Course

UNIT I                                                                                                                        6 Hours

Sets

Introduction, Sets and their Representations (1 hr) The Empty Set, Finite and Infinite Sets (1 hr) Equal Sets, Subsets (1 hr)

Power Set, Universal Set (1 hr)

Venn Diagrams, Operations on Sets (1 hr)

Complement of a Set, Practical Problems on Union and Intersection of Two Sets (1 hr)

 UNIT II   6 Hours

Matrices

Introduction matrices, Types of matrices (1 hr) Operation on matrices (1 hr)

Transpose of a matrix (1 hr) Matrix Multiplication (1 hr)

Properties of matrix addition and multiplication (1 hr)

Symmetric and skew-symmetric matrices, Invertible matrices (1 hr)

UNIT III                                                                                                                 3 Hours

 Relations and Functions

Introduction, Cartesian Product of Sets (1 hr) Relations (1 hr)

Functions (1 hr)

UNIT IV                                                                                                                  6 Hours

Sequences and Series

Introduction, Sequences (1 hr) Series (1 hr)

Arithmetic Progression (A.P.) (1 hr) Geometric Progression (G.P.) (1 hr)

Relationship between Arithmetic Mean (A.M) and Geometric Mean (G.M) (1 hr) Sum to n terms of Special Series (1 hr)

UNIT V                                                                                                                    3 Hours

Mathematical Reasoning

Introduction, Statements (1 hr)

New Statements from Old, Special Words/Phrases (1 hr) Implications, Validating Statements (1 hr) 

UNIT VI                                                                                                                6 Hours

Calculus

Differentiation: Introductions, Derivative of a function, Derivative of a constant (1 hr) Derivative of a product of a constant and a function, Derivativeof the sum or difference of two functions (1 hr)

Derivative of the product of twofunctions (product formula), Derivative of the quotient of two functions (Quotient formula) – Without Proof (1 hr)

Integration: Introduction, Definition (1 hr) Standard formulae, Rules of integration (1 hr)

Method of substitution, Method of Partial fractions (1 hr)

SCOPE:

This is an introductory course in mathematics. This subject deals with the introduction to Sets, Matrices, Relations and Functions, Calculus, Sequences and Series, Mathematical Reasoning.Calculus is a significant mathematic tool for investigating drug movement quantitatively. Differential equations are used to relate the absorptions of drugs in various body organs over time. Integrated equations are regularly used to model the cumulative therapeutic or toxic reactions of drugs in the body. Sets, relations, and functions help conduct logical and mathematical set operations on a mathematical and real-life basis. Sequence and series are used in the recognition of patterns.The series plays an important role in the differential equations and in the analysis process. Mathematical reasoning involves using logical arguments and principles to analyze and solve mathematical problems.

COURSE LEARNING OUTCOMES:

Upon completion of the course the student shall be able to;

KNOWLEDGE

K1: Define set theory in mathematics

K2: Classify different types of matrices

K3: Illustrate relations and functions in set theory

K4: Describe the relationship between Arithmetic Mean (A.M) and Geometric Mean (G.M)

K5: Explain statements and compound statements in mathematical reasoning

K6: Describe the rules of integration.

SKILL

S1: Construct Venn diagram.

S2: Interpret matrix multiplication.

S3: Determine Cartesian products of sets.

S4: Sum of terms of special series.

S5: Construct new statements from old statements.

S6: Apply Method of substitution and Method of Partial fractions in integration.

ATTITUDE

A1: Appreciate the work of others.

A2: Share and care for good harmony and work culture.

A3: Follow the mathematical theories and rules.

A4: Participate actively in the class room activities.

A5: Support other students for mutual improvement.

A6: Demonstrate sincerity and punctuality. 

TEXT BOOKS:

1. Mathematics Textbook for Class 11& 12, NCERT

REFERENCE BOOKS:

1. D Sharma, Mathematics class XI, Volume 1, Dhanpat Rai Publication
2. S. Aggarwal, Mathematics Class 11, Bharti Bhavan

*Latest edition of text books and reference books can be referred.