Applied Mathematics

Unit I: Numbers, Quantification and Numerical Applications

• Modulo Arithmetic
• Congruence modulo
• Simple arithmetic functions
• Allegation or Mixture
• Numerical problems on boats and streams; partnership; pipes and cistern; races and games, scheduling
• Numerical inequalities

Unit II: Algebra

• Solution of simultaneous linear equations using elimination method (up to 3 variables)
• Matrices and types of matrices
• Algebra of matrices
• Determinants
• Inverse of a matrix
• Cramer’s rule and its application
• Simple applications of matrices and determinants including Leontiff input output model for two variables

Unit III: Calculus

• Application of derivatives
• Increasing/Decreasing functions
• Maxima and Minima
• Marginal cost and marginal revenue using derivatives
• Integration
• Indefinite integral as family of curves
• Definite integral as area under the curve
• Integration of simple algebraic functions (primitive, by substitution, by parts)
• Application of Integration (consumer surplus-producer surplus)
• Differential equation (definition, order, degree)
• Formulating and solving linear differential equation
• Application of differential equation (Growth and Decay Model)

Unit IV: Probability

• Probability Distribution
• Mathematical Expectation
• Variance
• Binomial Distribution
• Poisson distribution
• Normal distribution
• Basic applications and inferences

Unit V: Inferential Statistics

• Population and sample
• Parameter, statistic and statistical inferences
• t-Test (one sample t-test and two independent groups t-test)

Unit VI: Index numbers and Time-based data

• Index numbers, uses of index numbers
• Construction of index numbers (simple and weighted)
• Tests of adequacy of index numbers (unit test and time reversal test)
• Time series, Time series analysis for univariant data sets
• Trend analysis by moving average method
• Trend analysis by fitting of linear trend line using least squares

Unit VII: Financial Mathematics

• Perpetuity, Sinking funds
• Valuation of Bonds (Present value approach and Relative price approach)
• Calculation of EMI
• Calculation of returns, nominal rate of return, effective rate of interest
• Compound annual growth rate
• Stock, shares and debentures
• Linear method of depreciation

Unit VIII: Linear Programming

• Introduction and related terminologies (constraints, objective function, optimization)
• Mathematical formulation of linear programming problems
• Different types of linear programming problems (Transportation and assignment problem)
• Graphical method of solution for problems in two variables
• Feasible and infeasible regions (bounded and unbounded)
• Feasible and infeasible solutions, optimal feasible solutions (up to three nontrivial constraints)