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Solutions for Numerical and Analytical Methods with MATLAB for Electrical Engineers, 1st Edition Bober (All Chapters included)
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Complete Solutions Manual for Numerical and Analytical Methods with MATLAB for Electrical Engineers, 1st Edition by William Bober ; Andrew Stevens ; ISBN13: 9781439854297. (Full Chapters included Chapter 2 to 11), ch 1 solutionsn not available....1.Numerical Methods for Electrical Engineers 2.MATL...

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  • March 20, 2024
  • 351
  • 2013/2014
  • Exam (elaborations)
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  • analytical methods
  • matlab
  • electrical engineers
  • 1st edition
  • bober
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SOLUTIONS MANUAL FOR
Numerical and Analytical
Methods with MATLAB ®



for Electrical Engineers




by
William Bober
Andrew Stevens



Complete Chapter Solutions Manual
are included (Ch 2 to 11)


** Immediate Download
** Swift Response
** Program & Projects Sol

, SOLUTIONS MANUAL FOR

Numerical and Analytical Methods with MATLAB

for Electrical Engineers


TABLE OF CONTENTS



CHAPTER 2. MATLAB FUNDAMENTALS............................................................................................. 1

CHAPTER 3. MATRICES ......................................................................................................................... 77

CHAPTER 4. ROOTS OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS......................... 100

CHAPTER 5. NUMERICAL INTEGRATION........................................................................................ 131

CHAPTER 6. NUMERICAL INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS ...... 173

CHAPTER 7. LAPLACE TRANSFORMS.............................................................................................. 218

CHAPTER 8. FOURIER TRANSFORMS AND SIGNAL PROCESSING ............................................ 237

CHAPTER 9. CURVE FITTING ............................................................................................................. 276

CHAPTER 10. OPTIMIZATION............................................................................................................. 292

CHAPTER 11. SIMULINK...................................................................................................................... 332

,CHAPTER 2. MATLAB FUNDAMENTALS


Exercise 2.1

Show that the Taylor Series expansion of cos( x) about x = 0 is:

x2 x4 x6
cos ( x) = 1 − + − +
2! 4! 6!


Solution:

Taylor series expansion of f (x ) about x = 0 is:

f ′′(0) 2 f ′′′(0) 3 f IV 4
f ( x) = f (0) + f ′(0) x + x + x + x +
2! 3! 4!

For cos( x) ,

f ( x ) = cos ( x ) , f (0) = 1,

f ′( x ) = − sin( x ), f ' (0) = 0,

f ′′( x) = − cos( x), f ′′(0) = − 1,

f ′′′( x) = + sin( x), f ′′′(0) = 0,

f IV ( x) = + cos( x), f IV (0) =1

We can see that

x 2 x 4 x 6 x8
cos( x) = 1 − + − + − +
2! 4! 6! 8!


Exercise 2.2

Show that the Taylor Series expansion of sin( x) about x = 0 is:

x3 x5 x 7
sin ( x) = x − + − +
3! 5! 7!

1

, Solution:

For sin( x) ,

f ( x ) = sin ( x ) , f (0) = 0

f ′( x) = cos ( x), f ′(0) = 1

f ′′( x) = − sin ( x), f ′′(0) = 0

f ′′′( x) = − cos ( x), f ′′′(0) = − 1

f IV ( x) = sin ( x), f IV (0) = 0

f V ( x ) = cos ( x ), f V (0) = 1

We can see that

x3 x5 x7 x9
sin ( x) = x − + − + − +
3! 5! 7! 9!


Exercise 2.3

Using the Taylor Series expansion of e x about x = 0 (see Example 2.1) , show that

e jx = cos x + j sin x and that e − jx = cos x − j sin x , where j = − 1.


Solution:

For e jx ,

f ( x) = e jx , f (0) = 1

f ′( x) = je jx , f ′(0) = j

f ′′( x) = − e jx , f ′′(0) = −1

f ′′′( x) = − je jx , f ′′′(0) = − j

f IV ( x) = e jx , f IV (0) = 1

2

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