Programming Fundamentals — DU B.Tech. Information Technology & Mathematical Innovation Previous Year Question Papers

CREDIT DISTRIBUTION, ELIGIBILITY AND PRE-REQUISITES OF THE COURSE Course title & Credits Credit distribution of the course Eligibilit y criteria Lecture Tutorial Pre-requisite of the course Single and Multivariable Calculus, 04 3 0 1 Class XII pass Mathematics till XII Learning Objectives Calculus is the most powerful tool in mathematics with widespread applications. The goal of this course is for students to gain proficiency in calculus computation. The course builds up on the topics, namely limits and continuity, differentiation and integration. These topics will use to solve application problem in a variety of fields such as physics, biology, business and economics. Learning outcomes Able to find points of discontinuity for functions and classify them and understand the consequences of the intermediate value theorem for continuous functions. Able to solve applied problems using basic concepts of calculus. Able to explain why calculus is valuable in daily life. Create a project using the fundamental knowledge and principle of differential and integral calculus that helps to provide a hands-on experience of the same. Able to plot and manipulate the curves appropriately to make various real-life models like studying the projectile motion in firecrackers and the flow of water in fountain. Create animations of given problems using MATHEMATICA software. SYLLABUS OF DSC-1 UNIT – I (12 hours) Limits and continuity - Optimization problems - Fluency in differentiation - Concavity and in flexion points - Sequences, infinite series including Taylor approximations, Power series UNIT – II (9 hours) Parametric equations of curves, arc length and surface area-Vector valued functions, differentiation and integration of vector valued functions UNIT – III (15 hours) Functions of several variables Level curves and surfaces - Limits and continuity of functions of two and three real variables - Partial differentiation (two variables), partial derivative as a slope, partial derivative as a rate, Maxima and Minima UNIT – IV (12 hours) Multiple Integrals Line, surface and volume integrals - Applications of Green’s, Stokes and Gauss’s Practical component – (32 hours) Engineering Kitchen Activity (Symbolic Mathematics Software) [Laboratory] Introduction of basic functions Plotting of graphs of functions and their derivatives Manipulating the parameters in a graph Fitting of a curve Parametric plot of curves (Eg. Trochoid, Cycloid, Epicycloid) Obtaining surfaces of revolution of curves Plotting functions of two variables and their level curves Graphical illustration of limits for functions of two variables Innovation Project Essential/recommended readings 1. Calculus, T. M. Apostol, V olumes 1 and 2, Wiley Eastern, 1980. 2. Calculus - Single and Multivariable, Hughes-Hallett et al., John-Wiley and Sons, 3. Calculus, James Stewart, Thomson, 2003. 4. Calculus and Analytic Geometry, G. B. Thomas and R. L. Finney,