
An engineering problem solution often depends on the application of numerical methods. Determination of a root to get the optimal of a problem, solving a system of equations in a structural calculation, a curve fitting to model a three-dimensional object, calculating an integral volume and solving a system of differencial equations to simulate the behavior of a physical system are examples of application of this course syllabus. The error associated with the computer representation of the number is essential to realize some of the difficulties of implementing a method.
Teaching Methodologies (Including Evaluation):
The methodology of teaching and learning is expository, interrogative and demonstrative. It seeks to apply the theory in examples of engineering. The method of assessment comprises two individual written tests.
Demonstration of the Coherence between the Teaching Methodologies and the Learning Outcomes:
The proposed methodologies are consistent with the objectives set for the course given the interpretation that emphasizes the practical application of the theory of numerical methods in engineering examples.
Reading:
[1] CHAPRA, S. C. and CANALE, R. P. - Numerical Methods for Engineers - McGRAW-HILL, 2015.
[2] SCHEID, F. - Análise Numérica - McGRAW-HILL, 1991.
[3] PINA, H. - Métodos Numéricos - McGRAW-HILL, 2010.
[4] HOFFMAN, J. D. - Numerical Methods for Engineers and Scientists - McGRAW-HILL, 2001.