• Comprehend the idea of logic and able to use it to support mathematical claims as well as practical issues.
• Use various set operations to solve the specific problem and determine the number of items in a given set.

Unit 1: Basic Concept [9 Hrs.]

Elementary Logic

Connectives, Quantifiers,

Basic laws of logic,

Quantifiers

Techniques of proof.

Sets, Types of sets, Venn diagram,

Set operations, Laws of the algebra of sets (without proof),

Real number system, Representation of real numbers on the Real line,

Properties of real numbers (without proof), ordered sets, Inequalities,

Intervals, Absolute value, Cartesian product, Relation.

• Identify the dependent and independent variables to find the domain and range of the function.
• Explain the concept of limit and continuity and use it in real-life problems.

Unit 2: Functions, Limit, and Continuity  [8 hrs.]

2.1. Constants and variables, Concept of functions,

2.2 Domain, and range of a function, Types of functions (algebraic, logarithmic, Trigonometric, and exponential functions),

2.3. Graphic representation

2.4 Application of functions to business and economics.

2.5 Limit of a function, properties of Limit, Indeterminate Forms,

2.6 Limits of Polynomial and Rational Functions, Limits at infinity,

2.7 Continuity, Continuity at a Point,

2.8 Business Application of Limit.

• Identify the rate change of a function at a particular point.
• Find the derivative of algebraic, exponential, logarithmic, and trigonometric functions.

Unit 3: Derivative  [6 Hrs.]

3.1 Derivative

3.2 Average rate of change

3.3 Derivative as a slope of the tangent to curves

3.4 Methods of differentiation (power rule sum rule, product rule, quotient rule and chain rule)

3.5 Differentiation     of     implicit     and parametric functions

3.6 Derivative as a rate of change. Higher order derivatives.

• Establish the relationship between the derivative and concavity of the function.
• Identify the increasing and decreasing function.
• Find the maxima minima of a function, using the first and second-order derivative.

Unit 4: Application of Derivatives [6 Hrs.]

4.1 Increasing and decreasing functions

4.2 Critical point, Point of inflection

4.3 Maximum and minimum value of the function

4.4 Marginal analysis in Business and Economics

4.5 Concavity of the function, Marginal Profit Analysis

4.6 The mean value theorem, Optimization problem

• Use     different    Rules     and    techniques     of integration to solve the related problems.
• Identify the value of the function from the corresponding marginal value.

Unit 5: Integrals    [6 Hrs.]

Techniques of Integration (Integration by simplification, Substitution method, Integration by parts)

Definite integral,

Properties of the definite integral

• Perform matrix operations and solve related problems
• Evaluate the value of the determinant and use the concept of determinant for solving linear equations.

Unit 6: Matrices and Determinants [7 Hrs.]

Types of matrices

Matrix operations

Transpose of a matrix, Determinant of a matrix, Minors, and cofactors of the matrix

Properties of determinants(Singular and non- singular matrix)

Solution of a system of linear equations having a unique solution of up to three variables (Cramer’s rule).

• Identify the difference between permutation and combination.
• Use     the     concept     of     permutations     and combinations in real-life problems.

Unit  VII: Permutations  and Combinations   [6 hrs]

7.1 Basic principles of counting, factorial notation,

7.2 permutation, Permutation of objects alike,

7.3 Permutation     with     restrictions, Circular permutation,

7.4 Combination, and Combination with restrictions.

Semester-End examination

50

50