FOUNDATIONS OF MATHEMATICS

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

The course will enable the students to

  1. Make familiar with the basics of mathematics.
  2. This module is introductory in nature and focuses on numerical aspects, keeping those students in mind those did not have mathematics at 10+2 level.

 

Course Outcomes (COs):

 

Learning Outcome (at course level)

Learning and teaching strategies

Assessment Strategies

The students will:

CO 21.Build a foundation of basic mathematical concepts needed for general computations.

CO 22.Analyse, solve and compute real-world applications of mathematics.

CO 23.Solve applied problems using matrices, differentiation and integration.

CO 24.Demonstrate a working knowledge of set notation and elementary set theory.

CO 25.Compute limits, derivatives, and definite & indefinite integrals of algebraic, logarithmic and exponential functions.

CO 26.Solve discrete mathematics problems that involve: computing permutations and combinations of a set.

 

Approach in teaching:

Interactive Lectures, Discussion, Tutorials, Reading assignments, Demonstration.

 

Learning activities for the students:

Self-learning assignments, Effective questions, Giving tasks.

 

Class test, Semester end examinations, Quiz, Solving problems in tutorials, Assignments, Presentation.

 

 

9.00
Unit I: 

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: 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: 

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

 

9.00
Unit IV: 

Integration: - Indefinite Integrals, Rules of Integration, Integration by substitution, Integration by Partial Fractions, Definite Integration, Properties of Definite Integral, finding areas of simple closed curves.

 

9.00

Permutation and Combination: Fundamental Principles of Counting, Addition Principle, Factorial, Permutations, Combinations.

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

 

ESSENTIAL READINGS: 
  1. G. C. Sharma & Madhu Jain, “Mathematics for BCA”, Oscar Publication.
  2. R.D. Sharma, “Mathematics for class 12 part-1”, Dhanpat Rai and Co. New Delhi.
  3. R.D. Sharma, “Mathematics for class 12 Part-2”, Dhanpat Rai and Co. New Delhi.
  4. R.S. Agarwal, “Mathematics for class 12”, Bharati Bhavan, New Delhi.
  5. R. D. Sharma, “Mathematics Vol-2”, Dhalpat Raj & Sons. (For Unit-I)
  6. 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: 
2021-22
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