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FE Exam Preparation

FE Mechanical Course Access through App (For One Month)

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$49.00
SKU
FES0002
Price
$49.00

Straight Lines

Learning Objectives
  • Find and interpret equation of a straight line in various forms.
  • Perform slope calculations including parallel and perpendicular lines.
  • Find angle between two coplanar, non-parallel lines.
Notes
\[y = mx + b\]

where m = slope and b = y-intercept For the above line, y-intercept = 1, and slope = $\dfrac{\mathrm{Rise}}{\mathrm{Run}}$ = $\dfrac{2}{4}$ = $\dfrac{1}{2}$ So the equation will be, \[y = 0.5x + 1\] \[2y = x + 2\] \[x - 2y + 2 = 0\]

Taylor's and Maclaurin's Series

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Learning Objectives:

  • State the definition of the Taylor/McLaurin series of a function and describe its properties.

  • To understand how Taylor polynomials can be used to approximate functions.

Taylor’s Series is defined as:

\[{f\left( x \right) }={ \sum\limits_{n = 0}^\infty {{f^{\left( n \right)}}\left( a \right)\dfrac{{{{\left( {x - a} \right)}^n}}}{{n!}}} }\] \[= {f\left( a \right) + f'\left( a \right)\left( {x - a} \right) }+{ \dfrac{{f^{\prime\prime}\left( a \right){{\left( {x - a} \right)}^2}}}{{2!}} + \ldots } + {\dfrac{{{f^{\left( n \right)}}\left( a \right){{\left( {x - a} \right)}^n}}}{{n!}} }+...\]

If a=0, the series is called Maclaurin’s Series:

\[{f\left( x \right) }={ \sum\limits_{n = 0}^\infty {{f^{\left( n \right)}}\left( 0 \right)\dfrac{{{x^n}}}{{n!}}} } = {f\left( 0 \right) + f'\left( 0 \right)x }+{ \dfrac{{f^{\prime\prime}\left( 0 \right){x^2}}}{{2!}} + \ldots } +{ \dfrac{{{f^{\left( n \right)}}\left( 0 \right){x^n}}}{{n!}} }+...\]

Some Important MacLaurin’s Series

\[{{e^x} = \sum\limits_{n = 0}^\infty {\dfrac{{{x^n}}}{{n!}}} }={ 1 + x + {\dfrac{{{x^2}}}{{2!}}} }+{ {\dfrac{{{x^3}}}{{3!}}} + ...}\] \[{\cos x = \sum\limits_{n = 0}^\infty {\dfrac{{{{\left( { - 1} \right)}^n}{x^{2n}}}}{{\left( {2n} \right)!}}} }={ 1 - {\dfrac{{{x^2}}}{{2!}}} }+{ {\dfrac{{{x^4}}}{{4!}}} }-{ {\dfrac{{{x^6}}}{{6!}}} + ... }\] \[{\sin x = \sum\limits_{n = 0}^\infty {\dfrac{{{{\left( { - 1} \right)}^n}{x^{2n + 1}}}}{{\left( {2n + 1} \right)!}}} }={ x - {\dfrac{{{x^3}}}{{3!}}} }+{ {\dfrac{{{x^5}}}{{5!}}} }-{ {\dfrac{{{x^7}}}{{7!}}} + ... }\] \[{\cosh x = \sum\limits_{n = 0}^\infty {\dfrac{{{x^{2n}}}}{{\left( {2n} \right)!}}} }={ 1 + {\dfrac{{{x^2}}}{{2!}}} + {\dfrac{{{x^4}}}{{4!}}} }+{ {\dfrac{{{x^6}}}{{6!}}} + ... }\] \[{\sinh x = \sum\limits_{n = 0}^\infty {\dfrac{{{x^{2n + 1}}}}{{\left( {2n + 1} \right)!}}} }={ x + {\dfrac{{{x^3}}}{{3!}}} }+{ {\dfrac{{{x^5}}}{{5!}}} }+{ {\dfrac{{{x^7}}}{{7!}}} + ... }\]

