Course Code: BCA113 |
Course Title: Basic mathematics (4 Credits) |
Course Contents
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 θ when θ 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 e^{x} 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; n^{th }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.