## University College Utrecht, Spring 2008

Lecturer:
Karma Dajani (k.dajani1@uu.nl)

Instructor exercise class (+ student assistent):
Alexander Quintero Velez
and Wouter Stekelenburg (W.P.Stekelenburg@students.uu.nl)

Spring semester
January 28 – May 19
Spring Break: March 24-28

Lectures: Tuesday, 16:00 - 18:00 -UCU Newton Building room E
Exercise classes: Thursday 13:45-15:45--UCU Newton Building room E
Office hours: Tuesday 14:00-16:00-UCU, Newton Building room Ee.

Course description:
In this course you will learn basic mathematical methods needed for application in the sciences. In particular, we will discuss complex numbers, matrix algebra, the scalar and vector product of vectors, determinants, linear transformations, eigenvalues and eigenvectors, integration, Taylor series, partial differentiation. The emphasis will be on linear algebra.

Text:
D.W. Jordan and P. Smith
Mathematical Techniques
An introduction for the engineering, physical and mathematical sciences
Oxford University Press, Oxford, 2002. x+862 pp.
ISBN: 0-19-9249972-0

Lecture Note (with pictures now)

Prerequisites: none.

Requirements: The course is divided into four periods of more or less equal duration.
At the beginning of each period a home work assignment is given; this has to be handed in by the end of the same period.
Moreover, each period will be concluded by a written test of 1 hour.

Advice: Mathematics can only be learned through lots of practice. It is therefore very important to do the suggested homework. Do not postpone it. It is typical of mathematics that you need to have digested basic material in order to be able to make progress with more advanced topics.
Also: if there are things you do not understand, do not hesitate to ask questions. This will not be frowned upon or counted against you. According to us there is no such thing as a stupid question!

Theory, homework and assignments
Week 5 (1)
Tues 29/1:
• first hour: Lecture Notes 2.4 - 2.5: systems of equations + geometric interpretation
• second hour: Lecture Notes 3.1 - 3.2: basics of complex numbers
• Homework: do the introductory Mathematica session, Notebook Introduction to Mathematica on a UCU computer as follows: 1) download the file to the computer 2) open the program Mathematica 3) use Mathematica's menu to open the file. Then follow the instructions.
• Thur 31/1:
• Exercises from Lecture Notes: 2.7.3, 2.7.4, 2.7.7; 3.5.1, 3.5.2.
• Exercises from book Ch. 6: 6.1, 6.5, 6.6.
• Solving Equation Notebook
• hand out assignment 1. Deadline Thursday 28 February.
• Week 6 (2)
Tues 5/2:
• Lecture Notes: 3.3 - 3.4, book 6.4 - 6.7 (complex numbers);
• Thur 7/2:
• Exercises Lecture Notes: 3.5.3, 3.5.4,
• Exercises Book: 6.11, 6.12, 6.16 a,c, 6.23(a,b,d), 6.25
• Week 7 (3)
Tues 12/2:
• Lecture Notes: 6.1-6.4 (vectors in eulidean spaces, dot products, equations of lines and planes)
• Thur 14/2:
• Exercises Lecture Notes: 6.5.1 (2,4), 6.52 (1,2,4,6,10, 13, 14), 6.5.3 (1), 6.5.4 (1)
• Exercises Book:10.14
• Week 8 (4)
Tues 19/2:
• 16:00 - 17:00: written test 1 Material: all theory and exercises from weeks 5, 6, and 7 as listed above.
open book: you are allowed to use the book and lecture notes, but no personal notes.
• 17:15 - 18:00:  Lecture Notes Ch 7.1 and Book Ch 7 7.1-7.3: matrices.
• Solutions Test 1

• Thur 21/2:
• Exercises Lecture Notes: 7.3.1 - 7.3.4, 7.3.6, 7.3.8
• Exercises Book: 7.2, 7.10
• practice matrix operations with mathematica Mathematica and Matrices

