NUMERICAL METHODS AND PROGRAMMING
Group of Numerical Methods in Engineering  
School of Civil Engineering (E.T.S. de Ingeniería de Caminos, Canales y Puertos)  
Universidade da Coruña   

 

COURSE  PROGRESS 2024/2025

 

11-SEP-2024 First day of classes. Presentation of the subject. 
Topic 1 FUNDAMENTALS: Practical examples of using Numerical Methods in Engineering. Historical development of Numerical Analysis.
12-SEP-2024 Topic 1 FUNDAMENTALS: Historical development of Numerical Analysis. Fundamental ideas.  
Topic 1 FUNDAMENTALS: Use and abuse of Numerical Methods.
16-SEP-2024 Topic 1 FUNDAMENTALS: computers Programming.  
Topic 1 FUNDAMENTALS: computers Programming.
18-SEP-2024 Topic 1 FUNDAMENTALS: computers Programming.  
Lab. programming practice
23-SEP-2024 Lab. programming practice  
Lab. programming practice
25-SEP-2024 Lab. programming practice  
Topic 2 STORAGE OF NUMBERS IN DIGITAL COMPUTERS: Concept of number and number base. Commonly used numbering bases. Change of number base. Bases related by integer powers. Any bases. Expression of a number in a base.
30-SEP-2024 Topic 2 STORAGE OF NUMBERS IN DIGITAL COMPUTERS: Integers. Encoding and storage. Real numbers. Fixed and floating point representation.  
Topic 2 STORAGE OF NUMBERS IN DIGITAL COMPUTERS: Encoding and storage. Rounding. Precision. Operations with limited precision.
2-OCT-2024 Topic 2 STORAGE OF NUMBERS IN DIGITAL COMPUTERS: Rounding. Precision. Operations with limited precision. [Follow-up test 1]  
Topic 3 ALGORITHMS: Concept. Classification and properties. Direct or finite algorithms. Computing time.
07-OCT-2024 Topic 3 ALGORITHMS: Classification. Iterative algorithms. Convergence order. Linear convergence. Convergence speed. Super-linear convergence. 
Topic 3 ALGORITHMS: Iterative algorithms. Convergence order. Linear convergence. Convergence speed. Super-linear convergence.
09-OCT-2024 Topic 3 ALGORITHMS: Practical convergence criteria Truncation. Operations with polynomials. Horner's rule. Synthetic division. 
Resolution of practice 1
14-OCT-2024 Resolution of practice 1. 
Topic 4 ERRORS: Concept and Clasification.
16-OCT-2024 Topic 4 ERRORS: Concept and Clasification. Bounding. Error propagation. Errors in elemental arithmetic operations. [Follow-up test 2]  
Topic 4 ERRORS: Error propagation. Errors in elemental arithmetic operations.
21-OCT-2024 Topic 4 ERRORS: Error Analysis: Error propagation and iterative algorithms. Global error. Storing data, operating with data, truncation. Avoiding instabilities.  
Resolution of practice 2.
22-OCT-2024 Resolution of practice 2.  
Topic 5 MATRICES STORAGE AND HANDLING: Introduction and motivation, examples in engineering. Full Matrix. Triangular Matrix.
23-OCT-2024 Topic 5 MATRICES STORAGE AND HANDLING: Triangular Matrix. Full Symmetric Matrix. Banded Matrix.  
Topic 5 MATRICES STORAGE AND HANDLING: Banded Matrix, Symmetric Banded Matrix, Symmetric Skyline Matrix. Skyline matrix.
29-OCT-2024 Topic 5 MATRICES STORAGE AND HANDLING: Skyline matrix, sparse matrix. Efficient adaptation of an algorithm to the specific shape of a matrix  
Topic 5 MATRICES STORAGE AND HANDLING: Efficient adaptation of an algorithm to the specific shape of a matrix.
