|
Teaching GuideTerm Higher Polytechnic University College |
| Grao en Enxeñaría Mecánica |
 Subjects |
| Calculus |
| Contents |
|
|
|
| Identifying Data | 2018/19 | |||||||||||||
| Subject | Calculus | Code | 730G03001 | |||||||||||
| Study programme |
|
|||||||||||||
| Descriptors | Cycle | Period | Year | Type | Credits | |||||||||
| Graduate | 1st four-month period |
First | Basic training | 6 | ||||||||||
|
||||||||||||||
| Topic | Sub-topic |
| The following topics develop the contents established in the verification report |
-Mean value theorems. -Introduction to vector calculus. -Taylor theorem and higher order derivatives. -Maximum and minimum. -Implicit function and inverse function. -Definite and indefinite integral. -Primitive Calculus. -Double and triple integrals. Applications to computing areas and volumes. |
| Complex numbers | The field of complex numbers. Operations: sum, produt. Module and argument. Polar form. Operating in polar form. |
| The space R^n | The vector space R^n. Scalar product: norms and distances. Classification of points and sets. Topology of R^n: bounded set, extrema. Coordinates systems: polar, cylindrical and spherical coordinates. |
| Functions of several variables | Scalar and vector functions. Level sets. Continuity. Continuity in compact sets. |
| Differenciation of funcions of several variables | Directional derivative. Partial derivatives: properties and practical computing. Differential map of a function. Gradient, relation with partial derivatives. Relation between the differential map and partial derivatives: jacobian matrix. Higher order partial derivatives. Introduction to vector calculus. |
| Applications of the differenciation of functions of several variables | Taylor polynomial for funcions of one and several variables. Critical points. Classification: Hessian matrix. Constrained optimization: dimensionality reduction, Lagrange multipliers method. Implicit function and inverse function theorems. |
| Integration of funcions of one variable | Riemann sums. Integrable functions. Integral Calculus Theorems: Mean Value Theorem, Fundamental Theorem and Barrow's rule. Primitive Calculus. Polinomial interpolation. Numerical integration. Compound Simpson's Rule. Application of integral calculus to computing arc lengths, volumes of revolution and surface areas of revolution. |
| Integration of functions of several variables | Double integrals. Triple integrals. Change of variable in double and triple integrals. Application of integral calculus to computing volume and mass of a solid body and its center of mass. |
|
