Mathematics II Syllabus - BCIS (PU)

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.

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.

Basic texts:    

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

References:   

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