Cornelia Busch: Catalogue data in Autumn Semester 2016 |
Name | Dr. Cornelia Busch |
Address | Lehre Mathematik ETH Zürich, HG G 34.2 Rämistrasse 101 8092 Zürich SWITZERLAND |
Telephone | +41 44 632 82 69 |
cornelia.busch@math.ethz.ch | |
Department | Mathematics |
Relationship | Lecturer |
Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|
401-0203-00L | Mathematics | 4 credits | 2V + 1U | C. Busch | |
Abstract | This course gives an introduction to the following subjects: linear algebra (systems of linear equations, matrices), calculus, multivariable calculus, differential equations. | ||||
Objective | Basic mathematical knowledge for engineers. Mathematics as a tool to solve engineering problems. | ||||
Content | This course gives an introduction to the following subjects: linear algebra (systems of linear equations, matrices), calculus, multivariable calculus, differential equations. | ||||
Literature | Tom M. Apostol, Calculus, Volume 1, One-Variable Calculus with an Introduction to Linear Algebra, 2nd Edition, Wiley Tom M. Apostol, Multi-Variable Calculus and Linear Algebra with Applications, 2nd Edition, Wiley | ||||
401-3180-66L | Homological Algebra Number of participants limited to 12. | 4 credits | 2S | C. Busch | |
Abstract | Basic concepts of homological algebra, homology and cohomology of groups. | ||||
Objective | |||||
Literature | Peter J. Hilton, Urs Stammbach: A Course in Homological Algebra, Second Edition, Graduate Texts in Mathematics 4, Springer 1997 Kenneth S. Brown: Cohomology of Groups, Graduate Texts in Mathematics 87, Springer-Verlag 1982 Charles A. Weibel: An Introduction to Homological Algebra, Cambridge Studies in Advanced Mathematics 38, Cambridge University Press, 1994 | ||||
406-0242-AAL | Analysis 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 | M. Akveld, C. Busch | |
Abstract | Mathematical tools of an engineer | ||||
Objective | Mathematics as a tool to solve engineering problems, mathematical formulation of problems in science and engineering. Basic mathematical knowledge of an engineers. | ||||
Content | Multi variable calculus: gradient, directional derivative, chain rule, Taylor expansion, Lagrange multipliers. Multiple integrals: coordinate transformations, path integrals, integrals over surfaces, divergence theorem, applications in physics. Ordinary differential equations. | ||||
Literature | Textbooks in English: - J. Stewart: Multivariable Calculus, Thomson Brooks/Cole - V. I. Smirnov: A course of higher mathematics. Vol. II. Advanced calculus - W. L. Briggs, L. Cochran: Calculus: Early Transcendentals: International Edition, Pearson Education - M. Akveld, R. Sperb, Analysis II, vdf - L. Papula: Mathematik für Ingenieure 2, Vieweg Verlag | ||||
406-0243-AAL | Analysis I and 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. | 14 credits | 30R | M. Akveld, C. Busch | |
Abstract | Mathematical tools for the engineer | ||||
Objective | Mathematics as a tool to solve engineering problems. Mathematical formulation of technical and scientific problems. Basic mathematical knowledge for engineers. | ||||
Content | Complex numbers. Calculus for functions of one variable with applications. Simple Mathematical models in engineering. Multi variable calculus: gradient, directional derivative, chain rule, Taylor expansion, Lagrange multipliers. Multiple integrals: coordinate transformations, path integrals, integrals over surfaces, divergence theorem, applications in physics. Ordinary differential equations. | ||||
Literature | Textbooks in English: - J. Stewart: Calculus, Cengage Learning, 2009, ISBN 978-0-538-73365-6. - J. Stewart: Multivariable Calculus, Thomson Brooks/Cole. - V. I. Smirnov: A course of higher mathematics. Vol. II. Advanced calculus. - W. L. Briggs, L. Cochran: Calculus: Early Transcendentals: International Edition, Pearson Education. ISBN 978-0-321-65193-8. Textbooks in German: - M. Akveld, R. Sperb: Analysis I, vdf - M. Akveld, R. Sperb: Analysis II, vdf - L. Papula: Mathematik für Ingenieure und Naturwissenschaftler, Vieweg Verlag - L. Papula: Mathematik für Ingenieure 2, Vieweg Verlag |