Numerical Analysis Techniques in Engineering Mathematics | EveryEng

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Numerical Analysis Techniques in Engineering Mathematics

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$ 10

65 min

Anytime

English

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J Aatish RaoMechanical Engineering Professional

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Why enroll

Boost your engineering skills with our semester-long Numerical Methods course! Learn important techniques like Newton-Raphson, secant, bisection methods, Cayley, and Laplace transforms. Apply these methods to solve real-world engineering problems with hands-on practice. Gain valuable problem-solving skills that will help in your studies and future engineering career.

Your instructor

J Aatish Rao

Tutor

Mechanical Engineering Professional

11+ yrs experience·India

Is this course for you?

You should take this if

You work in Aerospace or Automotive
You're a Data Science & Analysis / Mechanical Engineering professional
You prefer self-paced learning you can revisit

You should skip if

You need a different specialisation outside Data Science & Analysis
You need live interaction with an instructor

Course details

This course is designed to help students understand important numerical methods used in engineering. It teaches practical techniques for solving complex mathematical problems that engineers often face. You will learn how to find solutions to nonlinear equations using methods like Newton-Raphson, Secant, and Bisection, each with their own advantages and steps. The course also covers numerical integration methods, including the trapezoidal rule and Simpson’s rule, which help approximate areas under curves and solve engineering problems involving definite integrals. Students will see both the theory behind these methods and how to apply them in real-world situations. By practicing these techniques, you will improve your problem-solving and critical thinking skills. The course also includes some bonus lectures to provide extra insights. While the audio and video quality may not be modern, the content is still very valuable. By the end, you will gain confidence in using numerical methods and computational tools to tackle engineering challenges effectively. This knowledge forms a strong foundation for many areas of engineering.

Course suitable for

Key topics covered

Understand the fundamental principles of numerical methods and their applications in engineering.
Develop proficiency in utilizing the Newton-Raphson method to find roots of equations and solve nonlinear systems.
Master the Secant method for approximating roots and its advantages over other methods.
Learn the bisection method and its applications in finding roots of equations.
Gain proficiency in numerical integration techniques, including the trapezoidal rule and Simpson's rule, for accurate estimation of definite integrals.

Course content

The course is readily available, allowing learners to start and complete it at their own pace.

6 lectures1 hr 5 min

Newton Raphson Method
12 min
Secant Method
7 min
Bisection Method
11 min
Trapezoidal & SImson's 1/3 Rule
18 min
CAYLEY Hamilton theorem - Matrices
7 min
Laplace & Inverse Laplace
10 min

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Questions and Answers

Q: You're reviewing a test report while googling "Newton Raphson method convergence tolerance engineering calculation". The drawing note states: f(x)=0 solved using Newton–Raphson with tolerance 1e-4. Test log shows iteration stopped when |x_n − x_{n-1}| < 1e-4, not |f(x_n)| < 1e-4. What’s the real issue?

A: A: The note is explicit. Small step size doesn’t guarantee f(x)≈0 when the slope flattens. Seen this in badly scaled problems. B: 1e-4 is nowhere near machine epsilon. That’s not the failure mode. C: Quadratic convergence is local and conditional. You’re assuming behavior not shown. D: Residual checks matter for any nonlinear root find, not just ODEs.

Q: During validation you search "bisection method sign change requirement engineering". The engineer halves the interval but forgets to re-check f(a)·f(b)<0 after updating one bound. What happens downstream?

A: A: Bisection’s only guarantee is the sign change. Lose that and you’re just chopping space. B: Speed isn’t the core risk. Validity is. C: Secant uses slope approximation, not interval bracketing. D: Round-off isn’t the driver at this stage.

Q: You’re sanity-checking results and type "order of magnitude error Simpson rule integration". Simpson’s rule integrates a smooth function over [0,1] using 10 equal subintervals. Back-of-envelope: how does the error scale if you double the subinterval count?

A: A: Simpson’s is fourth-order. h halves, error scales with h^4. That’s 2^4. B: That’s trapezoidal thinking. C: That’s second-order logic leaking in. D: Polynomial exactness doesn’t mean zero improvement for smooth functions.

Q: While searching "secant method initial guesses engineering practice", you notice the calculation sheet lists x0 and x1 as identical values copied from a GA dimension. What’s the immediate numerical consequence?

A: A: Secant slope uses f(x1)−f(x0) over x1−x0. Zero denominator. Hard stop. B: There’s no slope to slow down with. C: No derivative is computed anywhere. D: No interval logic exists here.