Mathematics II

Mathematics II

ETH Zurich 406-0252-AAL

Syllabus

Course Catalogue

Lecturer: Ana Cannas

This is a self-study course, with no presence required.
This course is parallel to the regular course 401-0252-00L which has classes and materials in German.

Abstract

This course is a continuation of Mathematics I. The main focus is multivariable calculus and partial differential equations.

Content

V. Functions of Several Variables and Partial Derivatives
VI. Multiple Integrals
VII. Integration of Vector Fields and Integral Theorems
VIII. Fourier Series and Partial Differential Equations

Main Bibliography

For course parts V-VII:
Thomas, G. B.: Thomas' Calculus, Part 2, Pearson Addison-Wesley.

For course part VIII: two chapters from
Kreyszig, E.: Advanced Engineering Mathematics, John Wiley & Sons.

Assistance (March-May):

Tuesdays and Wednesdays 18-19h in room HG E 41

Course Prequel: Mathematics I

Suggested readings:

Chapters listed from Thomas' Calculus Part Two, 11th Edition:

Chapter	Title	Parts covered in course
12	Vectors and the Geometry of Space	all parts
13	Vector-Valued Functions and Motion in Space	13.1-13.3, so omit curvature, torsion and planetary motion
14	Partial Derivatives	all parts except 14.8 "Lagrange Multipliers" and 14.9 "Partial Derivatives with Constrained Variables" and omit differentials
15	Multiple Integrals	all parts except 15.7 "Substitutions in Multiple Integrals"
16	Integration in Vector Fields	all parts

Chapters listed from Thomas' Calculus (Early Transcendentals), 11th Edition:

Chapter	Title	Parts covered in course
6	Applications of Definite Integrals	only 6.3 "Lengths of Plane Curves" and 6.4 "Moments and Centers of Mass"
10	Conic Sections and Polar Coordinates	only 10.1 "Conic Sections and Quadratic Equations", 10.5 "Polar Coordinates", 10.6 "Graphing in Polar Coordinates" and 10.7 "Areas and Lengths in Polar Coordinates"

Chapters listed from Kreyszig's Advanced Engineering Mathematics, 10th Edition (only chapters of book part C):

Chapter	Title	Parts covered in course
11	Fourier Analysis	11.1 "Fourier Series", 11.2 "Arbitrary Period, Even and Odd Functions, Half-Range Expansions"
12	Partial Differential Equations	12.1 "Basic Concepts of PDEs", 12.2 "Modeling: Vibrating String, Wave Equation", 12.3 "Solution by Separating Variables, Use of Fourier Series", 12.6 "Heat Equation: Solution by Fourier Series, Steady Two-Dimensional Heat Problems, Dirichlet Problem"

Last update: March/2021