|
Subject : MATHEMATICS-1 |
||
|
Year : I B-Tech |
Semester : I |
Branch :CSE-I |
|
Faculty : B.SARATH KUMARI |
Reg : R19 |
Academic Year : 2019-20 |
COURSE OBJECTIVES:
In this course the students are introduced to some basic tools in Mathematics which are useful in modelling and analyzing physical phenomena involving continuous changes of variables or parameters. The differential and integral calculus of functions of one or more variables and functions of several variables taught in this course have applications across all branches of engineering. This course will also provide basic training in plotting and visualizing graphs of functions and intuitively understanding their properties.
COURSE OUTCOMES:
|
1 |
Factual |
Ability to understand and explain concepts of convergence and mean value theorems |
|
2 |
Conceptual |
Student’s gain knowledge on solving differential equations and its applications
to various Engineering fields. |
|
3 |
Procedural |
Ability to apply the basic knowledge of
differential equations. Ability to
apply the basic knowledge of
Linear differential equations in electrical systems |
|
4 |
Applied |
Ability to apply Euler’s theorem for
multivariable function and to find extreme values. Students
are introduced finding areas and
volumes using integrals. |
TEXT BOOKS/ REFERENCE BOOKS:
|
T/R |
BOOK
TITLE/AUTHORS/PUBLICATION |
|
T |
B. S.
Grewal, Higher Engineering Mathematics, 43rd Edition, Khanna Publishers. |
|
T |
B. V. Ramana, Higher Engineering
Mathematics, 2007 Edition, Tata Mc. Graw Hill Education. |
|
R |
Erwin Kreyszig,
Advanced Engineering Mathematics, 10th Edition, Wiley-India. |
|
R |
Joel Hass, Christopher Heil and
Maurice D. Weir, Thomas calculus, 14th Edition, Pearson. |
|
R |
Lawrence Turyn, Advanced Engineering
Mathematics, CRC Press, 2013. |
|
R |
Srimantha Pal, S C Bhunia, Engineering Mathematics, Oxford University
Press. |
WEB SOURCE REFERENCES: (Detailed Topic link)
|
W1 |
|
|
W2 |
|
|
W3 |
UNIT – 1: Sequences, Series and Mean value theorems: [Total Classes : 16] Activity:
|
1 |
Factual |
Reading Prerequisite concepts- Sequence, series and Basic definitions, Videos
of Sequence and Series, Referring the content on the Internet |
|
2 |
Conceptual |
Video Lectures related to sequence and series, Mean
value theorems. NPTEL Videos Links from the Internet |
|
3 |
Procedural |
Refer to text book content and syntax Other Implementation of Sequence and series with
examples(simple to complex) |
|
4 |
Applied |
Solving Exercises, Implementing practice for problem solving Assignments Quiz etc… |
Pre-Class : Videos, E-books, Web links etc…
In-Class : Explanation on concept, discussion, Poll, doubts clarification, Demo etc.. Post-Class : Discussion Forum, Review on topic, Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Introduction to Sequence and series (revise) |
To introduce Basic concepts of Sequence and series |
Video Link : https://www.youtube.c om/watch?v=cr8pmBL mlL8 Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cours es/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
2. |
Limit of a sequence |
To Understand the
concept of Limit of a sequence |
Video Link : https://youtu.be/LBSn manUU2Q Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cours es/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
3. |
Types of sequences – definitions |
To Understand the
concept of various sequences |
Video Link : https://youtu.be/rOmeN K6NqF0 Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cours es/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion
or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
4. |
Geometric series test – problems |
To Understand the
concept of |
Video Link : https://youtu.be/m7AT bosllvs Text Book : Pdf (e- |
Discussion on pre-requisites (5 Min) PPT presentation |
. Discussion Forum on the topic in the group |
|
|
|
Convergenc
e of geometric series test |
book) CANVAS INSTRUCTURE Web Link :
https://nptel.ac.in/cours
es/122/104/122104017/ |
(30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Review on the topic Share material on the topic |
|
5. |
P-series Test – problems |
To Understand the
concept of P-series Test |
Video Link : https://youtu.be/m7AT bosllvs Text Book : Pdf (e- book)
CANVAS INSTRUCTURE |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic |
|
|
|
|
Web Link :
https://nptel.ac.in/cours
es/122/104/122104017/ |
Share material on the topic |
|
|
6. |
Comparison
Test – problems |
To Understand the concept of limit Comparison
Test |
Video Link : https://youtu.be/YYZm WBYTuhU Text Book
: Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cours es/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion
or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
|
|
|
|
Exercises to solve |
|
|
7. |
Cauchy’s integral test – problems |
To Understand the
concept of Integral Test |
Video Link : https://youtu.be/vxwlE zfweMs Text Book : Pdf (e- book)