• Week 9 (5)
Tues 26/2:
• Lecture Notes: 7.2
• Book: section 7.4 Inverse of a matrix
• Thur 28/2:
• Exercises Book: 7.9, 7.10, 7.12, 7.14, 7.16, 7.19
• Hand in Assignment 1. Give your assignment to Alexander Quintero Velez at the beginning of the exercise hour.
• Hand out Assignment2. Due Date Thursday March 20.
• Week 10 (6)
Tues 4/3:
•  Chapter 8 Determinants
• Lecture Notes: Chapter 8
• Thur 6/3:
• Exercises Book: 8.1(b,c,e,f), 8.2, 8.3, 8.4, 8.5, 8.7, 8.8
• Week 11 (7)
Tues 11/3:
• Lecture Notes: 9.1-9.2
• Book: 13.1-13.3 Eigenvalues and Eigenvectors
• Thur 13/3:
• Exercises Lecture Notes: 9.4.1, 9.4.2,.
• Exercises Book: 13.2, 13.3, 13.4(a,c), 13.5, 13.6,13.8, 13.11
• Week 12 (8)
Tues 18/3:
• First hour: Test II (material : the theory discussed in weeks 8, 9, 10 and 11).  Open book: you are allowed to use the book and lecture notes, but no personal notes.
• Second hour: Book: 13.4-13.7 Diagonalization and application.  Lecture Notes: 9.3.
• Solutions Test2

• Thur 20/3:
• Exercises Book: 13.12, 13.13,13.14, 13.15, 13.28
• Lecture Notes: 9.4.3
• Hand-in assignment 2.

• Week 13 (9)  Mid-Term Break

Week 14 (10)
Tues 1/4:
• Extra Lecture Notes  (General Vector Spaces and Linear Transformations).

• Thur 3/4:
• Exercises: 1-8 in the Extra Lecture Notes
• Due Date Thursday April 17.
• Week 15 (11)

Tues 8/4:
• Book 11.1-11.3 Cross-Products.

• Thur 10/4:
• Exercises:  book: 11.1 (a-e); 11.4, 11.5, 11.6. (The rest of the exercises from week 14 if need be)
• Week 16 (12)

Tues 15/4:
• First Hour: Test III, the material discussed in weeks 12, 14, and 15. Open book: you are allowed to use the book and lecture notes, but no personal notes.
• Second Hour: Lecture Notes Chapter 1, Book 5.1-5.3 (Taylor Series).
• Thur 17/4:

Fri 7/9:
• Exercises from book Ch. 5 (Taylor series): 5.1 b,c,f,g; 5.2 c,d; 5.4 e; 5.10 a,b.
• Notebook on Taylor series
• Hand in assignment III.
• Hand out assignment IV. Due May 7, 2008.

• Week 17 (13)

Tues 22/4:
• Book Chapter 5.4-5.8 (rest of Taylor Series).
• Thur 24/4:
• Exercises from book Ch. 5: 5.7; 5.8 a,b,c; 5.13; 5.14; 5.18.
• Exercises from Lecture Notes: 1.5.3, 1.5.4.

• Week 18 (14)

Tues 29/4:
• Lecture Notes 4.1, and Book Chapter 28.1-28.4 (Functions of Several Variables).
• extra lecture notes, (self reading-these notes give a rigorous presentation of the material)
• Thur 1/5:
• Exercises: Lecture Notes: 4.3.1, 4.3.2
• Exercises: Book: 28.1 (a,d,e,f,g); 28.3 (a,c,e,f); 28.4.

• Week 19 (15)

Tues 8/5:
• Lecture Notes 4.2, and Book Chapter 28.5-28.8 (Gradients and Tangent Directions).
• Thur 7/5:
• Exercises: Book: 28.8 (b,d,h), 28.9, 28.10 (b,d,f), 28.11, 28.12 (b,c,h,k).
• notebook on contour plotting.