04-NOV-2024 Topic 6 DIRECT METHODS FOR SYSTEMS OF LINEAR EQUATIONS: Introduction. Standards. Spectral radius. Condition number. Ill-conditioned matrices. Matrix inversion and determinant calculation. Manipulation of symmetric, banded, profile and unstructured matrices.  
Topic 6 DIRECT METHODS FOR SYSTEMS OF LINEAR EQUATIONS: Systems with immediate solution. Diagonal matrix. Upper triangular matrix, Lower triangular matrix.
06-NOV-2024 Topic 6 DIRECT METHODS FOR SYSTEMS OF LINEAR EQUATIONS: Upper triangular matrix Lower triangular matrix.  
Topic 6 DIRECT METHODS FOR SYSTEMS OF LINEAR EQUATIONS: Elimination methods. Gaussian elimination.
12-NOV-2024 Topic 6 DIRECT METHODS FOR SYSTEMS OF LINEAR EQUATIONS: Gaussian Elimination. Gauss-Jordan elimination. Crout Decomposition.  
Topic 6 DIRECT METHODS FOR SYSTEMS OF LINEAR EQUATIONS: Recursive Crout Decomposition.
13-NOV-2024 Topic 6 DIRECT METHODS FOR SYSTEMS OF LINEAR EQUATIONS: Recursive Crout Decomposition. Factorization existence conditions. Storage on the original matrix. Decomposition of banded and column profile matrices.  
Topic 6 DIRECT METHODS FOR SYSTEMS OF LINEAR EQUATIONS: Recursive Crout Decomposition. Decomposition of banded and column profile matrices. Cholesky Decomposition. Algorithm adaptation to banded and column profile matrices. Decomposition of tridiagonal matrices
18-NOV-2024 Presentation of the Course Work  
Topic 6 DIRECT METHODS FOR SYSTEMS OF LINEAR EQUATIONS: Decomposition of tridiagonal matrices. Decomposition of tridiagonal symmetric matrices. Solution of batteries of S.L.E. [Follow-up test 3]
20-NOV-2024 Resolution of practice 3.  
Resolution of practice 3.
25-NOV-2024 Topic 7 ITERATIVE METHODS FOR SYSTEMS OF LINEAR EQUATIONS: Introduction. Motivation. General approach. Convergence conditions.  
Topic 7 ITERATIVE METHODS FOR SYSTEMS OF LINEAR EQUATIONS: Methods with proper name. Gradient method. Jacobi's method. Gauss-Seidel method.
27-NOV-2024 Topic 7 ITERATIVE METHODS FOR SYSTEMS OF LINEAR EQUATIONS: Convergence improvement methods: over-relaxation and preconditioning. Semi-iterative methods: Conjugate directions and Conjugate gradients (PCG).  
Topic 7 Resolution of practice 4.
02-DEC-2024 Topic 8 NON LINEAR EQUATIONS: Introduction. Method of bisection. roots finding methods: Functional Iteration methods: convergence conditions (Lipschitz conditions).  
Topic 8 NON LINEAR EQUATIONS: Method of bisection. roots finding methods: Functional Iteration methods: convergence conditions (Lipschitz conditions).
04-DEC-2024 Topic 8 NON LINEAR EQUATIONS: Convergence conditions (Lipschitz conditions). Asymptotic convergence conditions; Fixed Point methods and Newton methods.  
Topic 8 NON LINEAR EQUATIONS: Fixed Point methods and Newton methods.
09-DEC-2024 Topic 8 NON LINEAR EQUATIONS: Newton methods.  
Topic 8 NON LINEAR EQUATIONS: Methods derived from Newton. Convergence acceleration techniques. Aitken acceleration.
11-DEC-2024 Topic 8 NON LINEAR EQUATIONS: Convergence acceleration techniques. Steffensen method.  
Topic 8 NON LINEAR EQUATIONS: Methods for solving systems of nonlinear equations: Successive approximations, Newton-Raphson, Newton-Raphson derivatives.
 

 

Academic year 2024/2025
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