Mumbai University | Chemical Engineering Branch | Second Year Semister-III Subject Applied Mathematics-III | Syllabus | Guidance | Marks Distribution.

Applied Mathematics - III

a) Nick Name by Student's :- M3 .

b) Short information of Subject :-

i) Theory Examination :- 100 Marks.

1) Question paper will comprise of 7 questions, each carrying 20 marks.

2) Total 5 questions need to be solved.

3) Question No.1 will be compulsory and based on entire syllabus.

4) Remaining Questions will be randomly selected from all the Chapters and will be mixed in nature.

ii) Term Work :- 25 Marks.

The distribution of marks for the Term Work will be as follows :-

Attendance (Theory and Tutorial) : 05 marks.

Class Tutorials on entire syllabus : 10 marks.

Test (atleast 1) : 10 marks

iii) Total :- 125 Marks.

Maths-III is basically an easy subject as compared to Maths I and II. Infact it can be scoring if you study it regularly . Not only Maths-III but to excell in any Maths whether 1,2,3 or 4 Practise is the only key to success. The more you practise, more you can score. But taking it lightly can make you pay heavy for it.

As a whole it is an easy subject. Stay in touch with the subject which will help you reduce your burden at the end. A slight hardwork will help you out.

c) Best Book to refer :- G.V. Kumbhojkar.

d) Short view of Syllabus :-

It comprises of in all 6 chapters. They are:-

1) Laplace Transform

2) Inverse Laplace Transform

3) Laplace Transform and Matrices

4) Matrices

5) Complex Variable

6) Bessels Equation

Average weightage of chapters :- The marks distribution among the Chapters is very clear and equal. However, in every question paper a slight variation can be seen as in MUMBAI UNIVERSITY the Paper pattern changes every now and then .

1) Chapter 1: Laplace Transform and Chapter 2 : Inverse Laplace Transform both in combination have an average weightage of 35 marks. These are formula based chapters. You have to just apply the formula and get the answer,But these chapters needs more practise.

2) Chapter 3 : Laplace Transform and Matrices and Chapter 4 : Matrices both in combination have an average weightage of 35 marks . We are studying Matrices since from our 10th standard, every time we study Matrices it becomes more and more Advanced. Similarly here the basic is same, only few new concepts are introduced. It is an easy chapter and can help you score well.

3) Chapter 5 : Complex Variable have an average weightage of 35 marks. As the name suggests it is a slightly complicated chapter. But once you get the concepts it is very easy. Don't keep this chapter as an option because all sums in this topic are similar and everyone can atleast solve half sum .

4) Chapter 6 : Bessels Equation have an average weightage of 35 marks . This is the key Chapter to score in Maths 3. It is a very small topic and has very few types of sums. Be through with the concepts in this chapter and you can definately grab more and more marks from this chapter.

Every chapter will give you some marks. But it's up to you how you fill your pockets with more and more marks .

Best of Luck......!!!!!!

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Mumbai University Chemical Engineering Branch Second Year Semister - III Guidance .

Mumbai University Second Year Chemical Engineering Semister - III

Guidelines :-

Dear Friends if you are unaware of Semister-III of Chemical Engineering and have no idea about it,Then this post can help you out.

After your First Year is completed, many of you must be having KT's in one or more subjects or if by chance Passed then you must be having Less Marks between 50-55% or even Less than it ,However some are exceptions who are All Clear with Good Marks. This happens as you all are new to the Semister Pattern of Mumbai University. But now after your 2 Semisters are completed you must be familiar with this Pattern. Don't be depressed or underestimate yourself for getting KT 's in the first year as it happens with almost every Engineering Student.

Apart from this Semister-III is a very scoring SEM and can help you to get your Aggregate levelled. Aggregate is the average of percentages scored by you in all your Eight Semisters. It is necessary to maintain your Aggregate, Because it's a common criteria of every Company that the Fresher Employee whom they are Recruiting should atleast have an Aggregate of 60% . If you try to maintain your Aggregate from Sem-3 itself it will reduce your Last Year's burden and will help you to easily get the job.

There are in all 6 Subjects in Semister-3 and are as follows :-

1) Maths-III

2) Advanced Chemistry-I

3) Computer Application

4) Electrical and Electronics Engineering

5) Process Calculation

6) Presentation and Communication Techniques.

The GRAND total of MARKS of all Subjects in Semister-3 is 800 .

Of these 800 marks, 300 marks are alloted for Practicals and Termwork whereas the remaining 500 marks are for Theory Examination.

Of the total 6 subjects, Three subjects Advanced Chemistry-I , Electrical and Electronics Engineering and Computer Application will have Practical Examination and Two subjects Process Calculation and Electrical and Electronics Engineering will have Oral Examination ( viva ).

