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B.Sc. SEMESTER -1
MATHEMATICS PAPER BSMT-101 (A) - Theory
GEOMETRY & CALCULUS
UNIT 1: [ 25 MARKS + 10 MARKS MCQ ]
(a) Polar, spherical & cylindrical co-ordinates:
Polar Co-ordinates in R 2, distance between two points in polar Co-ordinates. Polar
equations of a straight line, polar equations of circle. Relation between Cartesian and
polar coordinates, Relation between Cartesian and spherical coordinates, Relation
between Cartesian and cylindrical coordinates.
(b) Sphere: General equation of sphere with center (α, β, γ) and radius a. Plane section of a sphere,
intersection of two spheres, inertia of sphere and a line.
(c) Successive differentiation:
Successive differentiation, Calculation of nth derivative, Some standard results for nth
derivatives ofax
e , mxa , )sin( bax , )cos( bax ,
mbax )( ,1)(
bax ,
)log( bax , )sin( cbxeax , )cos( cbxe
ax . Leibnitz’s Theorem and its examples.
(d) Mean value theorems:
Roll’s theorem and problems related to it, Lagrange’s mean value theorem and problems
related to it, Cauchy’s mean value theorem and problems related to it.
(e) Taylor’s theorem, expansions and indeterminate forms:
Taylor’s theorem (Without proof), Maclaurin’s theorem (Without proof), Taylor’s and
Maclaurin’s infinite series expansions, expansions of
x
e , xsin , xcos ,n
x)1( ,)1log( x under proper conditions.
(f) Indeterminate Forms:
La’ hospital’s rules for various indeterminate forms (Without proof).Various
indeterminate forms like0
0 form,
form, 0. form, form,
00 form,
0
form.
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Notes:
There shall be SIX periods of 55 minutes per week for Mathematics- BSMT-101(A)-
Theory.
There shall be one question paper of 70 marks & 21
2 hours for Mathematics- BSMT-
101(A)-Theory
Format of Question Paper
There shall be TWO sections in this paper i.e. Section- A and Section -B.
Section – A
Section- A is of 20 Marks with 20 MCQ type questions (multiple choice questions) coveringthe whole syllabus in equal weight-age.
Section – B
Section B is of 50 Marks with the following type of TWO questions covering the whole
syllabus in equal weight-age, each of twenty five marks
Question 1 and 2 will cover unit 1 and 2 respectively.
Question no. (A) Answer any three out of six 6 Marks(B) Answer any three out of six 9 Marks
(C) Answer any two out of five 10 Marks _________
TOTAL 25 MARKS
Reference Books :
The Elements of Co-ordinate Geometry by S.L. Loney
Mac Millan & Co.
Elementary Treatise on Co-ordinate geometry of three dimensions by R.J.T. Bell MacMillan & Co.
A Text book of Analytical Geometry of three dimensions by P.K. Jain & Khalid Ahmad
Differential Calculus by Shanti Narayan
Differential Calculus by Gorakh Prasad
Integral Calculus by Shanti Narayan
Integral Calculus by Gorakh Prasad
Differential Equations by D. A. Murray
Three Dimension Geometry, Krishna Prakashan Mandir, Meerut.
A Text book of Calculus, S. C. Arora and Ramesh Kumar,Pitamber Publishing Company Ltd. Delhi.
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SAURASHTRA UNIVERSITY
RAJKOT.Syllabus of B.Sc. Semester-1
According to Choice Based Credit System
Effective from June – 2010
(Updated on date:- 01-02-2013
and updation implemented from June - 2013)
Programme: B.Sc.
Semester: 1
Subject: Mathematics
Course code: BSMT-101(B) (Practical)
Title of Course: Mathematics Practical
Total Marks of
External Practical
Examination:
35 Marks
Total Marks of
Internal Practical
Examination:
15 Marks
Continuous internal assessment
of practical work
Total Marks of
Practical Examination:
External 35 Marks
Internal 15 Marks
_______________________
Total 50 Marks
Credit Of The Course 3 Credits
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SAURASHTRA UNIVERSITY, RAJKOT.
