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General

27 July - 2 August

3 August - 9 August

10 August - 16 August

17 August - 23 August

24 August - 30 August

31 August - 6 September

7 September - 13 September

14 September - 20 September

21 September - 27 September

28 September - 4 October

5 October - 11 October

12 October - 18 October

19 October - 25 October

26 October - 1 November

2 November - 8 November

9 November - 15 November

16 November - 22 November

23 November - 29 November

## SC105 Oultine

SC 105 – Calculus and Complex Variables

Instructor Manish K Gupta (www.mankg.com)

Room 2209 FB 2 mankg [at] daiict.ac.in

Phone: 91-79-30510549**Office Hours (Instructor):**

Friday 5:00 to 6:00 pm every week**Class Time and Place : Tuesday 12:00 am (LT-3) Wed 10:00 am (LT-3) and Friday 10:00 am (LT-3)****Tutors:**

Krishna Gopal

Email: krishna_gopal@daiict.ac.in

Dixita Limbachiya

Email: dixita_limbachiya@daiict.ac.in **Teaching Assistants**:

TA1: Kamal Captain ( kamal_captain@daiict.ac.in)

TA2: Karavadra Raju Duda(@daiict.ac.in)**Tutorials time, Group and Place: 2:00 pm all 5 days**

Monday (Group 3, Room CEP 203)

Tuesday (Group 4, Room CEP 203)

Wednesday (Group 5, Room CEP 203)

Thursday (Group 1, Room CEP 203)

Friday (Group 2, Room CEP 203)

Overview

This exciting course is 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 and partial differential equations with some applications.

Tentative Course Content

Week Topics

1 Week (Aug 3) Introduction, functions of single variable-Mean value

theorems and Taylor's theorem

2 week (Aug 10) Fundamental theorem of integral calculus, definite integrals, trapezoidal and Simpson's rules

3 Week (Aug 17) Functions of several variables-Partial derivatives, chain rule, chain differentiation, implicit functions and Jacobians

4 Week (Aug 24) Taylor's theorem for functions of several variables, maxima, minima and saddle points

5 Week (Aug 31) Multiple integrals

6 Week (Sep 7) **Revision Summary and Test 1 (Sept 10 to Sept 12) **

7 Week (Sep 14) Complex Variables-Introduction, Continuity

8 Week (Sep 21) Complex Variables-Differentiability and analyticity

9 Week (Sep 28) Complex Variables-definite integrals (contour integrals-line integrals)

10 Week (Oct 5) Cauchy integral theorem and formula, Taylor and Laurent series, zeroes, singularities and residues

**11 Week (Oct 12)** **Test 2 (Second Mid Term Week): Oct 15 to Oct 17**

12 Week (Oct 19) Ordinary differential equations-ODE of first order, linear ODE

of second and higher order with constant and non-constant coefficients

13 Week (Oct 26) Non-homogeneous equations, power series solutions to ODEs

14 Week (Nov 2) Partial differential equations-Classification of PDEs

Diffusion equation: separation of variables**15 Week (Nov 9) Semester Break (Application Assignment Week-Take Home)**

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

Fourier and Laplace transforms **17 Week (Nov 23) Week 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 to submit it every week.

Labs None

Course Web Page:

http://courses.daiict.ac.in//course/view.php?id=343**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 sometime I may change the % of quiz for 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

Notes are available in the lecture folder and it is advisable that you read them before coming to class this will help you to clear your doubts.