CANVAS INSTRUCTURE |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic |
|
|
|
|
Web Link :
https://nptel.ac.in/cours
es/122/104/122104017/ |
Share material on the topic |
|
|
|
|
|
|
Exercises to solve |
|
8. |
D-Alembert’s ratio test –
problems |
Able to solve Examples on Alembert’s Ratio Test |
Video Link : https://youtu.be/LvUh4 dk9AoU Text Book : Pdf (e- book)
CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cours es/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion
or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic Share material on the topic Exercises to solve |
|
9. |
Leibnitz test – problems |
To Understand the
concept of Leibnitz test |
Video Link : https://youtu.be/oG6Yo ERagXM Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cours es/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic Share material on the topic Quiz |
|
10. |
Absolute convergence – problems |
To Understand the concept of Absolute convergenc e |
Video Link : https://youtu.be/3_WB VrnO2w8 Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cours es/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion
or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
11. |
Conditional convergence – problems |
To Understand the concept of Conditional
convergenc e |
Video Link : https://youtu.be/3J3NB e5kiV0 Text Book
: Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cours es/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion
or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic Share material on the topic Quiz |
|
12. |
Rolle’s theorem - problems |
To understand the concept of Mean Value Theorem |
Video Link : https://youtu.be/_qv5x_ O9CaQ https://nptel.ac.in/cours es/111/105/111105121/ Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cours es/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion
or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
. Discussion Forum on the topic in the group Review on the topic Share material on the topic Assignment - 1 |
|
13 |
Lagranges theorem –
problems |
To understand the concept of Lagranges theorem |
Video Link : https://youtu.be/GvfjkR SUbBg https://nptel.ac.in/cours es/111/105/111105121/ Text Book : Pdf (e- book)
CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cours es/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion
or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
14 |
Cauchy’s mean value theorem – problems |
To understand the concept of Cauchy’s mean value theorem |
Video Link : https://youtu.be/EfkEC ElpU1s https://nptel.ac.in/cours es/111/105/111105121/ Text Book
: Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cours es/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
15 |
Taylor’s series with Remainder terms – problems |
To understand the concept of Taylor’s series with
Remainder terms |
Video Link : https://youtu.be/jiEaK YI0ATY Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link :
https://nptel.ac.in/cours
es/122/104/122104017/ |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
16 |
McLaren’s
series with Remainder terms – problems |
To understand the concept of McLaren’s series with Remainder
terms |
Refer the previous Links of all the concepts in unit-1 |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion
or Poll activity (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic Assignment-1 |
UNIT – 2 : Differential equations of first order and first degree [Total Classes : 13] Activity:
|
1 |
Factual |
Reading Prerequisite concepts- Ordinary Differential
Equations and Basic definitions, Videos related to Ordinary Differential
Equations, Referring the content on the
Internet |
|
2 |
Conceptual |
Video Lectures related to Ordinary Differential
Equations NPTEL Videos Links from the Internet |
|
3 |
Procedural |
Refer to text book content and Understanding the
Ordinary Differential Equations with examples(simple
to complex) |
|
4 |
Applied |
Problems Solving and Applications solving by practice
sessions and Assignments Quiz etc… |
Activity
/ Schedule of UNIT-2 :
Pre-Class: Videos, E-books, Web links etc…
In-Class: Explanation on concept, discussion, Poll, doubts clarification, Demo etc.. Post-Class: Discussion Forum, Review on topic, Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Introduction
on Ordinary differential equations |
To introduce The concept of Ordinary differential
equations |
Video Link : https://youtu.be/ClvF wUpi3ZA Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/108/11110808 1/ |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
2. |
Introduction to Linear differential equations – problems |
To enhance the understandin g of The concept of Linear differential equations |
Video Link : https://www.youtube.c om/watch?v=QC3z- NUkOcE&list=PLoci SetSILauNfkJkU0Pzb FyBHohCI0rT&index Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/108/11110808 1/ |
