**Applied Mathematics**

Applied mathematics for CA Foundation, CS Foundation, CMA Foundation, CBSE, ICSE, Class 11-12 (Commerce) courses and Competitive Exams.** **

**Numerical Applications** : Encryptions using Prime Numbers. Binary Numbers. Complex Numbers. Indices. Logarithm. Averages. Calendar. Clock. Time, Work & Distance. Mensuration. Seating arrangement. 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.

**Mathematical and Logical Reasoning** : Mathematically acceptable statements. Connecting words/ phrases. Examples related to real life and Mathematics. Problems based on logical reasoning (coding-decoding, odd man out, blood relation, syllogism etc)

**Applied Calculus** : Derivatives of algebraic functions using Chain rule. Tangent line and equations of tangents. 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 Algebraic functions. Application of Integration (consumer surplus-producer surplus). Differential Equation. Linear differential equation. Application of differential equation (Growth and Decay Model).

**Linear Equations** : Linear Equations. Solving Linear Equation by Elimination Method

**Financial Mathematics** : Simple & Compound Interest. Effective rate of interest. Present Value, Net Present Value and Future Value. Annuities. Tax. Calculation of GST, Income Tax. Calculation and interpretation of electricity bill, water supply bill and other supply bills. Perpetuity. Sinking funds. Valuation of Bonds. Calculation of EMI. Calculation of Returns, Rate of return, Effective Rate of Interest. Compound annual growth rate. Stock, shares and debentures. Linear method of Depreciation

**Determinants & Matrices Applications**: Applications of Matrices and Determinants. Leontiff Input Output model.

**Inferential Statistics** : Population and Sample. Parameter, Statistic and Statistical Inferences. t-Test

**Time Series Analysis **: Time series. Time series analysis for univariant data sets. Trend analysis by moving average method. Trend analysis of linear trend line using least squares.

**Linear Programming Applications**: Constraints. Objective Function. Optimization. Mathematical formulation of linear programming. Transportation and Assignment problem. Graphical solution of Linear Programming. Feasible and infeasible regions. Feasible and infeasible solutions, optimal feasible solutions (up to three nontrivial constraints)