SC105 Oultine

SC 105 – Calculus and Complex Variables
Instructor Manish K Gupta (
Room 2209 FB 2 mankg [at]
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)


Krishna Gopal 

Dixita Limbachiya

Teaching Assistants:

TA1:  Kamal Captain (
TA2:  Karavadra Raju Duda(

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)


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)


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:

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.

Click link to open resource.