Mathematics II
ETH Zurich 406-0252-AAL
Syllabus
Course Catalogue
Lecturer in 2023-2024: 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.
Content
V. Functions of Several Variables and Partial Derivatives
VI. Multiple Integrals
VII. Integration of Vector Fields and Integral Theorems
VIII. Introduction to 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:
Kreyszig, E.: Advanced Engineering Mathematics, John Wiley & Sons.
Assistance
October through December, Mondays and Tuesdays 12-14h in room HG E 41
March through May, Wednesdays 12-14h 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"
|
Suggested 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)
Recent exams - Math II
The solutions are provided only in German and for the larger Math I and II exam.
Mathematics II - August 2020 exam and the solutions
Mathematics II - August 2023 exam and the solutions
Mathematics II - January 2023 exam
and its solutions
Recent exams - Math I and II
The solutions are provided only in German.
Mathematics I and II - January 2020 exam
and its solutions
Mathematics I and II - August 2020 exam and its solutions
Mathematics I and II - January 2021 exam
and its solutions
Mathematics I and II - January 2023 exam
and its solutions
Mathematics I and II - August 2023 exam and its solutions
Last update: September/2023
|