Mathematics I

ETH Zurich 406-0251-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 401-0251-00L (with classes and materials in German).


Abstract

This course covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations.


Content

I. Differential Calculus
II. Integral Calculus and Ordinary Differential Equations
III. Linear Algebra
IV. Introduction to Systems of Linear Differential Equations


Main bibliography

For course parts I and II:
Thomas, G. B.: Thomas' Calculus - Early Transcendentals, Part 1, Pearson Addison-Wesley.

For course parts III and IV:
Bretscher, O.: Linear Algebra with Applications, Pearson Prentice Hall.


Assistance (October-December):

Tuesdays and Wednesdays 17:15-18:45 in room HG E 41


Course continuation: Mathematics II



Suggested readings:

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

Chapter
Title
Parts covered in course
1
Functions
1.1-1.3, 1.5, 1.6 - that is, omit 1.4 "Graphing with Calculators and Computers"
2
Limits and Continuity
all parts, but 2.1-2.5 (sections on limits) are covered in less depth than in the book
3
Differentiation
all parts, except that in 3.10 we only cover linearization and not differentials
4
Applications of Derivatives
all parts
5
Integration
all parts
6
Applications of Definite Integrals
- this is not covered in Mathematics 1 (it is partly covered in Mathematics 2)
7
Integrals and Transcendental Functions
all parts
8
Techniques of Integration
all parts, except that 8.6 and 8.7 (sections related to numerical methods) are left out, and parts 8.4 and 8.5 (sections on trigonometric integrals and substitutions) are covered in less depth than in the book
9
Further Applications of Integration
all parts; this chapter is titled "First Order Differential Equations" in later editions
10
Conic Sections and Polar Coordinates
- this is not covered in Mathematics 1 (it is partly covered in Mathematics 2)
11
Infinite Sequences and Series
essentially just 11.8 "Taylor and Maclaurin Series" and 11.9 "Convergence of Taylor Series; Error Estimates"

Appendices
most relevant for this course are A.5 "Complex Numbers", A.9 on basic formulas, all of Appendix B (B.1-B.3 on real numbers, lines, circles, parabolas and trigonometric functions), and Appendix C on differential equations except C.6 "First Order: Exact", C.7 "Special Types of Second Order Equations" and C.12 "Vibrations".

Chapters listed from Bretscher's Linear Algebra with Applications, 3rd Edition

Chapter
Title
Parts covered in course
1
Linear Equations
all parts
2
Linear Transformations
all parts
3
Subspaces of R^n and their Dimensions
all parts
4
Linear Spaces
all parts
5
Orthogonality and Least Squares
- this is not covered in Mathematics 1
6
Determinants
all parts
7
Eigenvalues and Eigenvectors
all parts
8
Symmetric Matrices and Quadratic Forms
- this is not covered in Mathematics 1
9
Linear Differential Equations
all parts

Appendix on Vectors
covered


Suggested study plan:

The following is a proposed plan for 14 weeks.
We suggest that you do most of the odd-numbered exercises for the relevant sections.
Solutions to those exercises can be found at the back of the books.

Week
Reading - please refer to tables above for chapter section exclusions
1
Thomas' chapter 1 and appendices A.9 and B
2
Thomas' chapters 2 and 3
3
Thomas' chapter 4 and sections 11.8 and 11.9
4
Thomas' chapters 5 and 7
5
Thomas' chapter 8
6
Thomas' chapter 9 and appendices C.1-C.5, C.8-C.11 and A.5
7
Review all the Differential and Integral Calculus material from weeks 1-6
8
Bretscher's chapter 1 and appendix on vectors
9
Bretscher's chapter 2 and section 3.1
10
Bretscher's sections 3.2-3.4 and chapter 4
11
Bretscher's chapter 6
12
Bretscher's chapter 7
13
Bretscher's chapter 9
14
Review all the Linear Algebra and Systems of Linear Differential Equations material from weeks 8-13


Two of the exercise sheets from the German version of this course in the fall of 2015 have been translated and may be found here.

Old exams:
Mathematics I - January 2018 exam and its solutions in German
Mathematics I - August 2018 exam and its solutions in German
Mathematics I - January 2019 exam and its solutions in German
Mathematics I - January 2020 exam and its solutions in German

There are more exams for the Math I & II sequence at the bottom of the Mathematics II webpage.



Last update: May/2020