Foundations of Mathematics

Paper Code: 
GBCA 101
Credits: 
03
Periods/week: 
03
Max. Marks: 
100.00
Objective: 

This module is designed to acquaint the students with the basics of mathematics. This module is introductory in nature, keeping those students in mind that did not have mathematics at 10+2 level.

9.00
Unit I: 
Introduction to Matrices

Matrices, Types of Matrices, Operations of addition, Scalar Multiplication and Multiplication of Matrices, Determinant of a Square Matrix, Minors and Cofactors. Transpose, adjoint and inverse of a matrix. Solving system of linear equations in two or three variables using inverse of a matrix.

9.00
Unit II: 
Sets, Relation & Functions

Sets, Relation & Functions: Definition of Set, Type of Sets, Operations on Sets, Venn diagram, Cartesian Product, Relations, Functions, Types of function, Some elementary functions with their graphs (Exponential, logarithmic, modulus). Limit & continuity of a function (Simple Problems).

9.00
Unit III: 
Differentation

Differentiation: Derivative and its meaning, Differentiation of algebraic, trigonometric, exponential & logarithmic functions, Rules of Differentiation, Differentiation by substitution, Higher order differentiation, Maxima and Minima of simple functions.

9.00
Unit IV: 
Integration

Integration: - Integral as Anti-derivative process, Indefinite Integrals, Rules of Integration, Integration by substitution, Definite Integration, Properties of Definite Integral, finding areas of simple closed curves.

9.00
Unit V: 
Coordinate Geometry & Conic Sections

Coordinate Geometry: - 2D Cartesian Co-ordinate system. Straight line (Equation & Slope of a line). Circle: Equation of Circle, Equation to Tangent.

Conic Sections: Focus, Eccentricity, Directrix, Axis of a conic section, Parabola, Ellipse (Definitions, equations and shape of curve only).

ESSENTIAL READINGS: 
  1. G. C. Sharma & Madhu Jain, “Mathematics for BCA”, Oscar Publication.
  2. R. D. Sharma, “Mathematics Vol-2”, Dhalpat Raj & Sons. (For Unit-I)
  3. S. L. Loney., “The Elements of Co-ordinate Geometry Part-I”, Book Palace, New Delhi.
REFERENCES: 
  1. Tom M. Apostol, “Calculus Volume II”, Second edition, John-Wiley & Sons, 2002.
  2. S. Balachandra Rao, C.K. Shantha,“Differential Calculus”,New Age International(P) Ltd.
  3. Frank Ayres Jr., Elliot Mendelson, “Calculus”, fourth edition, Mc-Graw Hill International Edition.
Academic Year: 
2018-19
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