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Teaching GuideTerm Higher Technical University College of Architecture |
| Grao en Estudos de Arquitectura |
 Subjects |
| Mathematics for Architecture 2 |
| Contents |
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| Identifying Data | 2023/24 | |||||||||||||
| Subject | Mathematics for Architecture 2 | Code | 630G02009 | |||||||||||
| Study programme |
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| Descriptors | Cycle | Period | Year | Type | Credits | |||||||||
| Graduate | 2nd four-month period |
First | Basic training | 6 | ||||||||||
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| Topic | Sub-topic |
| TOPIC 1. Curves and surfaces. | 1.1 Plane curves: Definitions. Ways of expressing a plane curve. Some important plane curves. Conics. 1.2 Twisted curves: Definitions. Ways of expressing a twisted curve. Differentiable curve. Tangent vector. 1.3 Surfaces: Definitions. Ways of expressing a surface. Coordinate curves. Tangent plane and normal line. 1.4 Quadrics. 1.5 Surfaces of revolution and translation. 1.6 Ruled surfaces. Types of ruled surfaces. Developable ruled surfaces. Non-developable ruled surfaces. |
| TOPIC 2.- Differential geometry of curves. | 2..1 Twisted curve arc. Definitions. Curvilinear abscissa. Differential element of arc. 2.2 Intrinsic or Frenet's trihedron. Elements of Frenet's trihedron. Equations. 2.3 Curvature and torsion of a twisted curve. Calculation of curvature and torsion. 2.4 Frenet's formulas. |
| TOPIC 3.- Differential geometry of surfaces. | 3.1 First Fundamental Form. 3.2 Angle of two curves on a surface. 3.3 Normal curvature and Second Fundamental Form. 3.4 Directions and asymptotic lines. 3.5 Principal curvature directions and lines of curvature. 3.6 Remarkable curvatures: principal curvatures, mean curvature and Gaussian curvature. 3.7 Classification of points on a surface by Gaussian curvature. Applications. |
| TOPIC 4. Multiple integration. | 4.1 Concept of multiple integral. Properties. 4.2 Calculation of double integrals. 4.3 Change of variable in double integrals. 4.4 Calculation of triple integrals. 4.5 Change of variable in triple integrals. 4.6 Applications of multiple integrals. |
| TOPIC 5. Curvilinear and surface integration. | 5.1 Fundamental concepts of vectorial analysis. 5.2 Line integrals. Green's theorem. 5.3 Surface integrals. 5.4 Gauss-Ostrogradski's theorem. Stokes' theorem. |
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