Revise previous class – (5 Mins) Asking Questions on previous class randomly (5 Mins) PPT presentation/
class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
3. |
Bernoulli’s differential equations – problems |
To understand the concept of Bernoulli’s differential
equations |
Video Link : https://www.youtube.c om/watch?v=QC3z- NUkOcE&list=PLoci SetSILauNfkJkU0Pzb FyBHohCI0rT&index Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation/class (30 min) Doubts clarification |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
|
|
|
|
(10 min) |
|
|
4. |
Exact differential equations – problems |
To understand the concept of Exact differential
equations |
Video Link : https://www.youtube.c om/watch?v=0CNoN mMdBuE&list=PLoci SetSILauNfkJkU0Pzb FyBHohCI0rT&index Text Book : Pdf (e- book)
CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/108/11110808 1/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation/
class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
5. |
Non-Exact Differential equations Type-I,II |
To understand the concept of Non- Exact Differential
equations Type-I,II |
Video Link : https://www.youtube.c om/watch?v=dtbLHto h_M0&list=PLociSetS ILauNfkJkU0PzbFyB HohCI0rT&index=6 https://www.youtube.c om/watch?v=Bk9sT1 BStlo&list=PLociSetS ILauNfkJkU0PzbFyB HohCI0rT&index=8 Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/108/11110808 1/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
6. |
Non-Exact Differential equations Type-III,IV,V |
To understand the concept of Non- Exact Differential
equations Type- III,IV,V |
Video Link : https://www.youtube.c om/watch?v=SxYI7Ez LVDA&list=PLociSet SILauNfkJkU0PzbFy BHohCI0rT&index=7 https://www.youtube.c om/watch?v=Bk9sT1 BStlo&list=PLociSetS ILauNfkJkU0PzbFyB HohCI0rT&index=8 Text Book : Pdf (e- book)
CANVAS INSTRUCTURE Web Link : |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
|
|
|
|
|
|
|
7. |
Newton’s law of cooling - problems |
To understand the concept of Newton’s law of cooling |
Video
Link : https://www.youtube.c om/watch?v=DqFdy6 Ad5mg Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/108/11110808 1/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
8. |
Natural law of growth – problems |
To understand the concept of Natural law of growth |
Video Link : https://www.youtube.c om/watch?v=tj993BD RAhU Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link :
https://nptel.ac.in/cour
ses/111/108/11110808
1/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
9. |
Natural law of decay – problems |
To understand the concept of Natural law of decay |
Video Link : https://www.youtube.c om/watch?v=tj993BD RAhU Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/108/11110808 1/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
10. |
RL & RC circuits - problems |
To understand the concept of RL & RC circuits |
Video Link : https://www.youtube.c om/watch?v=5AFJsT YPVo0 Text Book : Pdf (e- book)
CANVAS |
Revise previous class – (5 mins) Asking Questions on previous class |
Discussion Forum on the topic in the group Review on the |
|
|
|
|
INSTRUCTURE Web Link :
https://nptel.ac.in/cour
ses/111/108/11110808
1/ |
randomely (5 Mins) PPT presentation & demo of cluster configuration(30 min) Doubts clarification (10 min) |
topic Share material on the topic configure. |
|
11. |
Orthogonal Trajectories – Cartesian form – problems |
To understand the concept of Orthogonal Trajectories – Cartesian form |
Video Link : https://www.youtube.c om/watch?v=NV9nX1 a0qoU Text Book : Pdf (e- book)
CANVAS INSTRUCTURE Web Link :
https://nptel.ac.in/cour
ses/111/108/11110808
1/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation/class (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
12. |
Polar form, self orthogonal – problems |
To understand the concept of Polar form, self orthogonals |
Video Link : https://www.youtube.c om/watch?v=YfnIRG 4HAKE Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link :
https://nptel.ac.in/cour
ses/111/108/11110808
1/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic Assignment-2 Quiz - 2 |
UNIT – 3: Linear differential equations of higher order [Total Classes: 11] Activity:
|
1 |
Factual |
Reading
Prerequisite concepts- Linear differential equations of higher order Videos
Referring the content on the Internet |
|
2 |
Conceptual |
Video
Lectures On Linear differential equations of higher order NPTEL Videos Links from the Internet Solved Examples from Internet |
|
3 |
Procedural |
Refer to
text book content of Linear differential equations of higher order Understanding
the concept with examples(simple to complex) |
|
4 |
Applied |
Problems Solving and Applications solving by practice
sessions and Assignments Quiz etc… |
Activity / Schedule of UNIT-3:
Pre-Class: Videos, E-books, Web links etc…
In-Class: Explanation on concept, discussion, doubts clarification etc..
