# BCA Mathematics Syllabus

Har institutes ke BCA ke subject me difference ho sakta hai. Sabhi institute ek jaise topics nahi provide kariti. Mai kuch universitites ke maths ke topics ko mix karke aapko bataata hu.

UNIT 1: Set theory

Sets and their representations; The empty set; finite and infinite sets; equal and equivalent sets; subsets; power set; universal set; Venn diagrams; complement of a set operations on sets; applications of sets.

UNIT 2: Mathematical Logic

Basic Logical connections; Conjunction; Disjunction; Negation; Negation of Compound Statements; Truth tables. Tautologies; Logical Equivalence; Applications.

UNIT 3: Modern algebra

Binary Operation; Addition Modulo n; Multiplication modulo n; semi group; properties of groups; subgroup.

UNIT 4: Trigonometry

Radian or circular Measure; Trigonometric Functions; Trignometrical ratios of angle ? when ? is acute; trignometrical ratios of certain standard angles; allied angles; compound angles; multiple and sub- multiple angle.

UNIT 5: Limits and Continuity

The real number system; The concept of limit; concept of continuity.

UNIT 6: Differentiation

Differentiation of powers of x; Differentiation of ex and log x; differentiation of trigonometric functions; Rules for finding derivatives; Different types of differentiation; logarithmic differentiation; differentiation by substitution; differentiation of implicit functions; differentiation from parametric equation. Differentiation from first principles.

UNIT 7: Integrations

Integration of standard Functions; rules of Integration; More formulas in integration; Definite integrals.

UNIT 8: Differential equations

First order differential equations; practical approach to Differential equations; first order and first degree differential equations; homogeneous equations. Linear equations; Bernoulli’s equation; Exact Differential Equations.

UNIT 9: Complex Numbers

Complex Numbers; Conjugate of a complex number; modulus of a complex Number; geometrical representation of complex number; De Moivere’s theorem; nth roots of a complex number.

UNIT 10: Matrices and Determinants

Definition of a matrix; Operations on matrices; Square Matrix and its inverse; determinants; properties of determinants; the inverse of a matrix; solution of equations using matrices and determinants; solving equations using determinants.

UNIT 11: infinite Series

Convergence and divergence; series of positive terms; binomial series; exponential series; logarithmic series.

UNIT 12: Probability

Concept of probability; sample space and events; three approaches of probability; kolmogorov’s axiomatic approach to probability; conditional probability and independence of events; bay’s theorem.

UNIT 13: Basics Statistics

Measures of central Tendency; Standard Deviation; Discrete series. Methods; Deviation taken from assumed mean; continuous series; combined standard deviation; coefficient of variation; variance.