University of London The London School of Economics and Political Science
MA100
MA 212

Fall 2015
MA212 Further Mathematical Methods
Lecture 8: Double Integral (continued)
using Fubini Theorem
volume under the curve over bounded region
Previously on .
Double Integral: We would like to
calculate the volume under the surface z = f (x, y) over a region R
University of London The London School of Economics and Political Science
MA100
MA 212

Fall 2015
MA212 Further Mathematical Methods
Lecture 4: Limits unleashed
Continuity and approximation
Taylors Theorem and its use
LHspitals Rule
Previously on .
A function f (t) is continuous at point t = c if
lim f (t) = f (c).
tc
This means: For every > 0 there e
University of London The London School of Economics and Political Science
MA 212

Spring 2016
Lecture notes on linear algebra
David Lerner
Department of Mathematics
University of Kansas
These are notes of a course given in Fall, 2007 and 2008 to the Honors sections of our
elementary linear algebra course. Their comments and corrections have greatl
University of London The London School of Economics and Political Science
MA 212

Spring 2016
Physics 216
Spring 2012
ThreeDimensional Rotation Matrices
1. Rotation matrices
A real orthogonal matrix R is a matrix whose elements are real numbers and satisfies
R = RT (or equivalently, RRT = I, where I is the n n identity matrix). Taking
the determi
University of London The London School of Economics and Political Science
MA 212

Spring 2016
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University of London The London School of Economics and Political Science
MA 212

Spring 2016
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University of London The London School of Economics and Political Science
MA 212

Spring 2016
Mathematical Methods, Lecture Twelve
12. Matrices, 3 of 3
12.1 Minors, cofactors and the determinant
The determinant of an n n matrix A, denoted by A or detA, is a number
derived from A which determines whether or not the matrix A is invertible. By
the
University of London The London School of Economics and Political Science
MA100
MA 212

Fall 2015
MA212 Further Mathematical Methods
Lecture 3: Continuity, differentiability with
applications
Limits at a point
Continuity
Taylors Theorem
Homework
Exercises 2:
write solutions to problems 2, 3, 4a, 6, 8b, 9a
deadline: follow instructions laid down by you
University of London The London School of Economics and Political Science
MA100
MA 212

Fall 2015
MA212 Further Mathematical Methods
Lecture 6: Riemann Integral
Definition of integral
Worked example
Previously on.
LHospital Rule
Let c can be any real number or + or .
If lim f (t) = lim g(t) = 0 ,
tc
tc
or
if lim f (t) = + or , and lim g(t) = + or ,
tc
University of London The London School of Economics and Political Science
MA100
MA 212

Fall 2015
MA212 Further Mathematical Methods
Lecture 7: Riemann Integral
Why continuous functions have Riemann integral
Double Integrals
Fubini Theorem
Homework
Exercises 4:
write solutions to problems 1, 2, 3, 4
deadline: follow instructions laid down by your clas
University of London The London School of Economics and Political Science
MA100
MA 212

Fall 2015
MA212 Further Mathematical Methods
Lecture 9: More on Double Integral
change of variables
Homework
Exercises 5:
write solutions to problems 1, 2, 3, 4ab
deadline: follow instructions laid down by your class teacher
MA212 Lecture 9 27 October 2015
Previous
University of London The London School of Economics and Political Science
MA100
MA 212

Fall 2015
Welcome to MA 212
Further Mathematical Methods
Jozef Skokan
Calculus
Columbia House COL.3.04
Adam Ostaszewski
Linear Algebra
Columbia House COL.4.06
Department of Mathematics
London School of Economics and Political Science
Lectures
Calculus: weeks 110 in