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 (with 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 17:15-18:45 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"


Study plan (for approximately 14 weeks):
Besides reading the above book parts, we suggest that you do most of the corresponding odd-numbered exercises.
Solutions to those exercises can be found at the back of the books.



Eigenfunctions allowed in the exam without proof (PDF)


Old exams

Mathematics II - August 2016 exam and its solutions in German

Mathematics I and II - January 2015 exam and its solutions in German
Mathematics I and II - August 2015 exam and its solutions in German
Mathematics I and II - January 2016 exam and its solutions in German
Mathematics I and II - August 2016 exam and its solutions in German
Mathematics I and II - August 2019 exam and its solutions in German
Mathematics I and II - January 2020 exam and its solutions in German

Last update: 20/May/2020