Basic Mathematics

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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.

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