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 | |
---|---|---|---|---|---|

401-0251-00L | Mathematics I | 6 credits | 4V + 2U | 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. | ||||

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. Single-Variable Calculus: review of differentiation, linearisation, Taylor polynomials, maxima and minima, antiderivative, fundamental theorem of calculus, integration methods, improper integrals. 2. 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. 3. Ordinary Differential Equations: separable ordinary differential equations (ODEs), integration by substitution, 1st and 2nd order linear ODEs, homogeneous systems of linear ODEs with constant coefficients, introduction to 2-dimensional dynamical systems. | ||||

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

Prerequisites / Notice | Prerequisites: familiarity with the basic notions from Calculus, in particular those of function and derivative. Mathe-Lab (Assistance): Mondays 12-14, Tuesdays 17-19, Wednesdays 17-19, in Room HG E 41. | ||||

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

Abstract | Research colloquium | ||||

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. | ||||

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, antiderivative, fundamental theorem of calculus, integration methods, improper integrals. 3. Ordinary Differential Equations: separable ordinary differential equations (ODEs), integration by substitution, 1st and 2nd order linear ODEs, homogeneous systems of linear ODEs with constant coefficients, introduction to 2-dimensional dynamical systems. | ||||

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

Prerequisites / Notice | Prerequisites: familiarity with the basic notions from Calculus, in particular those of function and derivative. Assistance: Tuesdays and Wednesdays 17-19h, in Room HG E 41. | ||||

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. | ||||

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 flux, Green, 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, Parts 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. | ||||

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, antiderivative, fundamental theorem of calculus, integration methods, improper integrals. 3. Ordinary Differential Equations: separable ordinary differential equations (ODEs), integration by substitution, 1st and 2nd order linear ODEs, homogeneous systems of linear ODEs with constant coefficients, introduction to 2-dimensional 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, Green, 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 - Early Transcendentals (Pearson Addison-Wesley). - Thomas, G. B.: Thomas' Calculus, Parts 2 (Pearson Addison-Wesley). - Kreyszig, E.: Advanced Engineering Mathematics (John Wiley & Sons). | ||||

Prerequisites / Notice | Prerequisites: familiarity with the basic notions from Calculus, in particular those of function and derivative. Assistance: Tuesdays and Wednesdays 17-19h, in Room HG E 41. |