Basic Mathematics - I Year BCA One Series by Parth Publishers
This One Week Series is Written in English Language in Question Answer Series According to syllabus of Rajasthan University.
Unit-I Functions : Functions, domain & range of a function, types of functions constant, identity, polynomial, exponential, logarithmic, trigonometric, inverse- trigonometric, rational, periodic, modulus, signum and greatest integer functions with their graphs. Composite functions, Invertible Functions. Function domain and range, one to one and onto functions, composite functions, inverse of functions. Binary operations.
Unit-II Matrices and Determinant : Definition and Types of Matrices, Addition, Subtraction and Multiplication of Matrices, Non-commutatively of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix(restrict to square matrices of order 2), Scalar Multiplication. Transpose of a Matrix. Determinant of a square matrix (up to 3x3 matrices), properties of determinants, minors, cofactors. expansion of determinants, application of determinants in finding the area of a triangle. Invertible matrices. Adjoint and inverse of a matrix, Solution of system of linear equations by inverse matrix method and Cramer's Rule, EigenValues, Eigen Vectors.
UNIT III Numerical Methods: Floating Point Numbers and its representation. Normalized Floating point number and their arithmetic operations and consequences. Errors in Numbers. Finite Difference methods: The operators E, A and their algebraic properties and relations. Difference Table, Fundamental theorem of difference table. One missing term case. Factorial notion of a polynomial. Concept of Zero Difference. Effect of Error in tabular values. Quadratic Equation: Solution of Quadratic Equations, Nature ol Roots Solution of a quadratic equation by factorization method and Shridharacharya's formula. Relation between the roots of a quadratic equation, formation ol quadratic equation from given roots.
UNIT-IV Statistics : Frequency Distribution, Graphical representation of frequency distribution. Mean, Median, Mode and other measures of Central Tendency, Dispersion, Standard Deviations, Variance. Correlation and regression, Measure of Karl Pearson's coefficient of correlation, regression analysis, properties of regression lines.
UNIT-V Probability: Factorial notation n!, Combinations and Permutations, Classical approach of Probability- trial & events, exhaustive events, equally likely events, mutually exclusive events, favorable events, independent events. Classical or mathematical definition of probability. Law of addition of probabilities. Multiplication law of probability and conditional probability. Simple problems based on addition and multiplication law of probabilities.
Its also useful for Shekhawati, Matsya, Brij, JNU, MGSU, MDS, Kota, MLSU University Students. Almost All Units are covered according to syllabus.