B.Com. Semester-IV Business Mathematics Course Syllabus

Institutional and Administrative Course Details

• Institution: Department of Commerce, Dr. Harisingh Gour Vishwavidyalaya, Sagar (M.P.).
• Department: Department of Commerce.
• Academic Program: B.Com. (Semester-IV).
• Academic Session: 2023-24.
• Course Code: COM-MDM-411.
• Nomenclature of Paper: Business Mathematics.
• Course Type: Disciplinary Specific Major.
• LTP Credit Allocation:   - LTP: $5 \, 1 \, 0$   - Total Credit: $6$

Course Objectives (CO)

• CO1: To assist learners in understanding concepts regarding simple interest.
• CO2: To make learners understand the concept of matrices.
• CO3: To skill learners to compute average, percentage, brokerage etc.
• CO4: To impart knowledge about the Linear Programming-Formulation of LPP.
• CO5: To make learners efficient in dealing with problems of differential calculus.

UNIT I: Basic Mathematics of Finance

• Simple Interest:   - Notations and calculation of interest.   - Calculation of principal ($P$), rate ($R$), Time ($T$), and amount ($A$).
• Compound Interest:   - Calculation methods for compound interest when the number of periods is an integer.   - Calculation methods for compound interest when the number of periods is not an integer.
• Profit and Loss:   - General meaning and definition of profit and loss.   - Concept of purchase price (cost price).   - Concept of sales price (selling price).

UNIT II: Matrices and Logarithms

• Matrices:   - Definition of a matrix.   - Detailed study of the types of matrices.   - Algebra of matrices (addition, subtraction, and multiplication operations).
• Determinants:   - Calculation of values of determinants specifically up to the second order.
• Matrix Operations and Inversion:   - Adjoint of a matrix.   - Finding the inverse of a matrix through the use of the adjoint.
• Logarithms:   - Theory of Logarithms.

UNIT III: Commercial Calculations

• Average: Calculation and principles.
• Percentage: Calculation and applications.
• Commission: Understanding and computing commission components.
• Brokerage: Calculation and business applications of brokerage.

UNIT IV: Linear Programming, Ratios, and Proportion

• Linear Programming - Formulation of LPP:   - Techniques for formulating a Linear Programming Problem (LPP).   - Graphical method of solution for these problems.
• Variable Limitations:   - Problems relating to two variables.   - Handling cases of mixed constraints.
• Complex Solution Scenarios:   - Cases having no solution.   - Multiple solutions.   - Unbounded solution.   - Redundant constraints.
• Mathematical Comparisons:   - Ratios.   - Proportion.

UNIT V: Differential Calculus

• Scope of Calculus:   - General Calculus study, with the explicit exception of problems and theorems involving trigonometrically ratios.
• Differentiations:   - Partial Derivatives calculations up to the second order.
• Functional Analysis:   - Homogeneity of functions.   - Total differentials.   - Differentiation of implicit functions specifically with the help of total differentials.
• Optimization (Maxima and Minima):   - Cases involving one variable including second or higher order derivatives.   - Cases of two variables involving not more than one constraint.