Post-Class: Discussion Forum, Review on topic, Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Introduction
on Higher order linear differential
equations |
To introduce The concept of Higher order linear
differential equations |
Video Link : https://www.youtube.c om/watch?v=L7Yy0I MshbE Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link :
https://nptel.ac.in/cour
ses/111/107/11110709
8/ |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
2. |
Solution
of homogeneous |
To
introduce The concept |
Video Link : https://www.youtube.c om/watch?v=A1KyaR |
Revise previous class – (5 mins) |
Discussion Forum on the topic in the |
|
|
liner differential equation |
of Solution of homogeneou s liner differential equation |
https://www.youtube.c om/watch?v=W4GlSF Nm2N4 Text Book : Pdf (e- book)
CANVAS INSTRUCTURE Pdf : https://hci.stanford.edu |
Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
group Review on the topic Share material on the topic |
|
|
|
Web Link : https://nptel.ac.in/cour ses/111/107/11110709 8/ |
|
|
|
|
3. |
When Q(x) = 𝑒𝑎𝑥 𝑜𝑟 𝑒−𝑎𝑥
–
problems |
To introduce The concept of When Q(x) = 𝑒𝑎𝑥 𝑜𝑟 𝑒−𝑎𝑥 |
Video
Link : https://www.youtube.c om/watch?v=q2OVz0 z6xa4 Text Book : Pdf (e- book) CANVAS INSTRUCTURE |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) |
Discussion Forum on the topic in the group Review on the topic |
|
|
|
|
Pdf : https://hci.stanford.edu /courses/cs448g/a2/file s/map_reduce_tutorial. pdf Web Link : https://nptel.ac.in/cour ses/111/107/11110709 8/ |
PPT presentation & demo (30 min) Doubts clarification (10 min) |
Share material on the topic |
|
4. |
When Q(x) = sin(𝑎𝑥
+ 𝑏) 𝑜𝑟
cos(𝑎𝑥 + 𝑏) – problems |
To introduce the concept of When Q(x) = sin(𝑎𝑥
+ 𝑏) 𝑜𝑟
cos(𝑎𝑥 𝑏) |
Video
Link : https://www.youtube.c om/watch?v=eQ40pA W3z-0 https://www.youtube.c om/watch?v=SiJFc1Iu Wus Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/107/11110709 8/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
5. |
When Q(x) = 𝑥𝑛 + 𝑐
– |
To introduce the concept |
Video
Link : https://www.youtube.c om/watch?v=R0qXI6d |
Revise previous class – (5 mins) |
Discussion Forum on the topic in the |
|
|
problems |
of When Q(x) = 𝑥𝑛 + 𝑐 |
Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/107/11110709 8/ |
Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
group Review on the topic Share material on the topic |
|
6. |
When Q(x) = 𝑒𝑎𝑥. 𝑣(𝑥)
– problems |
To demonstrate Basic
When Q(x) = 𝑒𝑎𝑥.
𝑣(𝑥) |
Video Link : https://www.youtube.c om/watch?v=3LQAaA h4wM8 https://www.youtube.c om/watch?v=jRFIrkdn oMQ&list=PLhSp9OS VmeyLTuT8bf- DZIffkRLmXmLzN&i ndex=9 Text Book
: Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/107/11110709 8/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
7. |
When Q(x) = 𝑥. 𝑣(𝑥) – problems |
To demonstrate Basic
When Q(x) = 𝑥.
