Mathematics for Multimedia Applications

Math cafe

Please remember that we have a math-cafe where you can get help with your unsolved exercises (provided you have signed up as described here). Next session is:

  • Aalborg: Not scheduled yet.
  • Copenhagen: Not scheduled yet.

Literature

Edwards, Penney, Spence, Insel, Friedberg: Mathematics for Multimedia Applications, Compiled by Iver Ottosen Aalborg University, Pearson (2014), ISBN 978-1-78399-714-5

Exam and hand-ins

The course will be concluded with a 4-hour exam. Books and notes are allowed, but no calculators, computers, cell phones or the like.

To be eligible to take the exam, you must have at least 2 accepted self-study assignments (miniprojects) and 5 accepted ordinary hand-in exercises.

The final exam is a four hour written exam which takes place after the course has finished.

The course is graded using the 7-point scale.

Practical remarks regarding hand-ins and miniprojects

There is a deadline for handing in each assignment. After the deadline, a teaching assistant will check the hand-ins. The corrected hand-in will be returned with comments.

Hand-in exercises and miniprojects must be handed in before the deadline. The hand-in must include your name and the session number for the hand-in. MATLAB figures can be saved as pdf-files via File -> Save As -> choose pdf format.

Syllabus

Part 1: Calculus

  • Appendix C, page 1-5
  • Section 3.1, 3.2, 3.3, page 60-91
  • Section 3.7, 3.8, page 123-146
  • Section 5.3, page 195-203
  • Section 5.4, page 207-212 (middle)
  • Section 5.5, page 218-227
  • Section 5.9, page 259-267 (top)
  • Section 11.1, 11.2, 11.3, page 280-301 (middle)
  • Section 11.4, 11.5, page 305-323

Part 2: Linear Algebra

  • Section 1.1, 1.2, 1.3, 1.4, page 395-444
  • Section 2.1, page 485-494
  • Section 2.3, page 512-515
  • Section 2.4, page 525-527 (bottom)
  • Section 2.7, page 557-565
  • Section 2.8, page 575 (middle)-577
  • Section 6.9, page 587-589 (bottom)

Miniprojects

Remark that the notes are designed for the lectures, where they are accompanied by an oral presentation. They do not constitute a textbook.

Click here to download a collection of formulas for the first part of course.

Screencasts

Note that screencasts come with subtitles (both when played on YouTube and when downloaded).

1st Session: Review of Trigonometry

Lecture

Appendix C, Review of Trigonometry, page 1-5. Notes.

Hand-in Exercises

Appendix C, page 5, problems no. 11, 15, 21.

Exercises for 1st and 2nd session

Appendix C, page 5, problems no. 1, 3, 7, 9, 17, 26, 29, 37 (don't use the addition formula in part (c)), 39, 41, 43.

Notes regarding the exercises.

2nd Session: The Derivative and Rates of Change

Lecture

Section 3.1, The Derivative and Rates of Change, page 60-70, and Section 3.2, Basic Differentiation Rules, page 73-82. Notes.

Hand-in Exercises

Prove the following formula:
sin(α)sin(β) = ½ (cos(α–β)–cos(α+β))
Hint: Start with the right hand side of the equation. Use the addition formula for cosine.

Exercises

The rest of the problems from session no. 1.

Screencasts

3rd Session: Derivatives of Trigonometric Functions

Lecture

Section 3.7, Derivatives of Trigonometric Functions, page 123-131, and Section 3.3, The Chain Rule, page 84-91. Notes.

Hand-in Exercises

Section 3.1, page 71, problems no. 23, 27.
Section 3.2, page 82, problems no. 3, 9, 11, 60.

Exercises

Section 3.1, page 71, problems no. 21, 30-35, 38, 39.
Section 3.2, page 82, problems no. 13, 19.

MATLAB installation

Please download and install MATLAB on your computer before session no. 5. Screencast 1 on the AAU first year mathematics webpage describes how to do it. Use your AAU email account. Otherwise the installation will not work.

