Quantitative Aptitude

UNIT-I

Number System • H.C.F. and L.C.M. of Numbers • Decimal Fractions • Simplification • Square Roots and Cube Roots • Average • Problems on Numbers • Problems on Ages • Surds and Indices • Logarithms

Unit - II

Percentage • Profit and Loss • Ratio and Proportion • Partnership • Chain Rule • Pipes and Cisterns • Time and Work • Time and Distance • Boats and Streams • Problems on Trains • Alligation or Mixture • Simple Interest • Compound Interest

Unit – III

Area • Volume and Surface Area • Races and Games of Skill • Calendar • Clocks • Stocks and Shares • Permutations and Combinations • Heights and Distances

Unit – IV

 Data Interpretation • Tabulation • Bar Graphs • Pie Chart

•  Line Graphs

Aptitude and Reasoning

Basic Statistics

Unit-I

Concept of Sample Space - Events - Definition of Probability - Addition and Multiplication laws of Probability - Conditional Probability - Baye’s Theorem - Simple Problems.

Unit t-II

 Rando2 Variables - Distribution Function - Expectation and Moments - Moment Generating Function - Probability Generating Function - Simple Problems.

Unit – III

Concept of Bivariate Distribution - Correlation - Karl Pearson’s Coefficient of Correlation - Rank Correlation - Linear Regression.

Unit – IV

Standard distributions: Discrete distributions - Binomial, Poisson, Hyper Geometric and Negative Binomial Distributions - Continuous Distributions Normal, Uniform, Exponential.
 

SageMath software system

Syllabus Sagemath Software

1.      Introductory Tutorial

2.      Evaluating Sage Commands

3.      Functions in Sage

4.      Annotating with Sage

5.      Basic Symbolics and Plotting

6.      Basic 2D Plotting

7.      Basic 3D Plotting

 

8.      Calculus 1- Differentiation

9.      Calculus 2- Integration

10.   Advanced 2D Plotting

11.   Graphing Functions and Plotting Curves

12.  Plotting Data

Differential calculus

Syllabus for BSc Semester – I Paper -II BMT1T02: Differential Calculus

Unit I – Functions of Single Variable – Part 1: Intermediate value theorem, Rolle’s Theorem, Mean value theorems and their geometrical interpretations, Applications of mean value theorems. Maxima and Minima; cases of one variable involving second or higher degree polynomials

Unit II – Functions of Single Variable – Part 2: Successive differentiation and nth differential coefficient of functions, Leibnitz’s theorem, Maclaurin’s and Taylor’s theorems, Indeterminate forms and L’ Hospital’s Rule

Unit III -. Functions of Two Variables – Part 1: Limit and continuity of functions of two variables, Partial derivatives, Homogeneous functions, Total differentials, Composite functions, Asymptotes.

Unit IV - Functions of Two Variables – Part 2: Jacobians and its properties, Taylor’s series of function of two variables, Maxima and Minima of function of two variables, Lagrange’s method of multiplier.

Algebra and Trigonometry

Syllabus for B.Sc. Semester – I Paper - I BMT1T01: Algebra and Trigonometry

Unit I – Algebra: Set theory, equivalence relations, equivalence classes. Theory of Numbers: Divisibility, division algorithm, Euclidean algorithm, congruence, linear congruence.

Unit II - Matrices: Hermitian and skew- Hermitian matrices, idempotent, nilpotent, involuntary, orthogonal and unitary matrices. Rank of a matrix, Equivalent matrices, Row canonical form, Normal form, System of homogeneous and non-homogeneous equations, Characteristic equation and roots, Application of Cayley-Hamilton Theorem.

Unit III – Theory of Equations: Relation between the roots and the coefficients of general polynomial equation in one variable, Descartes’ rule of signs, Calculation of f(x + h) by Horner’s process, Transformation of equations, Reciprocal equations. Solution of cubic Equation (Cardon’s Method) and Biquadratic equations (Ferrari’s Method)

Unit IV - Trigonometry: De Moivre’s Theorem and its application, The nth roots of unity, series expansions of circular, inverse circular and Hyperbolic functions, Separation of f(z) into real and imaginary parts. Logarithm of a complex variable, Properties of logarithmic function.