Hacks to ace Engineering mathematics 4

Hey guys!

Well, I don’t know where to start about 18 scheme M3. I mean the name “Transform Calculus, Fourier Series and Numerical Techniques” scares me. The syllabus includes Laplace, Inverse Laplace, Fourier Series, Fourier and Z- Transforms and we are still at module 3. Modules 4 and 5 include Numerical Solutions of 1st and 2nd order ODEs and a little bit of Calculus of Variations. Seems daunting.

But I will help you. I will simplify and shorten the number of topics you need to cover for your exam. Just keep reading.

Now my suggestion for you is to select three modules and stick with them. Try and keep calm when somebody tells you some other topic is really easy. I will tell you about those topics also, as a bonus.

What are the 3 modules you should learn?

Start with Module 1 - Laplace Transform.

All you need to know for scoring 20 marks in this module is a set of Laplace Transform formulas. And basic differentiation of course.

In the exam, they will ask questions such as:

Find the Laplace transform of elementary functions. These are basically functions like polynomials, or sin or cos, or ex.
Find the Laplace transform of the product of the elementary functions. Like x ex or ex sinx or x sinx.
Find the Laplace transform of a Periodic function and a Unit-step function.

The remaining half of this module is - Inverse Laplace Transform.

Which is just the reverse of Laplace transform. If you can solve Laplace transform questions, then inverse Laplace transform is just doing everything in reverse. The prerequisites for solving Inverse Laplace questions is:

Partial fractions
Forming perfect square

The next module you need to learn is module 4 - Numerical Solutions of First Order ODEs.

There are no prerequisites for numerical solutions except basic algebra. And you only need to learn the algorithm or the steps of each method.

There are 5 numerical methods in this module:

Taylor’s Series Method
Euler's Method
Runge-Kutta Method of Fourth Order
Milne's Predictor & Corrector Method
Adam-Bashforth's Predictor & Corrector Method

There will be 6 questions asked in a module right? So they will ask all of these methods. So you can answer 3 questions by learning any 3 methods. Learn 1 extra method just to be safe.

Next module is - Numerical Solutions of Second Order ODEs & Calculus of Variations.

The first part of this module is:

Numerical Solutions of Second Order ODEs. This has the same strategy as the previous module. But there are only 2 numerical methods:

Runge-Kutta Method of Fourth Order
Milne’s Predictor & Corrector Method

These methods have the same name but you need to apply them twice because there will be an extra variable.

The remaining part of this module is Calculus of Variations. One definite question asked is the derivation of Euler’s formula. Another question will be asked on:

Finding the Extremal y of a Functional I
What is the shape of the Hanging Chain?
Show that the Geodesic of a Plane Surface is a straight line.

There are videos on our YouTube channel: youtube/Entuition on these Calculus of Variation topics. Make sure you don’t miss watching and learning.

These are the 3 modules that will get you past the M3 exam. All of these topics are a little harder to learn on your own. And need basics such as differentiation, integration, partial fractions etc.

If you want to learn all these topics in a short time and less effort, you can find help at entuition.org/courses/18mat31. At Entuition we have created an online video course for each of the 4 Engg Maths subjects. These video courses are easy-to-follow with basics and prerequisites covered for each topic. The topics are mapped to VTU syllabus and include solved PYQ papers. The videos are short length and load easily. The courses are very affordable but very valuable.

And finally the bonus questions that are asked in every sem-end exam. From module 2: Fourier Series, learn Practical Harmonic Analysis. Questions on this topic are easy to solve if you know the formula. That’s 7 more marks for you.

Scoring good marks in the exam requires 2 things. First, we should divide the syllabus into easier and scorable topics. That’s what I have done here for you. Second, you need to start learning from today. Do not wait till the exam. Practice a little everyday.

Good Luck.