Annexure ‘CD – 01’
FORMAT FOR COURSE CURRICULUM
Course Title: Fundamentals of Mathematics
Credit Units: 03
Course Level: UG
Course Code: MATH 107
L
T
P/S
SW/F
W
2
1
-
-
TOTAL
CREDIT
UNITS
3
Course Objectives: The main purpose of this course is to teach fundamentals of mathematics to those who have not studied Mathematics at the (10 + 2) level.
After qualifying this course, students will be able to follow the regular course on mathematics being taught at undergraduate level.
Pre-requisites: Students must have knowledge of 10th standard Mathematics which includes quadratic equations, arithmetic progressions, coordinate geometry
and some applications of trigonometry.
Course Contents/Syllabus:
Weightage (%)
Module I
20%
Sets and functions, mod function, greatest integer function, Trigonometric, logarithmic and exponential functions and
their properties, periodic functions, concept of periodicity of trigonometric functions, trigonometric functions of sum
and difference of numbers, trigonometric functions of multiples and submultiples of numbers, trigonometric equations,
conditional identities, inverse trigonometric functions.
Module II
25%
Principle of mathematical induction, quadratic equations, sequences, finite and infinite sequences, general term of a
series, sums of Arithmetic, geometric progressions, Arithmetic mean(A.M.), geometric mean (G.M.), and their insertion
between any two numbers, harmonic progressions, harmonic mean(H.M.) and insertion of H.M. between any two
numbers , relationship among A.M., G.M., and H.M., Sum of Arithmetico – geometric series, sums to n terms of the
n
special series of the form
n
k, k
k 1
k 1
n
2
, and
k
3
, sum of series using special series. Permutation and combination,
k 1
Binomial theorem and its application.
Module III
25%
Cartesian system of coordinates, various forms of equations of line parallel to axes, slope, intercept form, the point
slope form, symmetric form, parametric equation of a line, Two point form, normal form, general form, intersection of
lines, equation of bisector of angle between two lines, condition for concurrency of three straight lines, distance of a
point from a line, Equation of a circle, general form of the equation of the circle, its radius and the centre, equation of
the circle in the parametric form, points of intersection of a line and a circle, condition for a line to be a tangent to a
circle, equation of a tangent to a circle and length of the tangent, sections of a cone, equations of conic
section(parabola, ellipse, and hyperbola) in standard form, their applications
Module IV
xn  an
 n a n 1 ,
Limit of a function, some standard limits(without proof) lim
xa
xa
30%
lim sin x  0
x0
sin x
ex  1

1
 1 0  x  , lim (1  x )  1 , and lim
 1 , continuity of a function at a point,
x0
x0
x0
x
2 x0 x
x
examples of continuous functions, derivative of a function, relationship between continuity and differentiability of a
function, derivatives of xn, sin x, cos x, tan x from first principle, derivative formulae related to sum, difference, product
and quotients of functions, derivative of inverse trigonometric functions, derivative of logarithmic and exponential
function, derivative of functions expressed in parametric forms, higher order derivatives, integration as the inverse of
differentiation, indefinite integrals, properties of integrals, integrals of algebraic, trigonometric and exponential
functions, integration by substitution, integrals of the type
dx
dx
(p x  q ) dx
dx
dx
dx
 x2  a2 ,  a2  x2 ,  x2  a2 ,  a2  x2 ,  a x2  b x  c ,  a x2  b x  c ,
lim cos x  1 , lim

(p x  q ) dx
, integration by parts, integration of the type
 sin
1
x dx ,

x 2  a 2 dx,
ax  bx  c
Definite integrals, evaluation of definite integrals, properties of definite integrals, Differential equations, order and
degree of a differential equation, general and particular solution of a differential equation, solution of a differential
equation by the method of separation of variables.
2
Student Learning Outcomes: The students who passed in this course
 define sets and functions, mod functions and greatest integer function
 will be able to apply many trigonometric functions in problems of physics, architecture and engineering
 will be able to solve many engineering problems including sequences and series
 enables geometric problems to be solved algebraically by gaining the knowledge of co-ordinate geometry




define and analyze limits and continuity of functions.
will be able to define and evaluate special form of integrals and gain some properties of definite integrals
practice and develop logic/reasoning skills using tools of Calculus
will be able to bridge the gap between mathematicians, physical scientists and engineers using the knowledge of Vector Calculus
Pedagogy for Course Delivery:

Revising the related previously-learned topics.

Guiding the students to know their syllabus, resources and learner support system to respond to students’ questions timely.

Providing the guidance about how to use the course management tools effectively via discussions, assignments, assessments, etc

Taking tests and quiz on regular basis.

Taking feedback from the students from time to time.
Lab/ Practicals details, if applicable:
NA
List of Experiments: NA
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

Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term Examination
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components (Drop down)
CT
HA
End Term Examination
S/V/Q
ATTD
EE
Weightage (%)
10
7
8
5
70
Lab/ Practical/ Studio Assessment: NA
Text Reading:
 CBSE Books on Mathematics for class XI and XII
References:
 S. L. Loney, plane Trigonometry part – I, MacMillan India
 S. L. Loney, Coordinate Geometry, MacMillan India
 Hall, H.S. and K. Knight, Higher Algebra, MacMillan India
 J Edwards, Differential Calculus, MacMillan India
 J Edwards, Integral Calculus, MacMillan India
 C. E. Weatherburn, Elementary Vector Algebra, O U P (U.K.)
Additional Reading:
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Any other Study Material:
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