𝑣(𝑥) |
Video Link : https://www.youtube.c om/watch?v=NFxs1qq OHaQ https://www.youtube.c om/watch?v=jRFIrkdn oMQ&list=PLhSp9OS VmeyLTuT8bf- DZIffkRLmXmLzN&i ndex=9 Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/107/11110709 8/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
8. |
When Q(x) = 𝑥𝑛. 𝑣(𝑥) – problems |
To demonstrate When
Q(x) = 𝑥𝑛.
𝑣(𝑥) |
Video Link : https://www.youtube.c om/watch?v=NFxs1qq OHaQ https://www.youtube.c om/watch?v=jRFIrkdn oMQ&list=PLhSp9OS VmeyLTuT8bf- |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 |
Discussion Forum on the topic in the group Review
on the topic |
|
|
|
|
Text Book
: Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/107/11110709 8/ |
Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Share material on the topic |
|
9. |
Method of variation of parameters – problems |
To demonstrate Method
of variation of parameters |
Video Link : https://www.youtube.c om/watch?v=45S- 4tR6zCk https://www.youtube.c om/watch?v=jiQ2sX5 wGwM Text Book : Pdf (e- book)
CANVAS INSTRUCTURE Web Link :
https://nptel.ac.in/cour
ses/111/107/11110709
8/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
10. |
LCR-Circuits – problems |
To Introduce the concept of LCR-
Circuits |
Video Link : https://www.youtube.c om/watch?v=MfMiq MOu254 https://www.youtube.c om/watch?v=MPAk- R16fLY Text Book : Pdf (e- book)
CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/107/11110709 8/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
11. |
Simple Harmonic motion -
problems |
To Introduce the concept of Simple Harmonic motion |
Video
Link : https://www.youtube.c om/watch?v=V9bl02F
fo_o https://www.youtube.c om/watch?v=4Jezsfam 3w4 Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/107/11110709 |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
|
|
|
|
|
|
|
12. |
Revision of all the concepts in Unit-3 |
Revising all the concepts |
Refer above Links for data |
Revising the concepts discussed so far Any topic to Repeat
asked by students. |
Assignment-3
Quiz-3 |
UNIT – 4: Partial differentiation [Total Classes: 10] Activity:
|
1 |
Factual |
Reading
Prerequisite concepts- partial differentiation Videos Referring the content on the
Internet |
|
2 |
Conceptual |
Video Lectures On partial differentiation NPTEL Videos Links from the Internet Solved Examples from Internet |
|
3 |
Procedural |
Refer to text book content and Examples, Understanding
the partial differentiation with examples(simple to
complex) |
|
4 |
Applied |
Problems Solving and Applications
solving by practice sessions and Assignments Quiz etc… |
Activity
/ Schedule of UNIT-4 :
Pre-Class: Videos, E-books, Web links etc…
In-Class: Explanation on concept, discussion, Poll, doubts clarification etc..
