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
|