## SC 107 Outline

SC 107 – Calculus

Instructor Manish K Gupta (www.mankg.com)
Room 2209 FB 2 mankg [at] daiict.ac.in
Phone: 91-79-30510549

Office Hours (Instructor):

Google Hangout session and Whatupp group

Class Time: Monday (9:00-9:55 am) , Tuesday (11:00-11:55 am) and Friday (09:00-09:55 am)

Tutors:

Krishna Gopal
Email: krishna_gopal@daiict.ac.in

Dixita Limbachiya
Email: dixita_limbachiya@daiict.ac.in

Teaching Assistants:

TA1: TBD
TA2:  TBD

Tutorials time, Group and Place: 2:00 pm all 5 days (will be updated soon)

Overview

This exciting course is the foundation to your ICT degree. In this course, we shall study some basic calculus of real variables, complex variables and shall see how to solve basic ordinary the nd partial differential equations with some applications.

Tentative Course Content

Week                                    Topics

1 Week (Aug 8)          Introduction, functions of single variable-Mean value theorems and Taylor's theorem

2 week (Aug 16)       Fundamental theorem of integral calculus, definite integrals, trapezoidal and Simpson's rules

3 Week (Aug 24)       Functions of several variables-Partial derivatives, chain rule, chain differentiation, implicit functions and Jacobians

4 Week (Aug 29)        Taylor's theorem for functions of several variables, maxima, minima and saddle points

5 Week (Aug 30 - Sep 2) Test 1 (First Mid Term) (Aug 30 - Sep 2)

6 Week (Sep 4)        Multiple integrals

7 Week (Sep 7)           Complex Variables-Introduction, Continuity

8 Week (Sep 11)        Complex Variables-Differentiability and analyticity

9 Week (Sep 18)         Complex Variables-definite integrals (contour integrals-line  integrals)

10 Week (Sep 25)       Cauchy integral theorem and formula, Taylor and Laurent series, zeroes, singularities and residues

11 Week (Oct 2)         Ordinary differential equations-ODE of first order, linear ODE of second and higher order with constant and non-                                                     constant coefficients

12 Week (Oct 8)       Non-homogeneous equations, power series solutions to ODE

13 Week  (Oct 9-12) Test 2 (Second Mid Term) Oct 9 to Oct 12

14 Week (Oct 14- Oct 22) Semester Break (Application Assignment Week-Take Home)

15 Week (Oct 23)       Partial differential equations-Classification of PDEs Diffusion equation: separation of variables

16 Week (Oct 30)     Course Evaluation Week: Wave equation separation of  variables, vibrating string and d'Alembert's solution,

17 Week (Nov 6)      Fourier and Laplace transforms

18 Week (Nov 12)      Revision Week

19 Week  (Nov 27- Dec 04)  Test 3 (Final Exam Week)

Books

1. Thomas's Calculus (Text Book)
2. Advanced Engineering Mathematics, Jain, RK and SRK Iyengar, 3rd edition, Narosa, 2007
ISBN 978-81-7319-730-7, New Delhi, India (Reference Book)

Marks Distribution (Tentative) / Grading Policy

Test 1        20%
Test 2        20 %
Test 3        30%
Quiz          20%
Take-home 10%

Take-home Policy
Each of you need to work alone on an application and upload one application in latex and pdf files at Moodle.

Tutorials: 1 per week for each section. You need not submit it every week.

Labs None

Course Web Page:
http://courses.daiict.ac.in/course/view.php?id=410

Attendance Policy
Each of you must attend each lecture as I usually give few questions (called as type-2 questions) that you need to solve by that week only and clear your doubts about it. Note that I usually ask them in the exams or quizzes. There could be a surprise quiz at any time in Lectures or Tutorials and sometimes I may change the % of quiz for a final grade to quite a lot.  If for some reason beyond your control (for example you are sick) you are about to miss a lecture please fill leave application form in advance that you will not be able to attend the lecture that day.

Lecture Notes