Post-Class: Discussion Forum, Review on topic, Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Introduction to partial differentiation |
To introduce The concept of the partial differentiatio
n |
Video Link : https://www.youtube.c om/watch?v=OK88BF OKqQA https://www.youtube.c om/watch?v=eTp5wq- cSXY Text Book : Pdf (e- book)
CANVAS INSTRUCTURE Web Link :
https://www.sanfoundr y.com/engineering- mathematics- questions-answers- partial-differentiation- 1/ https://nptel.ac.in |
Discussion on pre-requisites (5 Min) PPT presentation (30 Min) Discussion (5 min) Summary
(5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
2. |
Taylors theorem – problems |
To Introduce the concept of Taylors theorem for
functions of several variables |
Video Link : https://www.youtube.c om/watch?v=oqjgn2X N3Dc Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link :
https://nptel.ac.in/cour
ses/111/107/11110710
8/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
3. |
Mc Lauren’s theorem - problems |
To
Introduce the concept of Mc Lauren’s theorem |
Video Link : https://www.youtube.c om/watch?v=pjv0Htk hifQ Text Book : Pdf (e- book)
CANVAS INSTRUCTURE Web Link :
https://nptel.ac.in/cour
ses/111/107/11110710
8/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
4. |
Jacobian, functional dependent and independent |
To Introduce the concept of Jacobian, functional
dependent and independent |
Video Link : https://www.youtube.c om/watch?v=xv8WKI rv5WU Text Book : Pdf (e- book)
CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/107/11110710 8/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
5. |
Functional
relation – problems |
To Introduce the concept of
Functional relation |
Video
Link : https://www.youtube.c om/watch?v=oP7RgpI O2Fw Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/107/11110710 8/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
6. |
Chain – rule problems |
To Introduce the concept of Chain – rule problems |
Video Link : https://www.youtube.c om/watch?v=Fbsm7Y Text Book : Pdf (e- book)
CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/107/11110710 8/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
7. |
Maxima and Minima (without constraint) - problems |
To Introduce the concept of Maxima and Minima (without
constraint) |
Video Link : https://www.youtube.c om/watch?v=N_CyeS qqYs4 Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/107/11110710 8/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
8. |
Maxima and Minima (with constraint) – problems |
To Introduce the concept of Maxima and Minima (with
constraint) |
Video Link : https://www.youtube.c om/watch?v=2bKosT C_YQU Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/107/11110710 8/ |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
9. |
Lagrange method of Undetermined multipliers- problems |
To
Introduce the concept of Lagrange method of Undetermine d multipliers-
problems |
Video Link : https://www.youtube.c om/watch?v=N_CyeS qqYs4 https://www.youtube.c om/watch?v=7f7q2jdF bcU Text Book : Pdf (e- book)
CANVAS |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
|
|
|
INSTRUCTURE Web Link :
https://app.writable.co m/explore/writable?ty
pe=Collection&grades |
Doubts clarification (10 min) |
|
|
10. |
Euler’s Theorem - problems |
To Introduce the concept of Euler’s Theorem - problems |
Video Link : https://www.youtube.c om/results?search_que ry=+Euler%E2%80% 99s+Theorem+- +problems+engineerin g+mathematics https://www.youtube.c
om/watch?v=BzYrhv
mlP34 Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://app.writable.co m/explore/writable?ty pe=Collection&grades |
Revise previous class – (5 mins) Asking Questions on previous class randomely (5 Mins) PPT presentation & demo (30 min) Doubts clarification (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic Assignment-4
Quiz – 4 |
UNIT – 5: Multiple integrals [Total Classes : 10] Activity:
|
1 |
Factual |
Reading Prerequisite concepts- line integral, Double integral
Videos Referring the content on the Internet |
|
2 |
Conceptual |
Video Lectures On line integral, Double integral, Triple
integral Videos and NPTEL Videos Links from the Internet Solved Problems, Examples from
Internet |
|
3 |
Procedural |
Refer to text book
content and Examples, Understanding
the multiple integrals with examples(simple to complex) |
|
4 |
Applied |
Problems Solving and Applications
solving by practice sessions and Assignments Quiz etc… |
Activity / Schedule of UNIT- 5:
Pre-Class: Videos, E-books, Web links etc…
In-Class: Explanation on concept, discussion, Poll, doubts clarification etc..
Post-Class: Discussion Forum, Review on topic, Assessment, Quiz, Notes etc….
