Mathematics II

Course Title: Mathematics II

Course No: CACS154

Nature of the Course: Theory + Lab

Semester: 2

Full Marks: 20 + 20 + 60

Pass Marks: 8 + 8 + 24

Credit Hours: 3

Course Description

This course includes the topics from calculus and computational methods such as limits and continuity, differentiation & its applications, integration and its applications, differential equation and different computational techniques which are essential as mathematical foundation for computing.

Course Objectives

This course makes students able to:

- Cognize the concept of Calculus, Computational methods and their applications in the area of Social Science and Computer Application.

Course Contents

1. Limits and Continuity

6 hrs

1.1. Limit of a function

1.2. Indeterminate forms

1.3. Algebraic properties of limit (without proof)

1.4. Theorems on Limits of Algebraic and Transcendental Function

1.5. Continuity of a function, types of discontinuity

1.6. Exercises on evaluation of limits and test of continuity (Mathematica)

2. Differentiation

6 hrs

2.1. Derivative of a Function, Techniques of Differentiation

2.2. Derivatives of Algebraic, Trigonometric, Exponential and Logarithmic Functions

2.3. Higher Order Derivatives

2.4. Derivatives of Implicit Functions

2.5. Derivatives of Parametric Functions

2.6. Applications (Rate of Change, Marginal Analysis) (Mathematica)

3. Application of Differentiation

8 hrs

3.1. The derivatives and slope of the curve

3.2. Increasing and decreasing function

3.3. Convexity of curves

3.4. Maximization and minimization of a function

3.5. Differentiation and marginal analysis; price and output; Competitive equilibrium of firm, Illustrations

3.6. Drawing graphs of algebraic function by using first and second order derivatives (Mathematica)

4. Integration and Its Applications

8 hrs

4.1. Riemann Integral

4.2. Fundamental Theorem (without proof)

4.3. Technique of Integration

4.4. Evaluation and Approximation of Definite Integrals

4.5. Improper Integrals

4.6. Applications of Definite Integrals; Quadrature, Rectification; Volume and Surface Integral

4.7. Trapezoidal and Simpson's Rules of Numerical Integration (Mathematica)

5. Differential Equations

7 hrs

5.1. Differential Equation and its order and Degree

5.2. Differential Equations of First order and First Degree

5.3. Differential Equations with Separable Variables

5.4. Homogeneous and Exact Differential Equations

6. Computational Method

10 hrs

6.1. Linear Programming Problem (LPP)

6.2. Graphical Solution of LPP in Two Variables

6.3. Solution of LPP by Simplex Method (up to 3 variables)

6.4. Solution of System of Linear Equations by Gauss Elimination Method, Gauss Seidel Method and Matrix Inversion Method

6.5. Bisection method, Newton-Raphson Method for Solving Non-linear Equations (Excel/Matlab)

Laboratory Works

Mathematica and/or Matlab should be used for the topics covered in this course.

1.Mathematica and/or Matlab laboratory works

Text Books

1.Thomas, G. B., Finney, R. S., "Calculus with Analytic Geometry", Addison-Wesley, 9th Edition.

Reference Books

1.Monga, G. S., "Mathematics for Management and Economics", Vikas Publishing House Pvt. Ltd., New Delhi.
2.Upadhayay, H. P., Paudel, K. C. & et al, "Elements of Business Mathematics", Pinnacle Publication.
3.Budnick, F. S., "Applied Mathematics for Business, Economics, and the Social Sciences".
4.Paudel, K. C., GC. F. B., and et al, "Higher Secondary Mathematics", Asmita Publication & Distributors Pvt. Ltd, Nepal.
5.Bajracharya, D. R., Shreshtha, R. M. & et al, "Basic Mathematics I, II", Sukunda Pustak Bhawan, Nepal.
6.Sthapit, A. B., Bajracharya, P. M. and et al, "Fundamentals of Business Mathematics", Buddha Academic Publishers & Distributors Pvt. Ltd., Nepal.
7.Yamane, T., "Mathematics for Economists", Prentice-Hall of India.
8.Snedden, I., "Elements of Partial Differential Equations", McGraw-Hill Book Company.

Notes:

This syllabus follows the official BCA curriculum of Tribhuvan University. In case of any doubt or revision, the university's published syllabus shall be considered authoritative.

Mathematics II

Mathematics II

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Mathematics II

Course Description

Course Objectives

Course Contents

Laboratory Works

Text Books

Reference Books

Notes: