Engineering Mathematics for B.Tech Students

Ranjit Tutorials

Textbook , 2014 , 82 Pages , Grade: 13

Mathematics - Applied Mathematics

Its applied mathematics notes for B.Tech students of Second Semester of Indian Universities.

Strictly according to the syllabus of P.T.U (Jalandhar)

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ENGINEERING MATHEMATICS

B.Tech,Semester-II

RANJIT TUTORIALS

ESTD.2000

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By

Ranjit Singh

Alumnus of Panjab University,Chandigarh

Associate Professor

CGC Technical Campus,Jhanjeri(Mohali)

Department of Applied Sciences

Ex-Head

Department of Applied Sciences

GGS College of Modern Technology,Kharar(Mohali)

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ORDINARY DIFFERENTIAL EQUATIONS

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ORDINARY

DIFFERENTIAL EQUATIONS

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1. Exact differential equation

2. Equations reducible to exact form by integrating factors

01

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ORDINARY DIFFERENTIAL EQUATIONS

3. Equations of first order & higher degree

4. Clairaut's Equation

5. Linear differential equation of first order

02

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ORDINARY DIFFERENTIAL EQUATIONS

6. Linear differential equations of second and higher order

03

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ORDINARY DIFFERENTIAL EQUATIONS

7. Method of variation of parameters to find P.I.

04

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ORDINARY DIFFERENTIAL EQUATIONS

05

8. Legendre's linear equation & Cauchy's homogeneous

equation

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...

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o6

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07

(

)

)

(

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ORDINARY DIFFERENTIAL EQUATIONS

13

(

)

(

(

(

)

)

)

(

)

(

)

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Expected Questions

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ORDINARY DIFFERENTIAL EQUATIONS

17

(

(

)

)

(

)

(

)

(

)

(

)

(

)

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ORDINARY DIFFERENTIAL EQUATIONS

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Problems for meritorious students

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APPLICATIONS OF ODE

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APPLICATIONS OF ODE

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Mean Position

Extreme Position

Extreme Position

o

P

x

a

1. Simple Harmonic Motion (S.H.M)

2. Electric LCR Circuits

L

C

R

E=kcosnt

i

23

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APPLICATIONS OF ODE

EXPECTED QUESTIONS

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APPLICATIONS OF ODE

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MATRICES

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MATRICES

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2. Rank of a matrix

(3)

1. Elementary Transformations

3. Normal form of a matrix

26

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4. Consistency and Solution of linear equations

5. Linearly dependent & Linearly independent vectors

27

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7. Cayley Hamilton Theorem (CHT)

8. Quadratic Form

6. Eigen Values & Eigen Vectors

28

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9. Complex matrices

10. Orthogonal matrix

vely

( )

( )

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11. Unitary matrix

12. Similar matrices

13. Linear transformation

14. Orthogonal transformation

30

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Expected Questions

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Problems for meritorious students

42

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WRITE YOUR OWN NOTES HERE

rt

...

...

...

...

...

...

...

...

...

...

...

...

...

43

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INFINITE SERIES

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FOURIER SERIES

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INFINITE SERIES

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1. Infinite Series

2. Convergence,Divergence & Oscillation of an Infinite Series

3. Auxiliary Series

44

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INFINITE SERIES

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INFINITE SERIES

ALTERNATING SERIES

POSITIVE TERM SERIES

CONVERGENT

CONVERGENT

DIVERGENT

OSCILLATORY

4. Tests of Convergence for positive term series

45

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INFINITE SERIES

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6

7

8

46

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INFINITE SERIES

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5. Leibnitz's test for convergence of alternating series

6. Absolute and conditional convergence of an alternating

series

7. Important Limits

47

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INFINITE SERIES

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RANJIT TUTORIALS

Regd. Office.

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RANJIT TUTORIALS

Regd. Office.

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FOURIER SERIES

RANJIT TUTORIALS

Regd. Office.

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RANJIT TUTORIALS

Regd. Office.

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RANJIT TUTORIALS

Regd. Office.

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Website:

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Regd. Office.

# 42,Ranjit Nagar,Near-Bus Stand,Kharar,Distt. Mohali(Punjab),Ph.9876313376

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RANJIT TUTORIALS

Regd. Office.

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Website:

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RANJIT TUTORIALS

Expected Questions

55

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Regd. Office.

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RANJIT TUTORIALS

Regd. Office.

# 42,Ranjit Nagar,Near-Bus Stand,Kharar,Distt. Mohali(Punjab),Ph.9876313376

Website:

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57

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FOURIER SERIES

RANJIT TUTORIALS

Regd. Office.

# 42,Ranjit Nagar,Near-Bus Stand,Kharar,Distt. Mohali(Punjab),Ph.9876313376

Website:

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RANJIT TUTORIALS

Problems for meritorious students

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FOURIER SERIES

RANJIT TUTORIALS

Regd. Office.

