|
Teaching GuideTerm Higher Technical University College of Architecture |
| Grao en Estudos de Arquitectura |
 Subjects |
| Mathematics for Architecture 1 |
| Contents |
|
|
|
| Identifying Data | 2023/24 | |||||||||||||
| Subject | Mathematics for Architecture 1 | Code | 630G02004 | |||||||||||
| Study programme |
|
|||||||||||||
| Descriptors | Cycle | Period | Year | Type | Credits | |||||||||
| Graduate | 1st four-month period |
First | Basic training | 6 | ||||||||||
|
||||||||||||||
| Topic | Sub-topic |
| Vector spaces. Linear applications. | Vectorial space. Subspaces. Bases. Dimension. Basis change. Orthogonality. Orthonormal bases. Linear application. Associated matrix. |
| Diagonalization of matrices. | Eigenvalues and eigenvectors of a square matrix. Characteristic polynomial. Diagonalizable matrices. Orthogonal diagonalization. |
| Geometric transformations. | Orthogonal transformations. Classification in R2 and R3. Isometries. |
| Numerical methods for solving systems of linear equations. | Direct methods for solving linear systems: LU factorization, Cholesky factorization. Iterative methods for solving linear systems: Gauss-Seidel. |
| Real functions and vector functions. | Real valued functions. Vector functions. Limit and continuity. Derivation: Partial derivatives. Total derivative. Successive derivatives. Derivation of composite functions. Derivation of implicit functions. Derivation of vector functions. |
| Integration. Numerical integration. | Continuation of integration methods. Numerical integration. |
| Introduction to ordinary differential equations. | Introduction to differential equations. First order ordinary differential equation. Higher order ordinary differential equation. Systems of ordinary differential equations. Differential equation in partial derivatives. |
| Methods for solving ordinary differential equations (I). | Analytical methods for solving first-order ordinary differential equations. Analytical methods for solving higher order ordinary differential equations. |
| Methods for solving ordinary differential equations (II). | Linear differential equations of order n. Analytical methods for solving linear differential equations. |
| Numerical methods for solving ordinary differential equations. |
Need for numerical methods. Numerical methods for solving first order ordinary differential equations. Numerical methods for solving systems of first order ordinary differential equations. |
|
