Mathematics-I Chapter (Sem -1)

Sets and Functions:

• Introduction to sets
• Types of sets (finite, infinite, empty, etc.)
• Operations on sets (union, intersection, complement, etc.)
• Functions: Definition, types of functions (one-to-one, onto), composition of functions

Basics of Algebra:

• Real numbers and their properties
• Algebraic expressions
• Laws of algebra (commutative, associative, distributive)
• Polynomials and polynomial operations (addition, subtraction, multiplication)

Linear Equations and Matrices:

• Linear equations and their solutions
• Matrix algebra: Basic operations (addition, scalar multiplication, matrix multiplication)
• Types of matrices (square, symmetric, identity, etc.)
• Determinants and their properties

Quadratic Equations:

• Quadratic equations and their solutions
• Nature of roots (real, complex, equal, distinct)
• Quadratic formula, discriminant

Sequence and Series:

• Arithmetic sequences and series
• Geometric sequences and series
• Summation notation (sigma notation)
• Arithmetic mean, geometric mean

Limits and Continuity:

• Introduction to limits
• Calculation of limits (algebraic methods, L'Hopital's rule)
• Continuity of functions

Differentiation:

• Definition of derivative
• Differentiation rules (power rule, product rule, quotient rule, chain rule)
• Higher-order derivatives
• Applications of derivatives (maxima and minima, rate of change)

Integration:

• Indefinite integrals and integration techniques (substitution, integration by parts)
• Definite integrals and their properties
• Fundamental theorem of calculus
• Applications of integration (area under curves, volumes of solids)

Introduction to Differential Equations:

• Definition and types of differential equations (ordinary, partial)
• Solution techniques for first-order differential equations (separation of variables, integrating factor)

Complex Numbers:

• Introduction to complex numbers
• Arithmetic operations with complex numbers
• Polar form and exponential form of complex numbers
• De Moivre's theorem

Introduction to Probability:

• Basic concepts of probability (sample space, events, probability axioms)
• Probability of events (addition rule, multiplication rule)
• Conditional probability and independence

Statistics:

• Measures of central tendency (mean, median, mode)
• Measures of dispersion (range, variance, standard deviation)
• Introduction to probability distributions (binomial, normal)