H5P

List of Videos

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As of July 21st, 2019, these are the 58 videos (with running time) available on the site:

  1. Mathematics
    • Straight Lines (9:14)
    • Video Explanation for Solved Example-AAA-02(6:56)
    • Equation of a Circle (10:40)
    • Equation of a Circle- Video Explanation for Solved Example- AAC-12 (8:25)
    • Properties of an Ellipse (8:15)
    • Video Explanation for Solved Example-AAF-06(9:05)
    • Properties of Dot Product (5:54)
    • Properties of Cross Product (9:45)
    • Gradient, Divergence and Curl (8:32)
    • Odd and Even Functions (8:03)
    • Differential Equations- Video Explanation for Solved Example-AEE-09 (3:59)
    • Exponential Growth or Decay (8:32)
    • Higher Order Differential Equations (11:15)
    • Trapezoidal Method (9:41)
  2. Probability and Statistics
    • Probability Basic Concepts (13:02)
    • Expected Value of a Variable- Solved Example- BAA-08 (8:34)
    • Binomial Distribution (7:57)
    • Chi-Squared Test- Part I and II (9:53 and 7:47)
    • Linear Regression- Part-I and II (5:28 and 7:14)
  3. Computational Tools
    • Flowchart Symbols (8:18)
  4. Ethics and Professional Practice
    • Elements of a Contract (10:05)
  5. Economics
    • Simple and Compound Interest (8:02)
    • Break-Even Analysis (7:03)
    • Depreciation Methods- Part I and II (4:12 and 6:24)
  6. Electricity and Magnetism
    • Electric Potential (11:04)
    • AC Impedance (6:43)
    • Average Value (8:33)
    • Principle of Superposition- Solved Example- FCB-07 (9:42)
  7. Statics
    • Principle of Virtual Work- Video Explanation for Solved Example-GCE-01(9:11)
    • Centroid of Composite Area (8:22)
    • Centroid of Composite Area- Video Explanation for Solved Example-GEB-05(11:10)
    • Resultant of Forces (Graphical) (6:35)
    • Radius of Gyration- Video Explanation for Solved Example-GFA-02 (10:57)
  8. Dynamics, Kinematics and Vibrations
    • Motion under Variable Acceleration (6:26)
    • Motion under Constant Acceleration (6:18)
    • Masses Connected to a Pulley (6:48)
    • Mass Moment of Inertia (8:40)
    • Projectile Motion (5:59)
    • Video Explanation for Solved Example-HHA-07(8:25)
    • Damped Free Vibrations (12:18)
  9. Mechanics of Materials
    • Mohr's Circle Procedure (9:45)
  10. Materials
    • Lever Rule (8:53)
  11. Fluid Mechanics
    • Fluid Properties Part-I, II and III (7:24, 8:25 and 4:37)
    • Pressure Measurement (10:48)
    • Energy Equation (10:04)
    • Reynold's Number (10:11)
  12. Thermodynamics
    • Video Explanation for Solved Example-LAC-05(8:03)
    • Thermodynamic Processes(10:13)
    • Psychrometric Chart- Part I and II(5:16 and 4:08)
  13. Heat Transfer
    • Lumped System Analysis- Video Explanation for Solved Example-MEA-06(8:48)
    • Critical Radius of Insulation (8:20)
    • Shape Factors (9:56)
    • Lumped Capacitance Model (8:45)
  14. Measurement, Instrumentation and Controls
    • Feedback Control System- Video Explanation for Solved Example-NBB-01 (7:27)
    • Laplace Transform (6:03)
    • Time Response of a First Order System (10:19)
  15. Mechanical Design
    • Comparison of Pneumatic and Hydraulic Components(9:53)
    • Components of Pneumatic Systems-I and II (7:47 and 6:37)

Mechanical

Comments

Mohd Hasan (not verified) Sun, 08/18/2019 - 22:38

How can i register myself. Please provide the information or you can reach to me through smhasan81@gmail.com
Thanks

Bitnami