B.Sc. SEMESTER - 1 (CBCS)MATHEMATICS PAPER- BSMT-101(B) (Practical)
Mathematics Practical
[ 50 Marks / 3Hours]
Practical No . (1) Draw the graph of y = sinx or y = cosx or y = tanx
Practical No . (2) Draw the graph of y = secx or y = cosecx or y = cot x
Practical No . (3) Draw the graph of y = sin-1x or y = cos-1x or y = tan-1x.
Practical No . (4) Draw the graph of y = sec-1x or y = cosec-1x or y = cot -1x.
Practical No . (5) Draw the graph of parabola y2 = 4ax for a < 0 or a > 0
Practical No . (6) Draw the graph of ellipse2 2
2 2 1
x y
a b
or hyperbola2 2
2 2 1
x y
a b
Practical No. (7) To solve given example of successive differentiation.
(a) Find the nth derivative of y =
(b) Show that the nth derivative of y = tan-1x is
yn = (-1)(n-1).(n-1) [sin{n( )}sinn( )]
(c) If y = x log then prove that
yn = (-1)n.(n-2) { - }
(d) If y = sinmx + cosmx then show that
yn =
Practical No. (8) To solve given example of Mean value Theorem.
(a) Using Lagrange’s mean value theorem show that
log(1+x) x for x 0 and hence
0 - 1 for x 0
(b) Using Lagrange’s mean value theorem show that
x - sinx x for x 0
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(c) Using Cauchy’s mean value theorem show that
(c) eb – ea = cec log(b/a) where 0 a c b ,ab 0
(d) Using Cauchy’s mean value theorem show that
bb – aa = cc{blog(b)- alog(a)} where a c b
Practical No. (9) To solve given example of reduction formula.
(a)
dx (b)
(b)
(d)
Ans: (a) (b) (c) (d)
Practical No.(10) To solve given example of Bernoulli’s Differential Equation.
(a)
Solve : + ytanx = y3secx ,
Ans. Y=
(b)
Solve : + ytanx = ,
Ans. Y2 sec2x = 2log( secx + tanx )+c
(c)
Solve : + ycosx = y3sin2x,
Ans.y-2 =(1+2sinx) + c e2sinx
(d)
Solve : (x3y3 + xy)dx = dy ,
Ans. y-2 = (1-x2)+ c
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Notes :
There shall be SIX periods of 1 hour per week per batch of 15 students.
10 practical should be done during semester-1.
At the time of examination candidate must bring his/her own practical journal
duly certified and signed by H.O.D.
There shall be one question paper of 35 Marks and 3 Hours for practical
examination
There shall be 15 marks for Internal Practical Examination
(i.e. Continuous internal assessment of performance of each student during the
practical work.)
Format of Question Paper for Practical Examination
Question 1 Answer any THREE out of FIVE [ 9+9+9= 27 Marks
Question 2 Journal and Viva: [ 8 Marks
Question 3: Internal Practical Examination [ 15 Marks
TOTAL [ 50 Marks
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SAURASHTRA UNIVERSITY
RAJKOT.Syllabus of B.Sc. Semester-2
According to Choice Based Credit System
Effective from June – 2010
(Updated on date:- 01-02-2013
and updation implemented from June - 2013)
Program: B.Sc.
Semester: 2
Subject: Mathematics
Course code: BSMT-201 (A) - Theory
Title of Course: Geometry, Trigonometry
And Matrix Algebra
Section-wise
Distribution of Marks
for External
Examination:
Section-A
(MCQ test) 20 Marks
Section-B
(Descriptive type) 50 Marks
__________________________
Total Marks 70 Marks
Segment-wise
Distribution of Marks
for Internal
Examination:
Assignments 10 Marks
QUIZ test 10 Marks
Internal exam. 10 Marks
_________________________
Total Marks 30 Marks
Credit Of The Course 4 Credits
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B.Sc. SEMESTER -2
MATHEMATICS PAPER BSMT – 201 (A) Theory
GEOMETRY, TRIGONOMETRY AND MATRIX ALGEBRA
UNIT 1: [ 25 MARKS + 10 MARKS MCQ ]
[a] Cylinder :
Definition of a cylinder, equation of a cylinder with given
Generating parallel to the line x y z
l m n and guiding curve ax2+ 2hxy + by2 + 2gx +
2fy + c = 0, z = 0. The equation of right circular cylinder with axis
x y z
l m n
and radius r.