Screencasts

4th Session: Exponential and Logarithmic Functions

Lecture

Section 3.8, Exponential and Logarithmic Functions, page 134-146. Notes.

Hand-in Exercises

Section 3.7, page 131, problems no. 1, 3, 5, 9, 15, 65.

Exercises

Section 3.7, page 131, problems no. 7, 11, 17, 19, 21, 67, 73, 77.

5th Session: Trigonometric Functions and Sound

Group work on Miniproject 1 which can be found on the AAU first year mathematics webpage.

Hand-in

Miniproject 1

6th Session: Areas, Sums and Integrals I

Lecture

Section 5.3, Elementary Area Computations, page 195-203 (top). Notes.

Hand-in Exercises

Section 3.8, page 146, problems no. 1, 3, 5, 21, 27, 33, 39, 63.

Exercises

Section 3.8, page 146, problems no. 23, 41, 43, 47, 48, 59, 64.

Screencasts

7th Session: Areas, Sums and Integrals II

Lecture

Section 5.4, Riemann Sums and the Integral, page 207-212 (middle), and Section 5.5, Evaluation of Integrals, page 218-227. Notes.

Hand-in Exercises

Section 5.3, page 205, problems no. 1, 3, 6, 9, 11, 19, 43.

Exercises

Section 5.3, page 205, problems no. 15, 23, 39.

Exercise: The number pi

In this exercise we estimate π via regular polygons inscribed in the unit circle.

  1. Compute h1 and h2.
  2. Compute the area of ΔOAC and the area of ΔABC.
  3. Use your results from 2. to find an underestimate for π.
  4. Let M be the midpoint of the (shortest) arc from B to C. Compute the area of ΔBMC
    and find a better estimate for π. How could one improve this estimate?

Screencasts

8th Session: Vectors

Lecture

Section 11.1, Vectors in the Plane, page 280-285, and Section 11.2, Three-Dimensional Vectors, page 286-290 (middle). Notes.

Hand-in Exercises

Section 5.5, page 227, problems no. 5, 7, 9, 11, 13, 21, 25, 31.

Exercises

Section 5.5, page 227, problems no. 35.
Section 5.7, page 245, problems no. 51, 53, 61.

9th Session: Dot Product and Cross Product

Lecture

Section 11.2, Three-Dimensional Vectors, page 290 (middle)-295, and Section 11.3, The Cross Product of Vectors, page 297-301 (middle). Notes.

Hand-in Exercises

Section 11.1, page 285, problems no. 1, 3, 5, 7, 9, 13, 19.

Exercises

Section 11.1, page 285, problems no. 31, 37, 43.

10th Session: Numerical Integration

Group work on Miniproject 2 which can be found on the AAU first year mathematics webpage.

Hand-in

Miniproject 2

11th Session: Lines and Planes in Space

Lecture

Section 11.4, Lines and Planes in Space, page 305-311. Notes.

Hand-in Exercises

Section 11.2, page 295, problems no. 1 (c), 5 (c), 62.
Section 11.3, page 304, problems no. 1, 14.

Exercises

Section 11.2, page 295, problems no. 39, 43, 47.
Exercise: Find the perpendicular projection of the vector a = (4, 4, -7) onto the vector b = (2, -1, -2).

Screencasts

12th Session: Curves and Motion in Space I

Lecture

Section 11.5, Curves and Motion in Space, page 313-316. Notes.

Hand-in Exercises

Section 11.4, page 311, problems no. 1, 3, 7, 23, 39.

Exercises

Section 11.4, page 311, problems no. 9, 17, 25, 31, 37.

Screencasts

13th Session: Curves and Motion in Space II

Lecture

Section 11.5, Curves and Motion in Space, page 316-323. Notes.

Hand-in Exercises

Section 11.5, page 324, problems no. 3 (t ≥ 0), 7, 8, 54.

Exercises

Section 11.5, page 324, problems no. 1, 2, 4, 21, 23.

