Syllabus

Course Catalogue

This is a

This course is parallel to the regular course 401-0251-00L (with classes and materials in German).

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

I. Differential Calculus

II. Integral Calculus and Ordinary Differential Equations

III. Linear Algebra

IV. Introduction to Systems of Linear Differential Equations

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.

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

Chapters listed from

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

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:

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

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

Last update: May/2020