# Mathematics II Syllabus - BCIS (PU)

### Course Description

**Course Objectives **The course aims to introduce students of computer science to those areas of mathematics which, from a modern point of view, are most important in connection with practical problems.

**Course Description**This course emphasizes the application of mathematics to selected computer science topics and problems, using mathematical concepts.

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

- translate given physical or other information and data into mathematical model;
- obtain the solution by selecting and applying suitable mathematical methods;
- interpret the meaning and the implications of the mathematical solutions for the original problems.

### Unit Contents

**Course Contents**

**Unit 1: Integration and its applications 12 hours **

Fundamental Formulae and rule of integration, Application of Definite integration, evaluation and approximation of definite integrals, improper integrals, quadrature, rectification, volume and surface integral.

**Unit II. Differential Equations 8 hours**

Introduction, Order and Degree of a differential Equation, Solution of first order first degree differential equation : variable separable, homogeneous, linear, exact linear differential equation, First and second order linear differential equation with constant coefficient, initial and boundary value problems

**Unit III. Infinite Series 10 hours**

Sequence, series Convergence Test of infinite Series, direct comparison test, limit comparison test, P-series test, De Almbert's ratio test, Cauchy root test, Alternating series test, Interval and radius of convergence.

**Unit IV. Fourier Series and Integrals 8 hours**

Definitions of Fourier series and coefficient(Without proof) , periodic function ,odd and even functions, half range series(sine and cosine Fourier series),Fourier integral, Fourier sine and cosine integral.

**Unit V. Functions of Complex Variable 10 hours**

Basic definitions, functions of a complex variable, Algebra of complex numbers, Properties of complex numbers, Conjugate of a complex number, Modulus of a complex numbers and its properties, Argand diagram, Polar representation, Square roots of a complex number, De’Moivres’s theorem (statement only) and its application to find up to cube roots of a complex number, limits, continuity and differentiation, Cauchy-Riemann equations, analytical functions, harmonic functions, complex exponential, trigonometric and hyperbolic functions.

### Text and Reference Books

**Basic texts: **

- Kreyszig, E.:
*Advanced Engineering Mathematics*, New Delhi*:*John Wiley & Sons Inc. - Thomas, G. B. Jr., & Finney, R. L.
*Calculus and Analytical Geometry.*New Delhi: Narosa Publishing House.

**References: **

- Sastry, S. S.
*Engineering Mathematics.*New Delhi*:*Prentice Hall of India. - Grewal, B. S.
*Higher Engineering Mathematics.*New Delhi: Khanna Publications

- Short Name MTH
- Course code MTH 104
- Semester Second Semester
- Full Marks 100
- Pass Marks 45
- Credit 3 hrs
- Elective/Compulsary Compulsary