B.A/B.Sc. (Three Years Degree Course)
In Applied Mathematics
B.A/B.SC. (1st Year) W.e.f. 2006
COURSE NO.
TITLE OF THE COURSE
AMM-01
AMM-02
AMM-03
Descriptive Mathematics
Differential Calculus
Complex Trigonometry and
Theory of Equations
MARKS
50
50
50
DESCRIPTIVE MATHEMATICS
AMM-01
Marks : 50
Unit I
Sets, Relation and Function:
Review of set operations, Algebra of sets, Cartesians product of sets, Functions,
Composition of functions, Binary Relations, Equivalence relation and partitions,
partial order relation and lattices. Pigeon Hole Principle.
Linear inequations:
Solution of linear Inequation in one variable and its graphical representation, Solution
of system of linear Inequations in one variable, Graphical solutions of linear
Inequation in two variable, Solution of system of linear Inequations in two variables.
Unit II
Quadratic Equations:
Solution of quadratic equation Relation betweens roots and coefficients, nature of
roots, formation of quadratic equations with given roots, symmetric functions of
roots, equations reducible to quadratic forms.
Sequence and Series:
Sequence and examples of finite and infinite sequences, Arithmetic progression
(A.P), Geometric progression (G.P) and Harmonic progression (G.P) ArithmeticGeometric series, Sum to n terms and sum of infinite arithmetic-geometric series,
special series.
Σn,
Σn²,
Σn³
Unit III
Permutations and Combinations:
Fundamental principle of counting and meaning of n, permutation as arrangements,
meaning of C (n,r), P (n,r). Simple applications including circular permutations.
Principle of Mathematical Induction and its simple applications, Binomial Theorem
for any index. Applications of binomial theorem for approximations. Properties of
Binomial Coefficients.
Unit IV
Coordinate Geometry:
Coordinate systems in a plane, Distance formula, Area of a triangle, Conditions for
collinearty for three points, equations of line, angle between two lines, conditions for
parallelism and perpendicularity. Distance of a point from a line. Homogeneous
equation of second degree representing pair of straight lines. Equation of parabola,
Equations of tangents and normals to a parabola, pole and polar pair of tangents from
a point, parametric equations of parabola.
Ellipse and Hyperbola:
Equation of ellipse, Tangents and Normals, pole and polar, parametric equations of
ellipse, Diameters, conjugate diameters and their properties.
Equations of hyperbola, tangents and normals, equation of hyperbola referred to
asymptotes as axes, Rectangular and conjugate diameters and their properties.
Books Recommended:
1) A text book of Algebra, M.L. Sath
2) A text book of Algebra, G.M. Shah
3) Linear programming, G.Hadley, Harosa Pub. 1995
4) Coordinate Geometry of Conic, M.R.Puri
5) Coordinate Geometry, M.L. Kochar
6) Coordinate Geometry, Ram Ballah
Differential Calculus
AMM-02
Marks : 50
Unit I
Limit of a function, Right hand and left hand limits, ε-δ definition of the limit of a
function. Basic properties of limits. Infinitesimals; Definition with examples.
Theorems on infinitesimals. Comparing infinitesimals, Definition with examples and
related theorems. Principal part of an infinitesimal and related theorems. Continuity
and basic properties of continuous functions on closed intervals. If a function is
continuous in a closed interval, then it is bounded therein. If a function is continuous
in a closed interval [a, b], then it attains its bounds at least once in [a,b].
Unit II
Definition of a derivative, Derivative as a rate of change, Derivative of some standard
functions, General rules of differentiation, Derivative of a function of a function,
Differentiation of implicit, circular and inverse circular functions, successive
differentiation, some standard results, Leibnitz Theorem and its applications.
Unit III
Tangents and Normal to plane curves, Equation of the tangent, equation of the
Normal, angle of intersection of two curves, Length of the tangent, sub-tangent,
normal and subnormal, polar coordinates, the polar tangent, polar sub-tangent, polar
normal, polar subnormal. Pedal equation. Derivative of the arc (Cartesian and polar
coordinates).
Curvature, radius of curvature for Cartesian and polar coordinates, double points,
Asymptotes, Cartesian and polar coordinates, envelopes, tracing of curves (Cartesian
coordinates only).
Unit
IV
Rolle’s theorem with proof and its applications. Lagrange’s Mean value theorem and
Cauchy’s Mean valu7e theorem with their applications. Taylor’s and Maclaurin’s
theorem with their applications. Partial differentiation of functions of two and three
variables. Euler’s theorem on homogeneous functions.
Books Recommended:
1. Dr.A.Aziz-ul-Auzeen, S.D Chopra and M.L.Kochar, Differential Calculus
(Thoroughly revised and enlarged New aEdition 2005-06).
2. Shanti Narayan, Differential Calculus.
3. Gorakh Prased, Differential Calculus.
AMM-03
Complex Trigonometry and Theory of Equations
Marks : 50
Unit I
Complex number, Argand’s diagram, modulus-amplitude form of a complex number,
Review of complex number system, triangle inequality and its generalization.
Equation of circle (Apollonius circle), Geometrical representation of sun, product and
quotient of two complex numbers. De Moiver’s Theorem for rational index and its
applications.
Unit II
Expansion of Sin nθ, Cos nθ etc. in terms of powers of Sin θ, Cos θ and expansion of
Sinⁿ θ and Cosⁿ θ in terms of multiple angles of Sinⁿ θ and Cosⁿ θ, Inverse of
trigonometric functions, Functions of complex variable. Exponential, circular.
Hyperbolic, Inverse hyperbolic and Logarithmic functions of a complex variable and
their properties. Summation of trigonometric series, Difference method, C + iS
method.
THEORY OF EQUATIONS
Unit III
General properties of equations, synthetic division, Relation betweens the roots and
the coefficients of an equation, Transformation of equations, Diminishing the roots of
an equation by a given number, Removal of terms of an equation, Formation of
equations whose roots are functions of the roots of a given equation, Equations of
squared differences.
Unit IV
Symmetric functions, Newton’s method of finding the sum of powers of the roots of
an equation. Cardan’s solution of the cubic, nature of the roots of a cubic.
BOOKS RECOMMENDED:
1. Dr. A.Aziz-ul-Auzeem and N.A.Rather, Differential Calculus (Edition 2005).
2. M.R. Puri,-Complex Trigonometry.
3. Hem Ram,- Pure Mathematics.
4. M.L.Sad,-Complex Trigonometry.
5. Samuel Borofsky,-Elementry theory of Equations.
6. W.S.Burnisde and A. W. Panton,- Theory of Equations.
7. J.C. Chaturvedi, - Theory of Equations.