# 2015PHYS769W1

## Welcome to PHYS769W1 Mathematical Methods

### Lecturer:

Dr. Ilya Sinayskiy |

### Hon. Coordinator:

Prof. M. Tame |

### Textbooks:

### Home assignments (Hassani's book):

2015/02/26: Problems -

2nd. ed - 1.1, 1.2, 1.3, 1.9, 1.10, 1.11

1st. ed - 0.1, 0.2, 0.3, 0.7, 0.8, 0.9

2015/02/27: Problems -

2nd. ed - 2.1, 2.2, 2.3, 2.5, 2.11, 2.12

1st. ed - 1.1, 1.2, 1.3, 1.5, 1.9, 1.10

2015/03/02: Problems -

2nd. ed - 2.15, 2.16, 2.18, 2.19, 2.21, 2.25, 3.1, 3.2

1st. ed - 1.13, 1.14, 1.16, 1.17, 1.19, 1.23, 1.29.

Problem 3.2 is absent in the 1st ed., here is the text of problem:

3.2 Show that the center of an algebra is a subspace of that algebra. If the algebra is associative, then its center is a subalgebra.

2015/03/03: Problems -

2nd. ed - 4.1, 4.2, 4.3, 4.4, 4.6, 4.7, 4.12, 4,19

1st. ed - 2.1, 2.2, 2.3, 2.4, 2.6, 2.7, 2.12, 2.19

2015/03/17: Problems -

2nd. ed - 4.22, 4.23, 4.29, 4.31, 5.3, 5.5, 5.8, 5.9, 5.42, 5.43

1st. ed - 2.22, 2.23, 2.29, 2.31, 3.3, 3.4, 3.6, 3.7, 3.37, 3.38

2015/03/19: Problems -

2nd. ed - 6.1, 6.5, 6.6, 6.7, 6.9, 6.12, 6.20

1st. ed - 4.2, 4.6, 4.7, 4.9, 4.12, 4.19

Problem 6.5 is absent in the 1st ed., here is the text of problem:

6.5 Let a1=(1,1,-1) and a2=(-2,1,-1)

(a) Construct (in the form of a matrix) the projection operators P1 and P2 that project onto the directions of a1 and a2 , respectively. Verify that they are indeed projection operators.

(b) Construct (in the form of a matrix) the operator P = P1 + P2 and verify directly that it is a projection operator.

(c) Let P act on an arbitrary vector (x,y,z). What is the dot product of the resulting vector with the vector a1 x a2 ? Is that what you expect?

2015/03/20: Problems -

2nd. ed - 7.2, 7.4, 7.7

1st. ed - 5.2, 5.4, 5.7

2015/03/23: Problems -

2nd. ed - 7.10, 7.15, 7.16, 7.19, 7.21

1st. ed - 6.3, 6.8, 6.9, 6.12, 6.14

2015/03/27: Problems - (Classical Orthogonal Polynomials)

2nd. ed - 8.1, 8.6, 8.8, 8.16, 8.20, 8.21, 8.25

1st. ed - 7.1, 7.6, 7.10,7.19, 7.20, 7.24

2015/03/27: Problems - (Fourier Analysis)

2nd. ed - 9.7, 9.8, 9.10, 9.11, 9.20, 9.21

1st. ed - 8.7, 8.8, 8.10, 8.11, 8.20, 8.21

2015/04/08: Problems

2nd. ed - 10.2, 10.18, 10.25, 10.30, 10.33, 10.34, 10.39, 10.42

1st. ed - 9.2, 9.19, 9.26, 9.30, 9.33, 9.34, 9.39, 9.42

2015/04/17: Problems

2nd. ed - 11.1, 11.3, 11.4, 11.5, 11.6, 11.7, 11.10, 11.11

1st. ed - 10.1, 10.3, 10.4, 10.5, 10.6, 10.7, 10.10, 10.11