DC01 MATHEMATICS -I
1. Algebra 6 hours
1.1
Arithmetic
progression.
1.2
Geometric
progression.
1.3
Sum
of squares and cubes of finite number of natural numbers.
1.4
Mathematical
Induction.
1.5
Exponential
and Logarithmic functions.
1.6
Binomial
Theorem (without proof) for any index.
1.7
Quadratic
equations and inequations.
1.8
Permutations
and combinations.
II [3, 11-14]
2.
Trigonometry 8 hours
2.1
Angles
and their measures.
2.2
Trigonometric
ratios.
2.3
Trigonometric
functions.
2.4
Periodicity
of trigonometric functions.
2.5
Sums
and Difference formulae (without proof) and their applications.
2.6
Trigonometric
ratios of multiple and sub-multiple of angles (2A, 3A and A/2 only).
2.7
Simple
Trigonometric identities.
2.8
Sine
and cosine formulae.
2.9
Napier
Analogy.
2.10
Law
of projection and Half angle formula.
2.11
Inverse
trigonometric functions.
II [2]; III [1, 2,
7-9]
3. Coordinate Geometry 16 hours
3.1
Cartesian
and polar coordinates of a point and their conversion.
3.2
Distance
between two points.
3.3
External
and Internal division formulae (without proof).
3.4
Coordinates
of centroid and incentre of a triangle.
3.5
Area
of a triangle when its vertices are given.
3.6
Equation
of straight line in various standard forms.
3.7
Intersections
of straight lines.
3.8
Angle
between two straight lines.
3.9
Perpendicular
distance formula.
3.10
Circle.
3.11
Standard
and general equation of a circle.
3.12
Finding
equation of circle when center and radius is given.
3.13
Conic.
3.14
Definition
of a conic.
3.15
Parabola,
ellipse, hyberbola and their standard equations (without proof).
3.16
Finding
equations of a conic when its focus, directrix and vertex are given.
I [4]; II [4, 5,
7,8]
4. Differential Calculus 12 hours
4.1
Limit
and continuity of a functions.
4.2
Standard
limits.
4.3
Evaluation
of simple limits.
4.4
Differentiation
– Definition and geometrical interpretation of derivative.
4.5
Physical
meaning of derivative.
4.6
Differentiation
from the first principle of 
.
4.7
Derivative
of sum, product, quotient and composite of two functions.
4.8
Differentiation
of sec x, cosec x, cot x and inverse trigonometric functions.
4.9
Differentiation
of functions in implicit and parametric forms.
4.10
Applications
of Differentiation-Tangents and normals, maxima and minima.
I [5]
5. Integral Calculus 12 hours
5.1
Indefinite
integrals.
5.2
Integration
as inverse of differentiation.
5.3
Simple
integration by substitution, integration by parts and by partial fractions.
5.4
Definite
integral.
5.5
Geometrical
interpretation of definite integral.
5.6
Properties
of definite integrals.
5.7
Evaluation
of simple definite integrals.
5.8
Reduction
formulae.
5.9
Evaluation
of 
(m, n being positive integers).
5.10
Applications:
Area under the curve and x-axis.
5.11
Volume
and surface of solids formed by revolution of areas under a curve, about
x-axis.
I [6]
6. Differential
Equations 6 hours
6.1
Order
and degree of differential equation.
6.2
Solution
of differential equations of first order and first degree – homogeneous
differential equation and solutions of differential equation in variable
separable form.
6.3
Linear
differential equation of first order.
I [7]
Text Book
I.
H K Dass, ‘ Applied Mathematics for Polytechnics’, CBS Publishers &
Distributors.
II. Mathematics, A text book for
Class XI National Council of Educational Research & Training.
III. S L Loney, ‘Plane
Trigonometry’ Part I.
Reference Books
1.
S
L Loney, ‘Elements of Coordinate Geometry
2.
Shanti
Narayan, ‘Differential Calculus’, S Chand & Co.,
3.
Shanti
Narayan, ‘ Integinl Calculus’, S Chand & Co.,