Check out sikkim manipal university distance education (SMUDE) Syllabus for BCA Basic Mathematics Subject on smude.edu.in
Check out sikkim manipal university distance education (SMUDE) Syllabus for BCA Basic Mathematics Subject on smude.edu.in
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.