Department of Mathematics
Indian Institute of Technology, Bombay
MA 106 : Linear Algebra
Handout
Spring 2017
0.1
AR, SK
One-sided Inverse
Definition 0.1.1 (Left inverse). For an m n matrix A, B is cal
Department of Mathematics
Indian Institute of Technology, Bombay
MA 106 : Linear Algebra
Handout 2
Spring 2017
0.1
AR, SK
Geometric vs algebraic multiplicity
Theorem 0.1.1. If a square matrix A has as
Eigenvalues are often introduced in the context of linear algebra or matrix theory. Historically,
however, they arose in the study of quadratic forms and differential equations.
In the 18th century Eu
Department of Mathematics
Indian Institute of Technology, Bombay
MA 106 : Linear Algebra
Handout 3
Spring 2017
0.1
AR, SK
Second derivative test
a b
is the Hessian at P , then upto
If P = (x0 , y0 )
MA 108 Differential Equations
Spring 2016
U.K. Anandavardhanan
Neela Nataraj
Department of Mathematics
Indian Institute of Technology Bombay
Contents
Chapter 1.
Introduction
1
1.1.
Syllabus
1
1.2.
Tex
Department of Mathematics
Indian Institute of Technology Bombay
Powai, Mumbai400 076, INDIA.
MA 105
Autumn 2017
Instructors:
Ravi Raghunathan,
202-E, Department of Mathematics.
Sandip Singh,
104-A, De
MA-105 Problem Set-I
Autumn Semester 2007-08
c INDER K. RANA
SWAPNEEL MAHAJAN
Department of Mathematics
Indian Institute of Technology Bombay
Powai, Mumbai 400076, India
Name
Division
These problem se
MA 105 D1 Lecture 2
Ravi Raghunathan
Department of Mathematics
July 27, 2017
Tutorial problems for August 2
The numbers refer to the tutorial sheet. E.g. 1.1 (iii) means
Problem no. 1 part (iii) of th
MA 105 D1 Lecture 5
Ravi Raghunathan
Department of Mathematics
Autumn 2017, IIT Bombay, Mumbai
The derivative
Arnolds problem
Maxima and minima
Properties of dierentiable functions
Beyond the first de
MA 108 : Spring 2011 : End-Semester Examination
Solutions and Partial Credit Scheme
Instructions
1. Study the solutions and marking scheme carefully.
2. Rechecking will be done according to the scheme
MA 105 D1: Tutorial 13
Ravi Raghunathan
Department of Mathematics
Autumn 2014, IIT Bombay, Mumbai
Solutions to problems from Tutorial 13
These slides provide some solutions to the problems assigned in
MA-108 Ordinary Differential Equations
M.K. Keshari
Department of Mathematics
Indian Institute of Technology Bombay
Powai, Mumbai - 76
Spring 2017
Lecture 1
M.K. Keshari
D1 - Lecture 1
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