Syllabus

Course Catalogue

This is a

This course is parallel to the regular course 401-0252-00L which has classes and materials in German.

This course is a continuation of Mathematics I. The main focus is multivariable calculus and partial differential equations.

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

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.

Tuesdays and Wednesdays 18-19h in room HG E 41

Chapters listed from

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

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

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):

Solutions to those exercises can be found at the back of the books.

Eigenfunctions allowed in the exam without proof (PDF)

Last update: March/2021