Future posts will give you a brief knowledge of Subjects in Semister-III and How to Crack them.

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Elements from the Periodic Table which do not exhibit Magnetism.

NO MAGNETISM

a) For a material to be magnetic, it must have electron spin.

b) Electron spin gives the substance an Electronic Angular Momentum to interact with the magnetic field.

c) Thus if the electrons in an atom spins in the same direction,the atom will produce a magnetic field and will respond to the forces of a magnet.

d) But in most atoms,electrons occur in pairs and these paired electrons spin in opposite directions.

e) These opposite spins of electrons causes their magnetic fields to cancel each other, such that no net magnetic field is produced and this could be the reason why some elements do not exhibit magnetism.

f) However at a low temperature a substance may have one kind of magnetic properties whereas at a higher temperature it may have another type of magnetic behavior.

g) Thus the conclusion is that Magnetic Properties of a substance is a very complicated topic, and it is very difficult to assign some materials as being strictly magnetic and others to be strictly non-magnetic.

Elements from the Periodic Table which do not exhibit any type of Magnetism are :-

1) Fluorine

2) Potassium

3) Scandium

4) Vanadium

5) Rubidium

6) Yttrium

7) Niobium

8) Technetium

9) Iodine

10) Cesium

11) Lanthanum

12) Praseodymium

13) Promethium

14) Ytterbium

15) Lutetium

16) Hafnium

17) Tantalum

18) Rhenium

19) Polonium

20) Astatine

21) Radon

22) Francium

23) Radium

24) Actinium

25) Thorium

26) Protactinium

27) Uranium

28) Neptunium

29) Plutonium

30) Americium

31) Curium

32) Berkelium

33) Californium

34) Einsteinium

35) Fermium

36) Mendelevium

37) Nobelium

38) Lawrencium

39) Rutherfordium

40) Dubnium

41) Seaborgium

42) Bohrium

43) Hassium

44) Meitnerium

45) Darmstadtium

46) Roentgenium

47) Ununbium

48) Ununtrium

49) Ununquadium

50) Ununpentium

51) Ununhexium

52) Ununseptium

53) Ununoctium

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What is Ferromagnetism ? Behaviour of Ferromagnetic Substances & the Elements which exhibit Ferromagnetism..!

FERROMAGNETISM

a) The term Ferromagnetism was coined by Curie Pierre in 1895 .

b) Those substances which when placed in a magnetic field, are strongly magnetised in the direction of the applied field are called as Ferromagnetic substances.

c) A Ferromagnetic substance when placed in a non-uniform magnetic field, show a very strong tendency to move from the weaker to the stronger parts of the magnetic field.

d) Ferromagnetic materials are made up of atoms with permanent dipole moments.

e) Ferromagnetic substances retain their magnetism even when the external magnetic field is removed. This tendency of Ferromagnetic substances to remember their magnetic history is called as " Hysteresis " .

f) Due to their this property Ferromagnetic substances can be converted into Permanant Magnets.

g) Being Permanant magnets the Ferromagnetic substances can give rise to a magnetic field even in the absence of an external magnetic field.

h) Ferromagnetic substances have very high Magnetic Susceptibilities, ranging from 1000 to 1,00,000 .

i) The Relative Permeability of the Ferromagnetic substances is much more greater than 1 and hence for a Ferromagnetic substance the magnetic lines of force are strongly attracted.

j) When a Ferromagnetic substance is heated above a certain temperature it loses it's ferromagnetism and become Paramagnetic.

k) The temperature at which a Ferromagnetic substance becomes Paramagnetic is called as Curie Temperature.

l) Ferromagnetism is exhibited by solid materials only.

Elements from the Periodic Table which exhibit Ferromagnetism are :-

1) Iron

2) Cobalt

3) Nickel

4) Gadolinium

Anti-Ferromagnetism

a) Antiferromagnetism was first discovered by Neel and Bitter and later extended by Van Vleck.

b) In the presence of a strong magnetic field, Antiferromagnetic materials are weakly magnetised in the direction of the applied field.

c) In Antiferromagnetic materials, the magnetic moments are aligned in opposite directions and are equal in magnitude.

d) Due to this the magnetic moments of the neighbouring atoms cancel each other and its net magnetisation is zero.

e) Antiferromagnetism occur commonly among transition metal compounds, especially oxides.

f) Antiferromagnetism generaly exist at low temperatures and vanishes at and above a certain temperature called the Neel temperature .

g) Above the Neel temperature, the Antiferromagnetic material is typically paramagnetic .

h) Chromium is an example of element which exhibit Antiferromagnetism.

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What is Paramagnetism ? Behaviour of Paramagnetic Substances & the Elements which exhibit Paramagnetism..!

