Business Mathematics II

व्यावसायिक गणित २ (कक्षा १२)

Matrices and Determinants (Cramer's rule, Matrix inversion, Gauss elimination, Leontief Input-Output model), Calculus applications in economics (marginal analysis, elasticity, profit maximization, consumer and producer surplus, first-order differential equations), Advanced Financial Mathematics (NPV, IRR, Annuities, Sinking funds), Linear Programming (Simplex Method), Statistics (Skewness, Correlation, Regression), and Advanced Probability (Bayes' theorem, Binomial distribution, Expected value) with MS Excel modeling.

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Prescribed Chapters

Showing 6 Lessons

Unit 1

Algebra: Matrices, Systems of Equations & Input-Output Analysis

1 Lesson

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Algebra: Matrices, Systems of Equations & Input-Output Analysis

बीजगणित: म्याट्रिक्स र इनपुट-आउटपुट विश्लेषण

Matrix algebra, determinant properties up to order 3, matrix inversion using adjoint, solving 3-variable linear systems using Cramer's rule, Matrix Inverse Method, and Gauss Elimination Method, and Leontief Input-Output Analysis (open and closed models).

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Unit 2

Calculus: Economic Applications of Derivatives & Optimization

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Lesson 2Syllabus Mapped

Calculus: Economic Applications of Derivatives & Optimization

क्यालकुलस: अवकलजका आर्थिक प्रयोग र अप्टिमाइजेसन

Monotonic functions, stationary points and inflection points, price elasticity of demand, relationship between MR, AR, and elasticity, and unconstrained optimization for profit maximization, revenue maximization, and cost minimization.

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Unit 3

Calculus: Definite Integrals, Surplus & Differential Equations

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Calculus: Definite Integrals, Surplus & Differential Equations

क्यालकुलस: निश्चित समाकलन, बचत र अवकल समीकरणहरू

Fundamental Theorem of Calculus, area under curves, marginal analysis to total functions, Consumer Surplus (CS) and Producer Surplus (PS) under market equilibrium, and first-order linear differential equations dy/dt + ay = b applied to price dynamics.

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Unit 4

Advanced Financial Mathematics: Annuities, NPV & IRR

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Lesson 4Syllabus Mapped

Advanced Financial Mathematics: Annuities, NPV & IRR

उन्नत वित्तीय गणित: बार्षिकी, खुद वर्तमान मूल्य र आन्तरिक प्रतिफल दर

Geometric progressions in finance, compound interest, nominal vs effective rate, Net Present Value (NPV), Internal Rate of Return (IRR), Ordinary Annuity, Annuity Due, Deferred Annuity, Perpetuity, and Sinking Funds with Excel financial formulas.

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Unit 5

Linear Programming Problem: Simplex Method & Duality

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Lesson 5Syllabus Mapped

Linear Programming Problem: Simplex Method & Duality

रैखिक योजना समस्या: सिम्प्लेक्स विधि र द्वैधता

Formulation of LP problems, standard form with slack variables, Simplex tableau, pivot column/row selection, optimality test, and Duality principle in minimization.

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Unit 6

Statistics & Advanced Probability: Correlation, Bayes & Binomial

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Statistics & Advanced Probability: Correlation, Bayes & Binomial

तथ्यांकशास्त्र र उन्नत सम्भाव्यता: सहसम्बन्ध, बेयस र द्विपद

Karl Pearson and Bowley coefficient of skewness, Five-number summary, Karl Pearson correlation coefficient, regression lines of Y on X and X on Y, conditional probability, Bayes' theorem, expected value and variance, and Binomial distribution.

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