# BA IN MATHEMATICS

University of DelhiPrice on request

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## Important information

- Bachelor
- New delhi

Starts | Location |
---|---|

On request |
New DelhiUniversity Road , Delhi 110007, 110007, Delhi, India See map |

## Course programme

BA IN MATHEMATICS

PAPER I : Algebra and Calculus

SECTION - I

Definition and examples of a vector space, Subspace and its properties,

Linear independence and dependence of vectors, basis and dimension of a

vector space. Types of matrices. Rank of a matrix. Invariance of rank under

elementary transformations. Reduction to normal form- Solutions .of linear

homogeneous and non-homogeneous equations with number of equations and

unknowns upto four. Cayley-Hamilton theorem, Characteristic roots and

vectors.

SECTION - II

De Moivres theorem (both integral and rational index). Solutions of equations

using trigonometry, Expansion for Cos nq. Sin nq in terms of powers of Sin q,

Cosq, and Cosq, Sinq in terms of Cosine and Sine of multiples of q, Summation

of series, Relation between roots and coefficients ofnth degree equation.

Solutions of cubic and biquadratic equations, when some conditions on roots

of the equation are given, Symmetric functions of the roots for cubic and

biquadratic equations. Transformation of equations.

SECTION - III

Limit and.Continuity, Types of discontinuities. Differentiability of functions.

Successive differentiation, Leibnitz s theorem, Partial differentiation, Euler s

theorem on homogeneous functions.

SECTION - IV

Tangents and normals, Curvature, Asymptotes, Singular points, Tracing of curves.

SECTION - V

Rolle s theorem, Mean Value Theorems, Taylor s Theorem with Lagrange s &

Cauchy s forms of remainder. Taylor s series, Maclaurin s series of sin x, cos x,

ex, log(l+x), (l+x)m, Applications of Mean Value theorems to Monotonic functions

and inequalities. Maxima & Minima. Indeterminate forms.

SECTION - VI

Reduction formulae, Integration of irrational and trigonometric functions.

Properties of definite integrals. Quadrature, Rectification of curves, Volumes

and areas of surfaces of revolution.

PAPER II

Geometre, Differential Equations and Algebra

UNIT-I : Geometry

Techniques for sketching parabola, ellipse and hyperbola. Reflection

properties of parabola, ellipse and hyperbola and their applications to signals,

classification of quadratic equation representing lines, parabola, ellipse and

hyperbola.

UNIT-II : 3-Dimensional Geometry and Vectors

Rectangular coordinates in 3-space; spheres, cylindrical surfaces cones.

Vectors viewed geometrically, vectors in coordinate system, vectors determine by

length and angle, dot product, cross product and their geometrical properties.

Parametric equations of lines in plane, planes in 3-space.

UNIT-III : Ordinary differential equations

First order exact differential equations including rules for finding

integrating factors, first order higher degree equations solvable for x, y, p, Wronskian

and its properties, Linear homogeneous equations with constant coefficients, Linear

non-homogeneous equations. The method of variation of parameters. Euler s

equations. Simultaneous differential equations. Total differential equations.

Applications of ordinary differential equations to Mixture Problems, Growth

and Decay, Population Dynamics and Orthogonal trajectories.

UNIT-IV: Partial differential equations

Order and degree of partial differential equations, Concept of linear and

non-linear partial differential equations, formation of first order partial differential

equations. Linear partial differential equations of first order, Lagrange s method,

Charpit s method, classification of second order partial differential equations into

elliptic, parabolic and hyperbolic through illustrations only.

Applications to Traffic Flow.

UNIT-V: Algebra

Integers modulo n, Permutations, Groups, subgroups, Lagrange's Theorem,

Euler's Theorem, Symmetry Groups of a segment of a line, and regular n-gons for

n=3, 4, 5 and 6. Rings and subrings in the context of C[0,1] and Zn.

PAPER III

UNIT-1 Analysis (38 marks)

Order completeness of Real numbers, open and closed sets, limit point of

sets, Bolzano Weierstrass Theorem, properties of continuous functions,

Uniform continuity.

Sequences, convergent and Cauchy sequences, sub-sequences, limit

superior and limit inferior of a sequence, monotonically increasing and

decreasing sequences, infinite series and their convergences, positive term

series, comparison tests, Cauchy s nth root test, D Alembert s ratio test,

Raabe s test, alternating series, Leibnitz s test, absolute and conditional

convergence.

Riemann integral, integrability of continuous and monotonic functions,

improper integrals and their convergences, comparison tests, Beta and

Gama functions and their properties, Pointwise and uniform convergence of

sequences and series of functions, Weierstrass M-test, Uniform convergence

and continuity, Statement of the results about uniform convergence and

integrability or differentiability of functions, Power series and radius of

convergence, Fourier series.

UNIT-2 Computer Programming

Programming: Preliminaries, constants, variables, type declaration,

expressions, assignment statements, input-output statements, Control

statements, functions, Arrays, simple programs using these concepts.

Control statements, functions, arrays, Format specification.