3‘ “kl: ‘. 5'9
Answer Questions 3 —- 5 from Part—.4 in Part—A answer script-
Answer Qua-anion: 6 * if] from Part-B in Part-B answer script-
Part—A and Part—B answer scripts will be consented separately.
Calculators, cell phones and other electronic devi

Classnotes - MA1101
Functions of Several Variables
Department of Mathematics
Indian Institute of Technology Madras
This material is only meant for internal use; not to be distributed for commercial purpose.
Maintained by A.Singh.
Contents
1
2
3
Differenti

Classnotes - MA1101
Functions of Several Variables
Department of Mathematics
Indian Institute of Technology Madras
This material is only meant for internal use; not to be distributed for commercial purpose.
Maintained by A.Singh.
Contents
1
2
3
Differenti

Classnotes - MA1101
Functions of Several Variables
Department of Mathematics
Indian Institute of Technology Madras
This material is only meant for internal use; not to be distributed for commercial purpose.
Maintained by A.Singh.
Contents
1
2
3
Differenti

Calculus - II
Multivariable Calculus
M.Thamban Nair
Department of Mathematics
Indian Institute of Technology Madras
February 2007
Revised: January 2009
Contents
Preface
v
1 Functions of Several Variables
1
1.1
Introduction . . . . . . . . . . . . . . . .

DEPARTMENT OF MATHEMATICS
I.I.T. MADRAS
MA 1101 Functions of several variables
Exercise Set 4: Multiple Integarls - II
(1) Use Polar co-ordinates to evaluate the integrals:
2
0
0
1(x1)2
dx dy
x+y
,
(b)
dy dx.
(a)
2 + y2
x2 + y 2
x
0
0
1 1x2 1 +
(2) Find t

DEPARTMENT OF MATHEMATICS
I.I.T. MADRAS
MA 1101 Functions of several variables
Exercise Set 2: Dierential Calculus - 2
(1) If z = x2 + y 2 + z 2 and z = x2 + y 2 , then nd
(a) wy , with y and z as independent variables.
(b) wz , with z and x as independen

DEPARTMENT OF MATHEMATICS
I.I.T. MADRAS
MA 1101 Functions of several variables
Exercise Set I: Dierential Calculus - 1
(1) Find the limit, if exists:
ey sin x
(a)
lim
x
(x,y)(0,0)
xy+2 x2 y
(b)
lim
x y
(x,y)(0,0)
x=y
x2
(x,y)(0,0)
(x,y)(0,0) x2 y
3 y3
2x

DEPARTMENT OF MATHEMATICS
I.I.T. MADRAS
MA 1101 Functions of several variables
Exercise Set 3: Multiple Integarls - I
(1) Find the volume of the solid generated by revolving the region bounded by the cuuve y =
x
and the lines y = 2 and x = 0 about
(a) the