PARAMAGNETISM

a) The term Paramagnetism was coined by Curie Pierre in 1895.

b) Those substances which when placed in a magnetic field are weakly magnetized in the direction of the applied field are called as Paramagnetic Substances .

c) A Paramagnetic Substance when placed in a non-uniform magnetic field, begins to move form the weaker region to the stronger region of the magnetic field.

d) Thus the magnetic field lines prefer to pass through the Paramagnetic substances and this is the reason why the Paramagnetic Substances are weekly attracted by a magnet.

e) When a rod of Paramagnetic substance is suspended freely in a uniform magnetic field, the rod comes to rest with its axis parallel to the applied field.

f) Paramagnetism is generally exhibited by the elements due to the presence of unpaired electrons.

g) The reason is that an unpaired electron being lonely can spin in any direction ,i.e., it can assign its magnetic moment in either positive or negative direction. Due to this there will be unequal number of positive and negative spins and hence after the cancellation of the opposite spins there will be some residual magnetic moment . This is the reason why in a Paramagnetic substance, the individual atoms / molecules / ions have small net magnetic moment.

h) The Magnetic Susceptibility of a Paramagnetic substance have a small positive value.

i) The Relative Permeability of Paramagnetic substances is slightly greater than 1 .

j) Paramagnetic substances lose their magnetism as soon as the external magnetic field is removed.Thus the total magnetization drops to zero when the applied field is removed.

k) The Magnetization of the Paramagnetic substances decreases with the increase in temperature.

l) Paramagnetism is normally stronger than Diamagnetism .

m) Below the Curie temperature , certain Paramagnetic materials exhibit Ferromagnetism .

n) All the three states of matter exhibit Paramagnetism. eg :- Aluminium,Oxygen,Platinum.

Elements from the Periodic Table which exhibit Paramagnetism are :-

1) Lithium

2) Oxygen

3) Sodium

4) Magnesium

5) Aluminium

6) Calcium

7) Titanium

8) Manganese

9) Strontium

10) Zirconium

11) Molybdenum

12) Ruthenium

13) Rhodium

14) Palladium

15) Tin

16) Barium

17) Cerium

18) Neodymium

19) Samarium

20) Europium

21) Terbium

22) Dysprosium

23) Holmium

24) Erbium

25) Thulium

26) Tungsten

27) Osmium

28) Iridium

29) Platinum

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What is Diamagnetism ? Behaviour of Diamagnetic Substances & the Elements which exhibit Diamagnetism..!

Diamagnetism

a) The term Diamagnetism was coined by Michael Faraday in 1845 .

b) Those substances which when placed in a magnetic field, are weekly magnetised in a direction opposite to that of the magnetising field are called as Diamagnetic Substances .

c) When a Diamagnetic substance is placed in a non-uniform magnetic field , it's atoms acquire a small magnetic dipole moment in a direction opposite to that of the magnetic field .

d) As a result , the Diamagnetic substances moves from stronger part of the magnetic field to it's weaker part i.e. they are weakly repelled by the magnet .

e) The Diamagnetic substances do not retain their magnetic properties when the external magnetic field is removed.

f) Diamagnetism is usually observed in Solids composed of atoms with completely filled electronic shells .

g) The reason is that in a completely filled shell there are equal number of electrons with positive and negative spins, so that the total magnetic moment is zero .

h) This is the reason why the individual atoms in a Diamagnetic substance do not posses any net magnetic dipole moment.

i) The magnetic susceptibility of a Diamagnetic substance has a small negative value.

j) The relative permeability of a Diamagnetic substance is slightly less than 1.

k) The behaviour of a Diamagnetic substance is independent of temperature.

l) That is why Magnetic susceptibility of Diamagnetic substances do not change with temperature and hence the Diamagnetic substances do not obey Curie's Law .

m) The Diamagnetic substances when placed in a uniform magnetic field, they set their longest axis at right angles to the direction of the field and the shortest axis along the direction of the field.

n) Orbital motion of electrons is the root cause of magnetism in Diamagnetic substances.

o) All Substances are Diamagnetic to some extent .

Elements from the Periodic Table which exhibit Diamagnetism are :-

1) Hydrogen

2) Helium

3) Beryllium

4) Boron

5) Carbon

6) Nitrogen

7) Neon

8) Silicon

9) Phosphorus

10) Sulphur

11) Chlorine

12) Argon

13) Copper

14) Zinc

15) Gallium

16) Germanium

17) Arsenic

18) Selenium

19) Bromine

20) Krypton

21) Silver

22) Cadmium

23) Indium

24) Antimony

25) Tellurium

26) Xenon

27) Gold

28) Mercury

29) Thallium

30) Lead

31) Bismuth

Of this all elements Bismuth and carbon graphite are the strongest Diamagnetic materials.

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