# 42,Ranjit Nagar,Near-Bus Stand,Kharar,Distt. Mohali(Punjab),Ph.9876313376

Website:

www.ranjittutorials.com,Email: [e-mail]

WRITE YOUR OWN NOTES HERE

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60

1. De-Moivre's Theorem

2. Properties of cis

3. Some important cis forms

4. Values of (cos +isin ) , where p,q are +ve coprime integers

p/q

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61

5. Euler's Formula

6. Circular Functions

7. Hyperbolic Functions

8. Relation between Hyperbolic & Circular Functions

9. Inverse Hyperbolic Functions

10. Logarithm of Complex Numbers

(

)

(

)

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62

11. Some Standard Series

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63

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RANJIT TUTORIALS

Regd. Office.

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Website:

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RANJIT TUTORIALS

Regd. Office.

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RANJIT TUTORIALS

Regd. Office.

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RANJIT TUTORIALS

Regd. Office.

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Website:

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RANJIT TUTORIALS

Regd. Office.

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Regd. Office.

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RANJIT TUTORIALS

FOURIER SERIES

RANJIT TUTORIALS

Regd. Office.

# 42,Ranjit Nagar,Near-Bus Stand,Kharar,Distt. Mohali(Punjab),Ph.9876313376

Website:

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WRITE YOUR OWN NOTES HERE

rt

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RANJIT TUTORIALS

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RANJIT TUTORIALS

Regd. Office.

# 42,Ranjit Nagar,Near-Bus Stand,Kharar,Distt. Mohali(Punjab),Ph.9876313376

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RANJIT TUTORIALS

Expected Questions

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RANJIT TUTORIALS

Regd. Office.

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Regd. Office.

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(

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(

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Regd. Office.

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Problems for meritorious students

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IMPORTANT FORMULAE

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IMPORTANT BASIC

FORMULAE & RESULTS

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1. Differentiation

77

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RANJIT TUTORIALS

IMPORTANT FORMULAE

2. Integration

78

Frequently asked questions

What is the title of this document?

The title of this document appears to be ENGINEERING MATHEMATICS.

What topics are covered in this book?

The book covers topics in Ordinary Differential Equations, Applications of ODE, Matrices, Infinite Series and Complex Numbers.

What chapters are included in the Ordinary Differential Equations section?

The Ordinary Differential Equations section includes chapters on:

1. Exact differential equation
2. Equations reducible to exact form by integrating factors
3. Equations of first order & higher degree
4. Clairaut's Equation
5. Linear differential equation of first order
6. Linear differential equations of second and higher order
7. Method of variation of parameters to find P.I.
8. Legendre's linear equation & Cauchy's homogeneous equation

What topics are covered in the Applications of ODE section?

The Applications of ODE section includes chapters on:

1. Simple Harmonic Motion (S.H.M)
2. Electric LCR Circuits

What topics are covered in the Matrices section?

The Matrices section includes chapters on:

1. Elementary Transformations
2. Rank of a matrix
3. Normal form of a matrix
4. Consistency and Solution of linear equations
5. Linearly dependent & Linearly independent vectors
6. Eigen Values & Eigen Vectors
7. Cayley Hamilton Theorem (CHT)
8. Quadratic Form
9. Complex matrices
10. Orthogonal matrix
11. Unitary matrix
12. Similar matrices
13. Linear transformation
14. Orthogonal transformation

What topics are covered in the Infinite Series section?

The Infinite Series section includes chapters on:

1. Infinite Series
2. Convergence, Divergence & Oscillation of an Infinite Series
3. Auxiliary Series
4. Tests of Convergence for positive term series
5. Leibnitz's test for convergence of alternating series
6. Absolute and conditional convergence of an alternating series
7. Important Limits

What topics are covered in the Complex Numbers section?

The Complex Numbers section includes chapters on:

1. De-Moivre's Theorem
2. Properties of cis
3. Some important cis forms
4. Values of (cos +isin ) , where p,q are +ve coprime integers
5. Euler's Formula
6. Circular Functions
7. Hyperbolic Functions
8. Relation between Hyperbolic & Circular Functions
9. Inverse Hyperbolic Functions
10. Logarithm of Complex Numbers
11. Some Standard Series

Who is the author of this book?

The author of this book is Ranjit Singh.

Who is the publishing company for this book?

The publishing company for this book is RANJIT TUTORIALS.

• Course: B.Tech, Semester-II
• Grade: 13
• Author: Ranjit Singh (Author)
• Publication Year: 2014
• Pages: 82
• Catalog Number: V267852
• ISBN (eBook): 9783656593720
• ISBN (Book): 9783656593744
• Language: English
• Tags: engineering, mathematics, tech, students, ranjit, tutorials