After successful completion of the course, students are able to...

• correctly use the terms vector space, linear dependency and basis,
• describe the properties of an inner product and a norm and to apply them in specific computations,
• explain the relation between linear functions and matrices,
• perform calculations with matrices, in particular to invert matrices and perform a change of basis,
• identify linear systems of equations and efficiently determine and interpret the set of solutions,
• determine and interpret determinant, eigenvalues and eigenvectors,
• differentiate real functions in several variables, expand them in Taylor series and determine their local extrema,
• parametrize basic paths and surfaces and determine and interpret integrals over those paths and surfaces,
• calculculate and interpret divergence, gradient and curl of vector resp. scalar fields and represent them using nabla,
• solve linear and exact differential equations as well as linear systems of differential equations,
• construct simple probability spaces and calculate (conditional) probabilities,
• calculate expectation value and variance of random variables,
• describe the applicability of the law of large numbers and the central limit theorem.

Linear algebra, ordinary differential equations, systems of linear differential equations, differential calculus, multiple integrals, basic concepts of vector analysis, linear partial differential equations.

Solving preassigned problems. Discussion of questions in the weekly plenum.

This exercise class uses examples to illustrate the content of the lecture Mathematics 2 for Civil Engineering. The exercise class takes place on 10 dates (see schedule) in groups (in presence). In addition, plenary revision sessions are held on Fridays. Furthermore, there are two midterm exams on separate dates. There is a points system for assessment, with a total of 100 points to be achieved.

Registration

Registration for the course (or for an exercise group) is possible in TISS from Tuesday, October 1, 2024, until Monday, October 7, 2024, 12:00 noon. In order to ensure an even occupancy rate of the various exercise groups, the participant limit will be raised gradually. As soon as the maximum number of participants has been reached in all groups, it will be increased further. There are enough places available - anyone who wants to attend the exercise class will be allocated a place. However, we cannot guarantee a place in the desired group. After the end of the registration period, it is no longer possible to change groups. When you register in TISS, you also register for the accompanying e-learning course (TUWEL).

Procedure of the exercise units

Approximately one week before each exercise unit, exercise sheets with examples are provided in the TUWEL course, which are discussed at the respective exercise unit. This is done partly through pre-arranged blackboard presentations or also through voluntary presentations. In addition, short tests are held in exercise units 2, 3, 4, 5, 7, 8, 9, and 10.

Blackboard presentations

From the second exercise unit onwards, selected examples (approx. 3-4 per unit) are presented by small groups (approx. 2-3 people). In order to pass this course/obtain a positive grade, you need at least one positively assessed blackboard presentation. No points are awarded for this compulsory presentation (points can, however, be earned for additional presentations; see bonus points). A date will be assigned at the beginning of the semester and the specific example to be presented will be assigned one week before the date. In the case of a negatively assessed presentation, this can be repeated once (individual appointment).

Short tests

In the 2nd, 3rd, 4th, and 5th exercise units and in the 7th, 8th, 9th, and 10th exercise units, short tests on the material from the previous exercise unit take place at the beginning of each exercise unit. Each short test lasts 10 minutes and is graded with up to 6 points. In the overall assessment, two strike results are taken into account - one for the short tests from exercises 2-5 and one for the short tests from exercises 7-10. This means that the three best short tests from the first half of the semester and the three best short tests from the second half of the semester are taken into account in the overall assessment. This means that a total of 36 points can be achieved on short tests.

Midterm exams

The first midterm exam will take place on Friday, November 8, 2024, at 16:00 in GM 1 Audi. Max. The second exam is expected to take place on Thursday, January 9, 2025, at 16:00. The working time for each of these exams is 60 minutes and no aids are permitted. Each exam is worth 32 points, which means that a total of 64 points can be achieved with midterm exams.

Bonus points

Problems of exercise sheets that are not assigned for compulsory presentations in advance can be presented voluntarily on the blackboard by motivated exercise participants. Up to 3 bonus points can be achieved per blackboard presentation, whereby the assessment is carried out by the respective instructor of the class. Only positive grades can be improved by bonus points, i.e. an otherwise negative grade cannot be improved to a positive grade by bonus points.

Retaking midterm exams

For students who have missed one of the two midterm exams on the regular date for good reason and with proof (illness, doctor's appointment, etc.), it is possible to participate in an exam at the end of the semester (Exam material is the material of the entire exercise class). A written confirmation of the reason for absence (e.g. confirmation from a doctor) is required for participation in this extra exam, which must be presented directly at the exam (in particular, such confirmations should not be sent by e-mail to the exercise instructors). Registration is required for participation in the extra exam (you will receive more detailed information in good time).

Grading

The grading is as follows:

• Sufficient/4 from 50 points
• Satisfactory/3 from 63 points
• Good/2 from 75 points
• Very Good/1 from 88 points

Please note that for a positive grade, you also need a positively evaluated blackboard presentation.

Attendance and partial performances

Partial performances

• Blackboard presentation
• 8 short tests (two strike results)
• 2 midterm exams

Repeatable partial performances

The compulsory blackboard presentation can be repeated in the event of a negative assessment. Short tests and midterm exams are not repeatable partial performances, as these are assessed with less than 50 points each, and therefore, a positive assessment is still possible without individual tests/exams.

Attendance

There is no particular attendance requirement or attendance quota. However, you must be present in order to take part in short tests and midterm exams. If you do not show up for your mandatory blackboard presentation, it will be assessed negatively, and you can repeat it once.

Schedule

The dates given in the TISS calendar only reflect the room reservations. The (provisional) dates for this course are as follows:

Tuesday 8.10.: 1st exercise
Friday 11.10.: revision course

Tuesday 15.10.: 2nd exercise (incl. short test)
Friday 18.10.: revision course

Tuesday 22.10.: 3rd exercise (incl. short test)
Friday 25.10.: revision course

Tuesday 29.10.: 4th exercise (incl. short test)

Tuesday 5.11.: 5th exercise (incl. short test)

Thursday 7.11.: exam preparation
Friday 8.11.: 1st midterm exam

Tuesday 12.11.: 6th exercise

Tuesday 19.11.: 7th exercise (incl. short test)
Friday 22.11.: revision course

Tuesday 26.11.: 8th exercise (incl. short test)
Friday 29.11.: revision course

Tuesday 3.12.: 9th exercise (incl. short test)
Friday 6.12.: revision course

Tuesday 10.12.: 10th exercise (incl. short test)
Friday 13.12.: revision course

Wednesday 8.1.: exam preparation
Thursday 9.1.: 2nd midterm exam

• Presenting preassigned problems on the blackboard
• Short tests
• Midterm exams

The positive completion of the exercise class Mathematics 1 for Civil Engineering is strongly recommended!