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Pailan College of Management and Technology
B.B.A
Lessons Plan
2nd Semester
2012 – 2013
MATHEMATICS II
Faculty
Nabanita Maity
Course Title
B.B.A
Course Code
BBA-202
Objective of the
Students will develop computational skills in calculus needed for more advanced
calculus-based courses. They will learn and retain basic knowledge in the core
branches of mathematics.
subject
Teaching
Methodology
Black board , Class exercises, Assignments.
Assessment of the Students will be on the basis of the following weightage :-
1. End Term Exam
70
2. Attendance
5
3. Assignment
5
4. Mid Term. I Exam
20
5. Mid Term. II Exam
20
Total
best of two
100 Marks
Text Books
S.N.Dey , N.K.Nag.
Reference books
Bhanja Ganguly , Amitava mitra ,Das Mukherjee.
Course Duration
40 lectures.
Time per
1 hour each
Lecture
1
Module
Detailed of
Course to be covered
Topic
Determinants of order 2 and 3; minors and cofactors;
expansion of determinants; properties of
determinants; Cramer’s rule for solving simultaneous
equations in two or three variables.
1
Matrices: Different types of matrices; Matrix Algebra –
addition, subtraction and multiplication of matrices;
Singular and non-singular matrices; adjoint and inverse of
a matrix; elementary row / column operations;
Solution of a system of linear equations using matrix
algebra.
Determinants:
Vectors: Row and column vectors and their significance
Assignment
Question
1.For a matrix A
2 -1
1 3
Show that A2 – 5A+7I2 =0 and hence find A-1.
2. Find A-1 when A =
3. If x +y +z =0
1 4
2 16
Show that
1 1 1
X y z
X3 y3 z3
=0
4. Solve the following equation by Cramer’s rule
i) x + y + z = 3 , 2y + z = 3 , z =1
ii) 2x +3y +z = 8 , 3x – 5y +2x = 7 , x+y=z = 4
5. Determine the matrices A and B where
2B + A = 1 2 0
and
6 3 -3
-5 3 1
6.If A =
7.Show that
1 2 1
1 -4 1
3 0 -3
and
2A –B =
2 1 5
2 -1 6
0 1 2
B=
2 1 1
1 -1 0
2 1 -1
(a2 +b2 )/c c
c
a
(b2 +c2)/a a
b
b
(c2 + a2)/b
8. Show that AB ≠BA where
A = 1 4
-1 1
and
B = 3 7
-3 -2
2
Compute AB.
= 4abc.
No. of Lectures.
9
Module
2
Detailed of
Course to be covered
Topic
Idea of conics as
sections of a cone
Brief ideas of Foci, Directrix, Eccentricity and Latus Rectum;
Equations of
parabola, ellipse, hyperbola and rectangular hyperbola in standard
form.
No. of
Lectures
7
Assignment
Questions
1. Find the points on the curve y = x2 -4x +9 the tangents of which pass through the origin.
2. The equation of a parabola is y2 = 6( x+y) find the vertex, equation of axis, focus , latus rectum.
3. The equation of a hyperbola is x2 - y2 = a2 . find out the eccentricity , focus and latus rectum.
4. If the ellipse x2/a2 + y2/b2 = 1 passes through (-3,2) and its eccentricity be √3/5 then find the latus rectum.
5. If the centre , vertex and eccentricity of a hyperbola be (2,4), (6,4), (√5) then find its equation.
6. The equation of the directrix of a hyperbola is x-y+3 = 0. Its focus is (-1,1) and eccentricity is 3. Find the
equation of the hyperbola.
7. If the straight line 3x +4y +1 is a tangent to the hyperbola y2 = 4ax. Then find the value of a.
8. Find the equation of an ellipse for which the principal axes are along the coordinate axis , the length of the latus
rectum is 4 and eccentricity is 1/3.
9. In the hyperbola 9x2 – 4y2 + 54x +16y + 29 = 0 find the coordinates of the centre , length of latus rectum,
eccentricity, coordinates of foci.
3
Module
Detailed of
Course to be covered
Topic
Limits:
3
No. of
Lectures
Notation and meaning of limits; Fundamental theorems on
limits; Evaluation of limits of algebraic,
exponential and logarithmic functions.
