# MT1652: Mathematics for Engineers 2B

This course introduces first year engineering students to
• Simple first order differential equations.
• Second order ordinary differential equations.
• Matrices, determinants, eigenvalues and eigenvectors.
• Basic ideas in statistics.

The course is currently taught by Dr. Matthias Heil. This page provides online access to the lecture notes, example sheets and other handouts and announcements.

Please note that the lecture notes only summarise the main results and will generally be handed out after the material has been covered in the lecture.

If you have any questions about the lecture, please see me in my office (18.07), contact me by email ( M.Heil@maths.man.ac.uk) or catch me after the lecture.

## Exam:

 EXAM:As far as I know (please check!), the exam will be on May 18, 2000 from 2-4pm Please note that this course has not been given before, so there are no (representative) old exams available. Here's a mock exam paper which should give you some idea of what to expect... GOOD LUCK!

The course will be examined in a two hour exam in June. Coursework (in the form of two module tests) will account for 20% of the final mark. The module tests will be held during the normal lecture times and the dates will be announced approximately 2 weeks in advance.

## Handouts:

• Example Sheet I (pdf).
• Table of elementary integrals(pdf).
• Example Sheet II (pdf).
• Handout for 1st order ODEs (pdf) .
• Example Sheet III (pdf).
• Reminder: How to find the roots of quadratic polynomials (pdf).
• Illustration of a purely damped motion (pdf).
• Illustration of a damped oscillatory motion (pdf).
• Illustration of a critically damped motion without overshoot (pdf).
• Illustration of a critically damped motion with overshoot (pdf).
• Example Sheet IV (pdf).
• Illustration of the amplitude of a harmonic oscillator in response to harmonic forcing (pdf).
• Illustration of the phase relationship of a harmonic oscillator in response to harmonic forcing (pdf).
• Handout for resonance (pdf) .
• Illustration of the forced and transient components in the response of a harmonic oscillator to harmonic forcing (pdf) .
• Example Sheet V (pdf).
• Handout for 2nd order ODEs (pdf ).
• Copy of the OHP transparencies covering the introduction to matrix algebra (pdf).
• Example Sheet VI (pdf).
• Copy of the OHP transparencies covering Gaussian elimination, pivoting and determinants (pdf).
• Example Sheet VII (pdf).
• Copy of the OHP transparencies covering eigenvalues and eigenvectors (pdf).
• Example Sheet VIII (pdf).
• Copy of the OHP transparencies for the introduction to Statistics and Probability (pdf).
• Example Sheet IX (pdf).
• Copy of the OHP transparencies for continuous probability distributions (pdf).
• Example Sheet X (pdf).
Please note a few corrections for previous handouts (the files above have already been corrected).

## Exam Revision:

Do you need more material to revise for the exam? Try this site: I also recommend Schaum's Outline Series (that's the title of the series -- Schaum is not the author!) which you can find in the library.