|
CLASS SL NO |
CONCEPT |
OBJECTIVES |
PRE-CLASS |
IN-CLASS |
POST-CLASS |
|
1. |
Introduction to line,surface,vo lume integrals |
To introduce The concept of line,surface, volume
integrals |
Video Link : https://www.youtube.c om/watch?v=NyG0vR n5FfU https://www.youtube.c om/watch?v=JiQW1T Q5MMs https://www.youtube.c om/watch?v=hG7h2g3 6jrQ Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/104/11110408 5/ |
Discussion on pre-requisites (10
Min) PPT presentation/Clas
s/demo (35 Min) Summary (5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
2. |
Evaluation of Double integrals – problems |
To introduce The concept of Double integrals |
Video Link : https://www.youtube.c om/watch?v=XX5- ZgFC85E https://www.youtube.c om/watch?v=aqu6v4v dfd4 Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/104/11110408 5/ |
Discussion on pre-requisites (10
Min) PPT presentation/Clas
s/demo (35 Min) Summary (5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
3. |
Change the order of integration – problems |
To introduce The concept of Change the order of
integration |
Video Link : https://www.youtube.c om/watch?v=QbkiHZf GdZU https://www.youtube.c om/channel/UCFp0m DTHxb4kmzYEI7idx OQ Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour |
Discussion on pre-requisites (10
Min) PPT presentation/Clas
s/demo (35 Min) Summary (5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
|
|
|
|
|
|
|
4. |
Changing in to polar co- ordinates – problems |
To introduce The concept of Changing in to polar
co-ordinates |
Video Link : https://www.youtube.c om/watch?v=oPLMH 4q3kNk https://www.youtube.c om/watch?v=TKM3M F2m7vU Text Book
: Pdf (e- book) CANVAS INSTRUCTURE |
Discussion on pre-requisites (10
Min) PPT presentation/Clas
s/demo (35 Min) Summary (5min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
|
|
|
Web Link : https://nptel.ac.in/cour ses/111/104/11110408 5/ |
Doubts clari- fication (10 min) |
|
|
5. |
Changing of variables – problems |
To introduce
The concept of Changing of variables |
Video Link : https://www.youtube.c om/watch?v=1MoIt6v C0gU https://www.youtube.c om/watch?v=3hyciaX 4cSQ Text Book : Pdf (e- book) CANVAS INSTRUCTURE |
Discussion on pre-requisites (10
Min) PPT presentation/Clas
s/demo (35 Min) Summary (5min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
|
|
|
Web Link :
https://nptel.ac.in/cour
ses/111/104/11110408
5/ |
Doubts clari- fication (10 min) |
|
|
6. |
Volume integrals – Evaluation |
To introduce
The concept of Evaluating Volume integrals |
Video Link : https://www.youtube.c om/watch?v=hG7h2g3 6jrQ https://www.youtube.c om/watch?v=g89jZhB 1X3s Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/104/11110408 5/ |
Discussion on pre-requisites (10
Min) PPT presentation/Clas
s/demo (35 Min) Summary (5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
7. |
Mass of triple integrals – problems |
To introduce
The concept of Evaluating Mass of triple integrals |
Video Link : https://www.youtube.c om/watch?v=yqstdcW dHDs https://www.youtube.c om/watch?v=Fm63pd zBl1o Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/104/11110408 5/ |
Discussion on pre-requisites (10
Min) PPT presentation/Clas
s/demo (35 Min) Summary (5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
8. |
Mass of triple integrals – problems |
To
introduce The concept of Checking out the Pig Script Interfaces |
Video Link : https://www.youtube.c om/watch?v=yqstdcW dHDs https://www.youtube.c om/watch?v=Fm63pd zBl1o Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link : https://nptel.ac.in/cour ses/111/104/11110408 5/ |
Discussion on pre-requisites (10
Min) PPT presentation/Clas
s/demo (35 Min) Summary (5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
9. |
Volume of cylindrical co-ordinates – problems |
To introduce The concept of Volume
of cylindrical co-ordinates |
Video Link : https://www.youtube.c om/watch?v=cghy5cE oCNg https://www.youtube.c om/watch?v=vjYPfdK PJJM Text Book : Pdf (e- book) CANVAS INSTRUCTURE Web Link :
https://nptel.ac.in/cour
ses/111/104/11110408
5/ |
Discussion on pre-requisites (10
Min) PPT presentation/Clas
s/demo (35 Min) Summary (5min) Doubts clari- fication (10 min) |
Discussion Forum on the topic in the group Review on the topic Share material on the topic |
|
10. |
Revision of all the concepts in Unit-5 |
Revising all the concepts |
Refer above Links for data |
Revising the concepts discussed so far Any topic to Repeat asked by students. |
Assignment-5
Quiz-5 |
TOTAL CLASSES: 60
Prepared by Approved by
Faculty Signature HOD
(B.SARATH KUMARI)
No comments:
Post a Comment