14th Session: Matrices and Vectors

Lecture

Section 1.1, Matrices and Vectors, page 395-403, and Section 1.2, Linear Combinations, Matrix-Vector Products, and Special Matrices, page 405-411. Notes.

Hand-in Exercises

Section 11.5, page 324, problems no. 11, 61.
Hint for 61 (a): Calculate the velocity vector v(t) and show that v(t)•r(t) = 0.

Exercises

Section 11.5, page 324, problems no. 13, 45 (g = 32 ft/s²).

15th Session: Matrix-Vector Products

Lecture

Section 1.2, Linear Combinations, Matrix-Vector Products, and Special Matrices, page 411-416. Notes.

Hand-in Exercises

Section 1.1, page 403, problems no. 1, 3, 5, 7, 9, 11, 19, 21.

Exercises

Section 1.1, page 403, problems no. 79, 80, 81.

16th Session: Systems of Linear Equations

Lecture

Section 1.3, Systems of Linear Equations, page 419-430. Notes.

Hand-in Exercises

Section 1.2, page 417, problems no. 1, 3, 5, 7, 9, 17, 19, 29, 33.

Exercises

Section 1.2, page 417, problems no. 13, 15, 31.

17th Session: Gaussian Elimination

Lecture

Section 1.4, Gaussian Elimination and The Row Reduction Algorithm, page 433-444. Notes.

Hand-in Exercises

Solve the following system of linear equations:
$$ \begin{align} x_1 - 3x_3 &= 8 \\ 2x_1 + 2x_2 + 9x_3 &= 7 \\ x_2 + 5x_3 &= -2 \end{align} $$

Exercises

Section 1.3, page 430, problems no. 1, 3, 5, 7, 9, 11, 23, 25, 81.

18th Session: Matrices, Vectors and Systems of Linear Equations

Group work on Miniproject 3 which can be found on the AAU first year mathematics webpage.

Hand-in

Miniproject 3

19th Session: Matrix Multiplication

Lecture

Section 2.1, Matrix Multiplication, page 485-494. Notes.

Hand-in Exercises

Section 1.4 page 444, problems no. 17, 19, 21, 27.

Exercises

Section 1.4, page 444. problem no. 15.
From the AAU first year mathematics webpage
Regular exam 2013

20th Session: The Inverse of a Matrix

Lecture

Section 2.3, Invertibility and Elementary Matrices, page 512-515, and Section 2.4, The Inverse of a Matrix, page 525-527. Notes.

Hand-in Exercises

Section 2.1 page 494, problems no. 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 25, 27.

Exercises

Section 2.1 page 494, problems no. 29, 63.
From the AAU first year mathematics webpage,
Regular exam 2013 (as in session no. 19).

21st Session: Linear Transformations and Matrices

Lecture

Section 2.7, Linear Transformations and Matrices, page 557-565, and Section 2.8, Composition and Invertibility of Linear Transformations, page 575 (middle)-577. Notes.

Hand-in Exercises

Section 2.3 page 520, problems no. 1, 2.
Section 2.4 page 532, problems no. 1, 3, 7, 13.

Exercises

Section 2.4 page 532, problem no. 5, 9, 11.
From the AAU first year mathematics webpage,
Regular exam 2012.

22nd Session: Applications to Computer Graphics

Group work on Miniproject 4 which can be found on the AAU first year mathematics webpage.

Hand-in

Miniproject 4
 

Miniprojects

Miniproject 1: Trigonometric Functions and Sound

This miniproject is supported by screencast 1 and 2 with installation and basic usage of MATLAB.

Miniproject 2: Numerical Integration

Miniproject 3: Matrices, Vectors and Systems of Linear Equations

This miniproject is supported by screencast 3 (MATLAB).

Miniproject 4: Applications to Computer Graphics

Click here to download tower.m (remember to rename to tower.m after download) and here to download linesegmentplot.m (remember to rename to linesegmentplot.m after download).

