Exercise for the lecture
Experimental Physics I
(Prof. Dr. R. Seidel)
Seminar Assistants: Dominik Kauert, Jingjing Ye, Andrey Krivoy, Hans Kubitschke
Issue date: 09/12/2016
Please write legible and put boxes around the final answers!
Write your group numb
Homework 6, Mathematics 1
submit by 21.11.
Only problems 2, 4ace, 6, 7ad, and 8cd will be graded.
Problem 1: Using the properties of the exponential function, show that for
any a > 0, x > 0 and R, it holds that
loga (x ) = loga x.
Problem 2 [2 points]: Le
Institut f
ur Theoretische Physik
Universitat Leipzig
Dr. A. Kreisel
Theoretical Physics 1: Classical Mechanics
Sheet 9
Winter Term 2016/2017
Due date: will be discussed only in the exercise classes of week 2: Monday 09.01.2017 or
Friday 13.01.2017
1. Con
Homework 12, Mathematics 1
submit by 16.1.
Only problems 1, 2, 3ac, 4bc, 5bcdf, 6c, and 8 will be graded.
R
Problem 1: Show that 1 sinx x dx
(a) [3 points] converges;
Hint: Integrate by parts.
(b) [3* points] does not converge absolutely.
Hint: Consider i
Homework 9, Mathematics 1
submit by 12.12.
Only problems 3de*, 4ace, 5, 6ad will be graded.
Problem 1: Compute the Taylor polynomial of nth order Pn (x) at x0 = 0 for
the function f (x) = cosh x. Do this
(a) from the definition;
(b) using the known expans
Homework 13, Mathematics 1
submit by 23.1.
Only problems 1ab, 4b, 5ac, 6, 7bc, and 9b will be graded.
Problem 1: Which of the following series of functions converge uniformly on
specified intervals?
(a) [3 points]
(b) [3 points]
X
xk
k2
k=1
X
k=1
(c)*
X
x
Homework 11, Mathematics 1
submit by 9.1.
Only problems 1adf, 2bd, 3, 6, 7ace, 8, and 9ace will be graded.
Problem 1: Use substitutions to compute the following integrals:
Z 2
x
(a) [2 points]
dx,
1
+
x2
0
Z
cos +
(b)
d,
3
0
Z 0
dx
(c)
,
2 + 2x + 2
x
2
Z
Homework 8, Mathematics 1
submit by 5.12.
Only problems 1d, 2bcd, 3, 4a, 6, 7abde and 8* will be graded.
Problem 1: Identify the intervals on which the following functions are monotone increasing:
(a)
f (x) = x2 x,
(b)
f (x) = sin x,
(c)
f (x) = arcsin x,
Exercise for the lecture
Experimental Physics I
(Prof. Dr. R. Seidel)
Seminar Assistants: Dominik Kauert, Jingjing Ye, Andrey Krivoy, Hans Kubitschke
Issue date: 13/01/2016
Please write legible and put boxes around the final answers!
Write your group numb
Exercise for the lecture
Experimental Physics I
(Prof. Dr. R. Seidel)
Seminar Assistants: Dominik Kauert, Jingjing Ye, Andrey Krivoy, Hans Kubitschke
Issue date: 16/12/2016
Please write legible and put boxes around the final answers!
Write your group numb
Homework 5, Mathematics 1
submit by 14.11.
Only problems 2, 3adf, 5 and 6 will be graded!
Problem 1: Prove that
1
lim (1 + x) x = e.
x0
1
, prove that
Hint: Proceed as in the lecture for limx0+ . If n1 x < n+1
1
1
n+1
n
1
x
(1 + x)
1
1
n
(n+1)
.
Manipul
Institut f
ur Theoretische Physik
Universitat Leipzig
Dr. A. Kreisel
Theoretical Physics 1: Classical Mechanics
Sheet 7
Winter Term 2016/2017
Due date: will be discussed only in the exercise classes of week 50: Monday 12.12.2016 or
Friday 16.12.2016
1. Ve
Homework 10, Mathematics 1
submit by 19.12.
Only problems 1acdg, 2acdf, 4ac, and 5 will be graded.
Problem 1: Use substitutions to compute the following indefinite integrals,
always stating the maximal interval(s) where the integral exists:
Z
(a) [3 point
Institut f
ur Theoretische Physik
Universitat Leipzig
Dr. A. Kreisel
Theoretical Physics 1: Classical Mechanics
Sheet 5
Winter Term 2016/2017
Due date: will be discussed only in the exercise classes of week 47: Monday 28.11.2016 or
Friday 25.11.2016
1. Di
Institut f
ur Theoretische Physik
Universitat Leipzig
Dr. A. Kreisel
Theoretical Physics 1: Classical Mechanics
Sheet 2
Winter Term 2016/2017
Due date: will be discussed only in the exercise classes of week 44: Monday 07.11.2016 or
Friday 04.11.2016
1. Ve
Homework 3, Mathematics 1
submit by 2.11. (Wednesday)
Problem 1 [2 points]: Prove that for all n N and k N such that 1 k n,
n+1
n
n
=
+
.
k
k
k1
Problem 2: Use mathematical induction to prove that for all n N,
(a) [2 points]
n
X
k2 =
k=1
(b) [3 points]
Homework 14, Mathematics 1
submit by 30.1.
Only problems 1, 2abc, 3, 5, 8 and 9 will be graded.
Problem 1 [3 points]: Use the trigonometric or exponential form of complex
numbers to compute
3
1 i 3 (1 + i)2 .
Problem 2 [3 2 points]: Find all complex solu
Exercise for the lecture
Experimental Physics I
(Prof. Dr. R. Seidel)
Seminar Assistants: Dominik Kauert, Jingjing Ye, Andrey Krivoy, Hans Kubitschke
Issue date: 02/12/2016
Please write legible and put boxes around the final answers!
( + )
Task 1: The Sto
Exercise for the lecture
Experimental Physics I
(Prof. Dr. R. Seidel)
Seminar Assistants: Dominik Kauert, Jingjing Ye, Andrey Krivoy, Hans Kubitschke
Issue date: 06/01/2016
Please write legible and put boxes around the final answers!
Write your group numb
Homework 15, Mathematics 1
submit by 1.2.
Only problems 1b, 2b, 3bc, and 4a will be graded.
Problem 1: Let F be a field. Prove that
(a) The multiplicative identily 1 is unique in F , i. e. , if for some F , =
for all F , then = 1.
(b) [3 points] For any
Homework 4, Mathematics 1
submit by 7.11.
Problem 1 [3 points]: For a function f : R R, formulate the exact definition
of when we say that limx f (x) = +. Give an example of a function with
this behavior and prove it from your definition.
Problem 2 [3 poi
Information: Exam TP
09.02.2017 10:00-11:30, Th. HS
Topics: as covered in the lecture, emphasis on physical problems (mathematical methods needed to
solve)
Aids allowed: scientific calculator, pen
Preparation
1) study content of lecture
2) prepare summary
Kristen Shamburger
English 1301
Dr. Williams
6/24/16
The Vocabulary Assignment
1. Indignant
a. feeling or showing anger or annoyance as what is perceived as unfair treatment
b. Kelly was indignant at being accused of a crime that she did not commit.
2. Em