Calculus(SC107) 

Course description: Calculus is a core course for first year BTech (ICT) program. It is 3 hours lecture every week and 5 tutorials per week .  Calculus is a foundational course; it plays an important role in the understanding of science, engineering, economics, computer science etc.  This introductory calculus course covers the following topics:

Functions of single variable-Mean value theorems and Taylor's theorem, Fundamental theorem of integral calculus, definite integrals, trapezoidal and Simpson's rules, Functions of several variables-Partial derivatives, chain rule, chain differentiation, implicit functions and Jacobians, Taylor's theorem for functions of several variables, maxima, minima and saddle points, Multiple integrals, Complex Variables-Introduction, Continuity, Complex Variables-Differentiability and analyticity, Complex Variables-definite integrals (contour integrals-line integrals),Cauchy integral theorem and formula, Taylor and Laurent series, zeroes, singularities and residues, Ordinary differential equations-ODE of first order, linear ODE of second and higher order with constant and non-constant coefficients, Non-homogeneous equations, power series solutions to ODEs Partial differential equations-Classification of PDEs  Diffusion equation: separation of variables. 

Course Goals: Upon successful completion of this course, students can develop ability to  apply the knowledge of mathematics, science, engineering fundamentals, and engg. specialization to the solution of complex engineering problems.  Understand and create mathematical arguments for solving problems. Understand mathematical structures such as functions, variable, integrations and learn their uses . Develop skills towards mathematical modeling and analysis of engineering problems. 

Suggested Textbook/references:  

 Thomas's Calculus, George B. Thomas, Jr.,  (as revised by) Maurice D. Weir,  Joel Hass,  and Christopher Heil, Pearson. 

Advanced Engineering Mathematics, Jain, RK and SRK Iyengar, 3rd edition, Narosa, 2007 ISBN 978-81-7319-730-7, New Delhi, India 

A basic course in real analysis, Ajit Kumar and S. Kumaresan, CRC press.

Visual Complex analysis, Tristam Needham, Clarendon press, Oxford.

Grading:  Test 1 (50%  ), Test 2 (50%  )