Name | Prof. Dr. Ana Cannas da Silva |

Address | Dep. Mathematik ETH Zürich, HG G 27.4 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 85 90 |

ana.cannas@math.ethz.ch | |

URL | http://www.math.ethz.ch/~acannas |

Department | Mathematics |

Relationship | Adjunct Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-0252-00L | Mathematics II | 7 credits | 5V + 2U | A. Cannas da Silva | |

Abstract | Continuation of the topics of Mathematics I. Main focus: multivariable calculus and partial differential equations. | ||||

Learning objective | Mathematics is of ever increasing importance to the Natural Sciences and Engineering. The key is the so-called mathematical modelling cycle, i.e. the translation of problems from outside of mathematics into mathematics, the study of the mathematical problems (often with the help of high level mathematical software packages) and the interpretation of the results in the original environment. The goal of Mathematics I and II is to provide the mathematical foundations relevant for this paradigm. Differential equations are by far the most important tool for modelling and are therefore a main focus of both of these courses. | ||||

Content | - Multivariable Differential Calculus: functions of several variables, partial differentiation, curves and surfaces in space, scalar and vector fields, gradient, curl and divergence. - Multivariable Integral Calculus: multiple integrals, line and surface integrals, work and flow, Gauss and Stokes theorems, applications. - Partial Differential Equations: separation of variables, Fourier series, heat equation, wave equation, Laplace equation, Fourier transform. | ||||

Lecture notes | See literature | ||||

Literature | - Thomas, G. B.: Thomas' Calculus, Part 2, Pearson Addison-Wesley. - Kreyszig, E.: Advanced Engineering Mathematics, John Wiley & Sons. | ||||

Prerequisites / Notice | Assistance: Tu 17-19, We 17-19, Fr 12-14 in Room HG E 41. | ||||

401-5580-00L | Symplectic Geometry Seminar | 0 credits | 2K | D. A. Salamon, P. Biran, A. Cannas da Silva | |

Abstract | Research colloquium | ||||

Learning objective | |||||

406-0251-AAL | Mathematics I Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 6 credits | 13R | A. Cannas da Silva | |

Abstract | This course covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations. | ||||

Learning objective | Mathematics is of ever increasing importance to the Natural Sciences and Engineering. The key is the so-called mathematical modelling cycle, i.e. the translation of problems from outside of mathematics into mathematics, the study of the mathematical problems (often with the help of high level mathematical software packages) and the interpretation of the results in the original environment. The goal of Mathematics I and II is to provide the mathematical foundations relevant for this paradigm. Differential equations are by far the most important tool for modelling and are therefore a main focus of both of these courses. | ||||

Content | 1. Linear Algebra and Complex Numbers: systems of linear equations, Gauss-Jordan elimination, matrices, determinants, eigenvalues and eigenvectors, cartesian and polar forms for complex numbers, complex powers, complex roots, fundamental theorem of algebra. 2. Single-Variable Calculus: review of differentiation, linearisation, Taylor polynomials, maxima and minima, fundamental theorem of calculus, antiderivative, integration methods, improper integrals. 3. Ordinary Differential Equations: variation of parameters, separable equations, integration by substitution, systems of linear equations with constant coefficients, 1st and higher order equations, introduction to dynamical systems. | ||||

Literature | - Bretscher, O.: Linear Algebra with Applications, Pearson Prentice Hall. - Thomas, G. B.: Thomas' Calculus, Part 1, Pearson Addison-Wesley. | ||||

406-0252-AAL | Mathematics II Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 7 credits | 15R | A. Cannas da Silva | |

Abstract | Continuation of the topics of Mathematics I. Main focus: multivariable calculus and partial differential equations. | ||||

