## Business Mathematics II Syllabus | MTH 102 | BBA Second Semester Syllabus | Pokhara University

### Course Objectives

The purpose of this course is to provide sound knowledge of derivatives of function of single variable as well as several variables, optimization techniques, and their applications in business and economics. The course also imparts the knowledge of integration and linear programming and their applications.

### Course Description

The first unit is concerned with limits, rates of change and techniques of differentiation. The second unit provides the applications of derivatives. Unit three is devoted to functions of several variables, partial derivatives, differentials, and total derivatives. Optimization problems are dealt in unit four and six. Unit five is devoted exclusively to integration and its applications.

### Course Outcomes

By the end of this course, students should be able to:

• apply differentiation techniques to solve the related problems;
• use derivatives to determine rate measures and solve optimization problems;
• solve the problems related to definite and indefinite integrals;
• understand the concept of linear optimization.

### Course Contents

#### Unit I: Derivatives  (10 hours)

Limit of function, Continuity and discontinuity of function, Average Rates of Change, Instantaneous Rates of Change: The Derivative, Techniques of differentiation, Derivative of: algebraic, exponential and logarithmic functions, Higher order derivatives, Applications related to rate measures.

#### Unit II: Applications of Derivatives (7 hours )

Concavity: Points of Inflection, Relative Maxima and Minima, Absolute Maxima and Minima, Optimization in Business and Economics (Maximizing Revenue, Minimizing Cost, Maximizing Profit, Profit in a Monopoly Market, Profit in a Competitive Market), Elasticity.

#### Unit III: Functions of Several Variables (8 hours)

Functions of Two or More Variables, Partial Differentiation (First-Order Partial Derivatives, Higher-Order Partial Derivatives), Applications of Partial Derivatives in Business and Economic, Differentials, Total Derivatives.

#### Unit IV: Optimization: Functions of Several Variables (6 hours)

Maxima and minima of functions of several variables, Discriminating monopolists, Constrained Optimization: The Method of Lagrange Multipliers.

#### Unit V: Integration and its Applications(10 hours)

Indefinite integrals, Techniques of integration, Definite integrals, Consumer’s Surplus and Producer’s Surplus, Improper integrals, Ordinary differential equations.

#### Unit VI: Inequalities and Linear Programming (7 hours)

Linear Inequalities in Two Variables, Linear Programming Model, Graphical Solution Method, Special Cases (infeasible solution, unbounded solution, alternative optima).

### Basic Texts

Harshbarger, R. J., & Reynolds, J. J. Mathematical Applications for the Management, Life, and Social Sciences. USA: Brooks Cole.

Budnick, F. S. Applied Mathematics for Business Economics and the Social Sciences. New Delhi: Tata McGrawHill.