Old exam problems

Note: new structure in the organisation of the exam. Relevant from spring 2016 and onwards.

Previous exams

Math cafe

Do you have a hard time understanding linear algebra and/or calculus at the first study year, and are you determined to do something about it?

Then Math cafe is just the right thing for you. It is held throughout the semester at all three campuses (specific times and places are listed below). It is an extra possibility for getting help with maths. A teaching assistant is available to help you with exercises from the last few lectures. All you have to do is to sign up by sending an email to the assistant at least two days before the planned session. If the assistant hasn't received any email by that time Math Cafe is cancelled without further notice. So you can only expect help if you have sent an email in due time and received a response!. Please indicate in the email what you need help with (typically just a specific exercise) without writing a long email about the details of you problem.

Note: This is an extra curricular activity, so it is NOT a valid excuse for not participating in other course activities or project work.

Information on when and where the math cafe will take place is coming soon.

Aalborg (email: dhaug16@student.aau.dk)

Currently the allocated dates if you have signed up by email are (will be updated throughout the semester):

  • Thursday 13/2 16:30–18:30 in A309, Strandvejen 12–14.
  • Thursday 20/2 16:30–18:30 in A309, Strandvejen 12–14.
  • Thursday 27/2 16:30–18:30 in A315, Strandvejen 12–14.
  • Thursday 5/3 16:30–18:30 in A309, Strandvejen 12–14.
  • Thursday 12/3 16:30–18:30 in A309, Strandvejen 12–14.
  • Thursday 19/3 16:30–18:30 in Auditorium 5, Badehusvej 13.
  • Thursday 26/3 16:30–18:30 on Discord.
  • Thursday 2/4 16:30–18:30 on Discord.
  • Thursday 16/4 16:30–18:30 on Discord.
  • Thursday 23/4 16:30–18:30 on Discord.
  • Thursday 30/4 16:30–18:30 on Discord.
  • Thursday 7/5 16:30–18:30 on Discord.
  • Thursday 14/5 16:30–18:30 on Discord.
  • Thursday 28/5 16:30–18:30 on Discord.

Esbjerg (email: dhaug16@student.aau.dk)

Currently the allocated dates if you have signed up by email are (will be updated throughout the semester):

  • Thursday 26/3 16:30–18:30 on Discord.
  • Thursday 2/4 16:30–18:30 on Discord.
  • Thursday 16/4 16:30–18:30 on Discord.
  • Thursday 23/4 16:30–18:30 on Discord.
  • Thursday 30/4 16:30–18:30 on Discord.
  • Thursday 7/5 16:30–18:30 on Discord.
  • Thursday 14/5 16:30–18:30 on Discord.
  • Thursday 28/5 16:30–18:30 on Discord.

Copenhagen (email: dhaug16@student.aau.dk)

Currently the allocated dates if you have signed up by email are (will be updated throughout the semester):

  • Thursday 26/3 16:30–18:30 on Discord.
  • Thursday 2/4 16:30–18:30 on Discord.
  • Thursday 16/4 16:30–18:30 on Discord.
  • Thursday 23/4 16:30–18:30 on Discord.
  • Thursday 30/4 16:30–18:30 on Discord.
  • Thursday 7/5 16:30–18:30 on Discord.
  • Thursday 14/5 16:30–18:30 on Discord.
  • Thursday 28/5 16:30–18:30 on Discord.

Q&A-sessions

We offer assistance with the exam preparation. This consists of a Q&A-session, where it is possible to ask questions within the syllabus and receive help in solving concrete exercises. During this session, it is also possible solve exercises on your own, and then ask for hints if you get stuck. The session takes as its starting point the old exam questions, which may be found here at first.math.aau.dk. We recommend that you solve as many as you can beforehand, such that you know where you come short. Note that the teaching assistants will not visit you in your group rooms. Instead, everyone will be solving exercises individually or in small groups in the rooms specified below.

We urge you to participate from the beginning in order not to disturb during the first part of the session.

Dates will come near the end of the semester.