University of London The London School of Economics and Political Science
MATHS 103

Winter 2011
B. Johnson Name Key
7
Table # _ .
March 2013 Alpha # Per. Date
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Calculus AB Quiz Chapter 7 .17.2 Applications of Integrals, Areas and Volumes 2%
I
Calculator Required on some problems in Part I and Part II. 0!
PART I ShowYourWork Multiple Choice. Show
University of London The London School of Economics and Political Science
MATHS 103

Winter 2011
This space on the weekly problem sheets will apart from the course webpage be used for important
announcements about the course. The course webpage is at
http : /www.mth.kcl.ac.uk/courses/cm131.html
Consult it regularly.
131A Problems  Set 1
Full solut
University of London The London School of Economics and Political Science
MATHS 103

Winter 2011
Introduction to Dynamical Systems
CM131A
R. Khn
u
Based on Lecture Notes by H. C. Rae
Department of Mathematics Kings College London
January 2005
2
Contents
Introduction and Overview
I
5
General Dynamics
9
1 Introduction
11
2 Dierential Equations
2.1 Basi
University of London The London School of Economics and Political Science
MATHS 103

Winter 2011
123
8. Exercises
CALCULUS 1 TUTORIAL EXERCISES I
1. Use the induction method to prove the following statements:
n
k4 =
1
n(n + 1)(2n + 1)(3n2 + 3n 1)
30
(n IN) :
k =1
(n IN) :
n + 1 2n (n + 1)!
(n IN, n 4) : n2 2n n!
2. Express the following three complex
University of London The London School of Economics and Political Science
MATHS 103

Winter 2011
CM111A Calculus I
Compact Lecture Notes
ACC Coolen
Department of Mathematics, Kings College London
Version of November 2011
2
3
1. Introduction
1.1. A bit of history .
1.1.1. Birth of modern science and of calculus
Stage I, 15001630: from speculation to s
University of London The London School of Economics and Political Science
MATHS 103

Winter 2011
CM121A, Abstract Algebra
Solution Sheet 1
1. Consider the following subsets of Z:
A = cfw_ multiples of 3 , B = cfw_ a Z  6 < a 6 , C = cfw_ 3, 2, 4, 9, 31 .
(a) Find B (A C ).
Solution: A C = cfw_3, 9, so
B (A C ) = cfw_5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5,
University of London The London School of Economics and Political Science
MATHS 103

Winter 2011
CM121A, Introduction to Abstract Algebra
Exercise Sheet 1
Due in tutorials, week of 30 January
1. Consider the following subsets of Z:
A = cfw_ multiples of 3 , B = cfw_ a Z  6 < a 6 , C = cfw_ 3, 2, 4, 9, 31 .
(a) Find B (A C ).
(b) Find (B A) C .
(c) F