Learning objective | Mathematics is of ever increasing importance to the Natural Sciences and Engineering. The key is the so-called mathematical modelling cycle, i.e. the translation of problems from outside of mathematics into mathematics, the study of the mathematical problems (often with the help of high level mathematical software packages) and the interpretation of the results in the original environment. The goal of Mathematics I and II is to provide the mathematical foundations relevant for this paradigm. Differential equations are by far the most important tool for modelling and are therefore a main focus of both of these courses. | ||||

Content | - Multivariable Differential Calculus: functions of several variables, partial differentiation, curves and surfaces in space, scalar and vector fields, gradient, curl and divergence. - Multivariable Integral Calculus: multiple integrals, line and surface integrals, work and flow, Gauss and Stokes theorems, applications. - Partial Differential Equations: separation of variables, Fourier series, heat equation, wave equation, Laplace equation, Fourier transform. | ||||

Literature | - Thomas, G. B.: Thomas' Calculus, Part 2, Pearson Addison-Wesley. - Kreyszig, E.: Advanced Engineering Mathematics, John Wiley & Sons. | ||||

406-0253-AAL | Mathematics I & II Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 13 credits | 28R | A. Cannas da Silva | |

Abstract | Mathematics I covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations. Main focus of Mathematics II: multivariable calculus and partial differential equations. | ||||

Learning objective | Mathematics is of ever increasing importance to the Natural Sciences and Engineering. The key is the so-called mathematical modelling cycle, i.e. the translation of problems from outside of mathematics into mathematics, the study of the mathematical problems (often with the help of high level mathematical software packages) and the interpretation of the results in the original environment. The goal of Mathematics I and II is to provide the mathematical foundations relevant for this paradigm. Differential equations are by far the most important tool for modelling and are therefore a main focus of both of these courses. | ||||

Content | 1. Linear Algebra and Complex Numbers: systems of linear equations, Gauss-Jordan elimination, matrices, determinants, eigenvalues and eigenvectors, cartesian and polar forms for complex numbers, complex powers, complex roots, fundamental theorem of algebra. 2. Single-Variable Calculus: review of differentiation, linearisation, Taylor polynomials, maxima and minima, fundamental theorem of calculus, antiderivative, integration methods, improper integrals. 3. Ordinary Differential Equations: variation of parameters, separable equations, integration by substitution, systems of linear equations with constant coefficients, 1st and higher order equations, introduction to dynamical systems. 4. Multivariable Differential Calculus: functions of several variables, partial differentiation, curves and surfaces in space, scalar and vector fields, gradient, curl and divergence. 5. Multivariable Integral Calculus: multiple integrals, line and surface integrals, work and flow, Gauss and Stokes theorems, applications. 6. Partial Differential Equations: separation of variables, Fourier series, heat equation, wave equation, Laplace equation, Fourier transform. | ||||

Literature | - Bretscher, O.: Linear Algebra with Applications, Pearson Prentice Hall. - Thomas, G. B.: Thomas' Calculus, Part 1, Pearson Addison-Wesley. - Thomas, G. B.: Thomas' Calculus, Part 2, Pearson Addison-Wesley. - Kreyszig, E.: Advanced Engineering Mathematics, John Wiley & Sons. | ||||

701-0106-00L | Mathematics V: Applied Deepening of Mathematics I - III | 3 credits | 2G | M. A. Sprenger, A. Cannas da Silva | |

Abstract | Selected mathematical topics are presented for later use in more specialised lectures. Part of the topics were already discussed in the lectures Mathematics I-III. Here, they should be shortly recapitulated and most importantly applied to practical problems. If necessary, new mathematical concepts and methods will be introduced in order to solve challenging and inspiring problems from practice. | ||||

Learning objective | The aim of this lecture is to prepare the students for the more specialised lectures. They should become more familiar with the mathematical background, the mathematical concepts und most of all with their application and interpretation. | ||||

Content | Practical examples from the following areas will be discussed: ordinary differential equations; eigenvalue problems from linear algebra; systems of linear and nonlinear differential equations; partial differential equations (diffusion, transport, waves). |