5
Assignment
Questions
1. Lt
(1 – cos x)/x2
x 0
2. Lt
(ex - e-x)/x
x 0
3. Evaluate Lt (1m +2m +3m +………nm) / nm+1
n ∞
4.
(m>-1)
A function is defined as
f(x) = x2
when x > 1
2
when x = 1
x
when x < 1
Find Lt f(x)
x
1
5. Exercises from S.N.DEY (Vol – 2)
Module
4
Detailed of
Course to be covered
Topic
Continuity
Continuity of a function at a point x = a and in an interval
Assignment
Questions
1. Show that the function defined below is continuous at x=1.
f(x) = x2 +1 when x > 1
2
when x = 1
2x
when x < 1
2. Show that the function defined below is continuous at x=2.
f(x) = x2 +4 when x > 2
8
when x = 2
3x2 - 4 when x < 2
3. Exercises from S.N.DEY (Vol – 2)
4
No. of
Lectures
2
Module
5
Detailed of
Course to be covered
Topic
Differentiation
Meaning and geometrical interpretation of differentiation;
Differentiation from first principles;
Standard derivatives; Rules for calculating derivatives;
Logarithmic differentiation; Derivatives of composite
functions, implicit functions and functions defined
parametrically.
Successive differentiation: Second and higher order
derivatives; forming equations with such derivatives.
Applications of differentiation: Optimization of functions;
Curve sketching; Equations of tangent and normal;
Derivative as a rate measurer; Sign of a derivative - increasing
and decreasing functions;
Partial derivatives: Homogenous functions; Euler’s Th
Assignment
Questions
1. If y = a cos (logx) + bsin(logx) then show that x2y2 + xy1 + y = 0
2. Verify Euler’s theorem for the function f(x ,y ) = x2+10xy+y2
3. If xy = ex-y then show that dy/dx = log x/ (1+logx)2
4. Verify Euler’s theorem for the function f(x ,y ) = (x2+y2) / (x2-y2)
5. Find dy/dx if y = x2(x4 – 1)5
6. If y = x / √(1+x2) prove that x3 dy/dx = y3.
7. If y = asin(mx) + b cos (mx) then show that y2 = -m2y
8. Verify Euler’s theorem for the function f(x ,y ) = (x2+y2) / (x-y)
9. If y = sin(msin-1x) then show that (1-x2)y2 – xy1 + m2y = 0.
10. If v = sin-1 (x2 +y2)/(x+y), then show that xVx + y Vy = tan V
11. If ax2 + 2hxy +by2 = 1 then show that y2 = (h2 – ab) / (hx +by)2
5
No. of
Lectures
10
Module
6
Detailed of
Course to be covered
Topic
Optimization
No. of
Lectures
Optimization of functions of more than one variable:
unconstrained and constrained optimization; cases of
two variables involving not more than one constraint.
3
Assignment
Questions
1. Examples and Exercises from the text book.
Module
7
Detailed of
Course to be covered
Topic
Integration
Indefinite Integrals: Integration as the inverse of
differentiation; Standard integrals; Integration by
substitution, by parts and by the method of partial fractions.
Definite Integrals: Definite integral as the limit of a sum;
Properties of definite integrals; Application of
definite integrals in calculating the areas under curves.
Assignment
Questions
п/2
1. ∫
√sinx / (√sinx + √cosx) dx
0
2. Evaluate ∫ x / (x+1)(x+2) dx.
3.
4.
5.
6.
7.
8.
No. of
Lectures
1
From the first principle find the value of ∫ (3x +5) dx
0
-1
2
Evaluate ∫ x sin x / √(1-x ) dx
1
From the first principle find the value of ∫ (x2 +5) dx
0
Evaluate ∫ x5 / √( 1+x3) dx
1
Evaluate ∫ sin-1 (2x/1+x2) dx
0
Evaluate ∫ ex (1/x - 1/x2) dx
9. Evaluate ∫ x2 / √(1+x3) dx
10. Evaluate ∫ ex(x logx +1) /x dx
11. Examples and Exercises from the text book.
6
10
7