Lectures: Monday 11:00-12:15, Wednesday 11:00-12:15, Lecture Hall

Problem sessions: Wednesday 15:30-16:45, Friday 9:30-10:45, East Hall 4

Tutorials: Tuesday 11:00-12:15, Thursday 12:15-13:30, West Hall 8

This course page provides the material to be discussed in the lecture General Mathematics II (transparencies as pdf files). You will find it most beneficial if you retrieve and have a look at the files in advance. Furthermore, you find the current problem sheet and the older ones on this page.

Date	Topics	PDF
Feb. 4	General information	A4, A5
	1.0 Intoduction to multivariable calculus	A4, A5
	1.1 Curves	A4, A5
Feb. 6	1.2 Functions of several variables	A4, A5
	1.3 Partial derivatives	A4, A5
Feb. 11	1.4 Chain rule, implicit differentiation	A4, A5
Feb. 13	1.5 Gradient, directional derivative	A4, A5
Feb. 18	1.6 Linear approximation	A4, A5
Feb. 20	1.7 Minimax problems	A4, A5
	Notes on 2nd-order derivatives	A4, A5
Feb. 27	SHORT EXAM on multivariable calculus

Date	Topics	PDF
Feb. 25	2.0 Introduction to Integration Theory	A4, A5
	2.1 Antiderivatives	A4, A5
	2.2 Definite Integrals	A4, A5
Mar. 04	2.3 Methods of Integration	A4, A5
Mar. 06	2.4 Riemann sums and the Integral	A4, A5
Mar. 11	2.5 Line integration	A4, A5
Mar. 13	2.6 Solids and surfaces of revolution	A4, A5
	2.7 Numerial integration	A4, A5
Mar. 18	2.8 More about integration	A4, A5
Mar. 20	SHORT EXAM on integration

Date	Topics	PDF
Mar. 25	3.1 Vectors in Space	A4, A5
Apr. 03	3.2 Lines and Planes in Space	A4, A5
Apr. 08	3.3 Systems of Linear Equations	A4, A5
Apr. 10	3.4 Matrix Calculus I	A4, A5
Apr. 15	3.5 Matrix Calculus II	A4, A5
Apr. 17	3.5 Matrix Calculus II	A4, A5
Apr. 24	SHORT EXAM on basic linear algebra

Date	Topics part 4a	PDF	Topics part 4b	PDF
Apr. 22	4a.0 Introduction to differential equations	A4,A5	4b.1 Vector spaces	A4, A5
Apr. 29	4a.1 First-order ODEs	A4, A5	4b.2 Linear mappings and matrices	A4, A5
May 06	4a.2 Exact differential equations	A4, A5	4b.3 Determinants	A4, A5
May 08	4a.3 Second-order ODEs	A4, A5	4b.4 Eigenvalues and Eigenvectors	A4, A5
May 13	4a.4 Linear ODEs	A4, A5	4b.5 Canonical forms of matrices	A4, A5
May 15	4a.5 Linear ODEs with constant coefficients	A4, A5	4b.6 Review session	A4, A5

No.	Topics	Due date	Problems	Solutions
11a	Separable variables	May 06	gm2-pro11a.pdf	gm2-sol11a.pdf
12a	Exact DEs, second-order ODEs	May 13	gm2-pro12a.pdf	gm2-sol12a.pdf
13a	Linear ODEs	May 21	gm2-pro13a.pdf	gm2-sol13a.pdf

No.	Topics	Due date	Problems	Solutions
11b	Vector spaces	May 06	gm2-pro11b.pdf	gm2-sol11b.pdf
12b	Linear mappings	May 13	gm2-pro12b.pdf	gm2-sol12b.pdf
13b	Eigenvalues	May 21	gm2-pro13b.pdf	gm2-sol13b.pdf

Short exams

• Part 1 (multivariable calculus): February 27, 2002.
• Part 2 (integration): March 20, 2002.
• Part 3 (basic linear algebra): April 24, 2002.

Final exam: May 24, 2002.

The course is designed for non-mathematics majors who need to use certain mathematical tools and methods in their discipline. It discusses a larger area of mathematics with an emphasis on how to use mathematical techniques. There is less stress on rigor of the mathematical foundations.

The course General Mathematics II is a continuation of General Mathematics I.

Topics:

1. Multivariable calculus
2. Integration
3. Basic linear algebra
4. (a) Differential equations
   (b) Advanced linear algebra

Course assessment:

• Solution of problem sheets: 25%
• Three short exams: 15% each
• Final exam: 30%

Textbook: Edwards & Penney, Calculus with analytic geometry

In response to some problems in General Mathematics I (heterogeneous audience with regard to prior knowledge, expectations and needs), we decided to provide several new features.

• Course material (slides) will available on the web before the actual lecture.
• More guidance for the solution of the current (not just the past) problem sheet will be provided in the problem sessions.
• Additional tutorials held by a professional lecturer are meant to recapitulate the material presented in class. Students are strongly encourage to pose questions and interact with the lecturer on an individual basis.
• The fourth part of the course is splitted into two:
  (a) Advanced linear algebra
  (b) Differential equations
  Students may select the material that suits their needs best.

The (additional) tutorials will be offered each Tuesday at 11:00 and each Thursday at 12:15.

Important note: If you want to benefit from the new features, you should download the transparencies and the problem sheets in advance and make yourself familiar with the material before the actual class session. Then you have some freedom of choice.

Students with prior knowledge:

On the basis of the material to be discussed in class, decide whether you want to attend or not. Attendance of problem solving sessions is not required either. Course assessment is only by homework and the results of the exams.

Students without prior knowledge:

Attend the regular class sessions. Have a thorough look at the current problem sheet before you go to your problem solving session to assess the main difficulties. The instructor will answer your questions, he or she will provide guidance and support (but won't give complete solutions, of course).

Students who need additional help:

In addition to the regular class sessions and your problem solving session, attend the tutorials where the course material is again discussed and strong interaction with the lecturer is encouraged.

To conclude, two important messages.

Mathematics is fun.

And, whatever happens during this lecture:

Don't panic.

• Dietrich Burde
• Joachim Vogt
• Angela Köhler
• Michael Kropf
• Felix Krahmer
• Akhil Agrawal
• Patrycja Kozik
• Gediminas Luksys