| Educational guide School of Engineering |
english |
| Bachelor's Degree in Electronic and Automation Engineering (2010) |
 Subjects |
| MATHEMATICAL ANALYSIS II |
| Contents |
| IDENTIFYING DATA | 2023_24 |
| Subject | MATHEMATICAL ANALYSIS II | Code | 17204006 | |||||
| Study programme |
|
Cycle | 1st | |||||
| Descriptors | Credits | Type | Year | Period | ||||
| 6 | Basic Course | First | 1Q 2Q |
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| Competences | Learning outcomes | Contents |
| Planning | Methodologies | Personalized attention |
| Assessment | Sources of information | Recommendations |
| Topic | Sub-topic |
| Multivariable Calculus | - 1. Function domain and range. Function operations. Composition of functions. Level curves. Conics. - 2. Limits and continuity. Directional derivative and partial derivative - 3. Differential and Gradient. Tangent plane and normal line. - 4. Partial Derivatives of Higher order. Taylor formula. Implicit functions. - 5. Local minimum and maximum. Relative extremes. Hessian. Absolute extremes in a compact domain. - 6. Conditional extremes. Lagrange multipliers. |
| Ordinary Differential Equations | - 11. Ordinary Differential Equations (ODEs). Order. Solution of a ODE. Existence and unicity of the solution. - 12. ODEs of First Order. Separation of Variables. Exact Differential. Integrating Factor. Linear Equations. - 13. Second Order ODEs. Particular Solution. Reduction of Order. Lineal ODEs with constant coefficients. Homogeneous and no homogeneous equations. Method of the indeterminate constants. - 14. Models. Population. Disintegration. Heat transfer. Oscillations. |
| Multiple Integration |
- 7. Double Integral. Properties. Geometric Interpretation. Fubini's Theorem. - 8. Change of variables. Jacobian of the transformation. Polar coordinates. Volume computation. - 9. Triple Integral. Properties. Cylindrical and Spherical coordinates. - 10. Center of Gravity. Inertia moments. |
