MATHEMATICS –I (G103)
DETAIL COURSE CONTENT
UNIT 1-ALGEBRA:
UNIT 1-ALGEBRA:
Arithmetic and Geometric Progressions (A.P. & G.P.) . Formula of the nth term of A.P. Properties and concept of G.P., the nth term of G.P. Complex Numbers :Definition of a Complex number Polar form of a complex number, Problems. Cube roots of unity, Fourth roots of unity, the nth roots of unity.Permutation and combination in elementary level with formulae & simple examples.Factorials .Quadratic Equation. Properties of quadratic Equation. Binomial Theorem : Positive integral index, Expansion of (x +a)n, where n is a positive integer.Rules for finding general term& middle term etc. Calculation of approximate value, when the number of terms, n is large.Properties of Binomial CoefficientsSets and Relation: Relational algebra,Sets & subsets Operations on sets,Product sets (Cartesian product) Concepts of relation, domain and Range,Sets arising from relations.
UNIT 2-TRIGONOMETRY:
Trigonometric functions. Trigonometric functions of allied angles.Trigonometric ratios. Half angle, double angle, triple angle – derivation & problems .Compound trigonometric functions. Properties of a Triangle .Solution of triangle using the properties. Trigonometric ratios with angles A±B and C±D.Definition of periodic function and the period of trigonometric function. Interpret the graphs of: a sin (bƏ + c), a cos (bƏ +c) . Use multiple.
UNIT 3-STATISTICS :
Data frequency distribution, tabulations and representation. Continuous and discontinuous variables. Frequency- relative and commutative relative.Graphical representation of frequency. Bar chart, Histogram and frequency polygon. Mean, median, mode and relationship. Harmonic mean ,Range, Deviation, Mean deviation, Standard Deviation.Probability : Event and different mathematical formulae. Probability for independent and dependent events .Problems based on probability. Introduction : Numerical Methods. Concept of difference tables. Newton’s Interpolation methods (Forward and backward).Lagrange’s interpolation method. Concept of extrapolation.
UNIT 4-MATRICES :
Matrix- definition, notations. Element of matrix.Type of matrices. Special Matrices Square, diagonal, row, column, scalar Unit, zero or null, upper and lower triangles, Symmetric, skew. Introduction to determinants. Addition and subtraction of matrices. Product of two matrices. Adjoint of a matrix. Inverse matrix. Solution of a system of linear equations using matrix method.
SUGGESTED LEARNING RESOURCES
Text Books:
1. College Algebra By A.R. Majumder & P.L. Ganguli
2. Plane Trigonometry Part I By S.L. Loney
3. Statistics By N.G. Das
4. Trigonometry By Das & Mukherjee
Reference Books:
1. Engineering Mathematics Part I By Shanti Narayan
2. Polytechnic Mathematics Vol. I By Dutta & Bera