[b] Concept of a matrix:
Some special matrices, adjoint of a matrix, Non-singular and singular matrices, inverse
of a matrix, Symmetric and skew symmetric matrices, Hermitian and skew Hermitian
matrices
Rank of a matrix:Elementary row and column operations on a matrix, row and column vectors, linear
independence of row and column matrices, rank of a matrix, row and column rank of a
matrix, equivalence of row and column ranks.
Eigen values of a matrix :
Characteristic equation of a matrix, eigen values and eigen vectors of a matrix, Cayley-
Hamilton theorem and its use in finding inverse of a matrix. Application of a matrices to
solve a system of linear (homogeneous and non-homogeneous both) equations.Theorems on consistency of a system of linear equations.
[c] Sequences:
Definition of a sequence, bounded sequences. Convergence of a sequence,
subsequences, Monotonic sequences, Cauchy’s sequence, General principle of
convergence of sequence (without proof). Some important sequences.n
n ;
n
aaan
21
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UNIT 2: [ 25 MARKS + 10 MARKS MCQ ]
[a] De’Moivre’s theorem:
De’Moivre’s theorem and its ap plications, Value of az, zC or R.
Expansions of ncos , nn tan,sin :
Expansions of ncos , nn tan,sin in terms of tan,sin,cos respectively.
(n being positive integer) Expansions of nn
sin,cos in a series of cosines or sines
of multiples of (n being positive integer ). Expansion of trigonometric functions. i.e.
expansions of sin ,cos , tan in terms of .
[b] Exponential, circular and hyperbolic functions:
Exponential, circular and hyperbolic functions.
Logarithmic & inverse functions:
Logarithmic functions for complex and real numbers
Inverse circular and hyperbolic functions for complex and real numbers.
Notes:
There shall be SIX periods of 55 minutes per week for Mathematics- BSMT-201(A)-
Theory.
There shall be one question paper of 70 marks & 21
2 hours for Mathematics- BSMT-
201(A)-Theory
Format of Question Paper
There shall be TWO sections in this paper i.e. Section- A and Section -B.
Section – A
Section- A is of 20 Marks with 20 MCQ type questions (multiple choice questions) covering
the whole syllabus in equal weight-age.
Section – B
Section B is of 50 Marks with the following type of TWO questions covering the whole
syllabus in equal weight-age, each of twenty five marks .
Question 1 and 2 will cover unit 1 and 2 respectively.
Question no. (A) Answer any three out of six 6 Marks(B) Answer any three out of six 9 Marks
(C) Answer any two out of five 10 Marks _________
TOTAL 25 MARKS
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Reference Books:
The Elements of Co-ordinate Geometry by S.L. Loney Mac Millan & Co.
Elementary Treatise on Co-ordinate geometry of three dimensions by R.J.T. Bell Mac
Millan & Co.
A Text book of Analytical Geometry of three dimensions by P.K. Jain & Khalid Ahmad
Theory of matrices by Shanti Narayan
Plane Trigonometry Part -2 by S.L.Loney Mac Millan & Co.
A Course of Mathematical Analysis by Shanti Narayan
Mathematical Analysis by S.C. Malik
Mathematical Analysis by T.M. Apostol
Real Analysis by R.R. Goldberg
Three Dimension Geometry by Krishna Prakashan Mandir,Meerut.
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SAURASHTRA UNIVERSITY
RAJKOT.Syllabus of B.Sc. Semester-2
According to Choice Based Credit System
Effective from June - 2010
(Updated on date:- 01-02-2013
and updation implemented from June - 2013)
Programme: B.Sc.
Semester: 2
Subject: Mathematics
Course code: BSMT-201(B) (Practical)
Title of Course: Mathematics Practical.
Total Marks of
External Practical
Examination:
35 Marks
Total Marks of
Internal Practical
Examination:
15 Marks
Continuous internal assessment
of practical work
Total Marks of
Practical Examination:
External 35 Marks
Internal 15 Marks
_______________________
Total 50 Marks
Credit Of The Course 3 Credits
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SAURASHTRA UNIVERSITY, RAJKOT.
B.Sc. SEMESTER -2 (CBCS)MATHEMATICS PAPER- BSMT-201(B) (Practical)
Mathematics Practical
[ 50 Marks / 3Hours]
Practical No. (1) Draw the graph of y =ex or y = 2 x or y = 3 x.
Practical No. (2) Draw the graph of y =loge x or y = log10 x.
Practical No. (3) Draw the graph of y =sinh x or y = cosh x.
Practical No. (4) Draw the graph of y =sech x or y = cosech x
Practical No. (5) Draw the graph of y =tanh x or y = coth x.
Practical No. (6) Draw the graph of cardioid.
Practical (7)
To find inverse of a matrix using Cayley- Hamilton theorem
Practical No(7) (a)
a =
1 0 1
0 1 0
0 0 1
Answer:- b = inv(a)
b =
1 0 -1
0 1 0
0 0 1
Practical No(7) (b)
a =
2 -1 1
-1 2 -11 -1 2
Answer:- b = inv(a)
b =
0.7500 0.2500 -0.2500
0.2500 0.7500 0.2500
-0.2500 0.2500 0.7500
Practical No(7) (c)
a = 2 1 -1
0 2 1
5 2 -3
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Answer:- b = inv(a)
b =
8 -1 -3
-5 1 2
10 -1 -4
Practical No(7) (d)
a =
1 0 2
2 -1 3
4 1 8
Answer:- b = inv(a)
b =
-11 2 2
-4 0 1
6 -1 -1
Practical No(8)
To find inverse of a matrix using Gauss-Elimination Method
Practical No(8) (a)
a =
7 -3 -3
-1 1 0
-1 0 1
Answer:- b = inv(a)b =
1 3 3
1 4 3
1 3 4
Practical No(8) (b)
a =
-4 -3 -3
1 0 1
4 4 3
Answer:- b = inv(a)
b =
-4 -3 -3
1 0 1
4 4 3
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Practical No(8) (c)
a =
1 -8 10
0 2 -3
0 -1 2
Answer:- b = inv(a)
b =
1 6 4
0 2 3
0 1 2
Practical No(8) (d)
a =
5 8 4
2 3 2
1 2 1
Answer:- b = inv(a)
b = 1 0 -4
0 -1 2
-1 2 1
Practical No(9)
To solve the system of simultaneous linear algebraic equations using
Gauss Elimination Method.
Practical No(9) (a)
3x + y - z = 3
2x - 8y + z = -5
x - 2y + 9z = 8
Answer: - x = 1, y = 1, z =1
Practical No(9) (b)
28x + 4y - z = 32
x + 3y + 10z = 24
2x + 17y + 4z = 35 Answer: - x = 0.9936, y = 1.5070, z =1.8485
Practical No(9) (c)
3x + 4y - z = 8
-2x + y + z = 3
x + 2y - z = 2
Answer: - x = 1, y = 2, z = 3
Practical No(9) (d)
10x + y + z = 12
2x +10y + z = 132x + 2y + 10z = 14
Answer: - x = 1, y = 1, z = 1
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Practical No(10)
To solve the given system of simultaneous linear algebraic equations
using Gauss-Jordan Method.
Practical No(10) (a)
10x + y + z = 12
2x + 10y + z = 13
x + y + 5z = 7
Answer: - x = 1, y = 1, z = 1
Practical No(10) (b)
10x + y + z = 12
x + 10y - z = 10
x - 2y + 10z = 9
Answer: - x = 1, y = 1, z = 1
Practical No(10) (c)
10x + y + z = 12
x + 10y + z = 12
x + y +10z = 12
Answer: - x = 1, y = 1, z = 1
Practical No(10) (d)
x + 2y + z = 8
2x + 3y + 4z = 20
x + 3y + 2z = 16 Answer: - x = 1, y = 2, z = 3
Notes :
There shall be SIX periods of 1 hour per week per batch of 15 students.
10 practical should be done during semester-2.
At the time of examination candidate must bring his/her own practical journal
duly certified and signed by H.O.D.
There shall be one question paper of 35 Marks and 3 Hours for practical
examination
There shall be 15 marks for Internal Practical Examination
(i.e. Continuous internal assessment of performance of each student during the
practical work.)
Format of Question Paper for Practical Examination
Question 1 Answer any THREE out of FIVE [ 9+9+9= 27 Marks
Question 2 Journal and Viva: [ 8 Marks
Question 3: Internal Practical Examination [ 15 Marks
TOTAL [ 50 Marks