Engineering Mathematics 2 Course
Our Engineering Mathematics-II course covers vector calculus and the theorems of Green, Gauss and Stokes, higher-order differential equations, Laplace transforms, Fourier series and transforms, complex variables and partial differential equations. Lessons are live and one-to-one with a verified subject expert, who explains each concept with worked examples, solves problems from your own module and helps you prepare for exams and coursework. Suitable for engineering students in their first and second year, following university syllabi in the UK, US, Australia and India (including AKTU, VTU and Anna University style courses).
Reviewed by H. Rao, Master's in Mathematics with Computer ScienceLast updated
$14 – $44
per hour
Free demo class · pay only if you continue
What you will learn
Learning outcomes
- Solve ordinary differential equations
- Apply multivariable calculus
- Use Laplace transforms
- Understand Fourier series and transforms
- Work with complex variables
- Apply probability and statistics
- Use numerical methods
- Solve engineering mathematical problems
Prerequisites
- Engineering Mathematics-I
- Basic calculus
- Algebra
- Trigonometry
- Matrices and determinants
Tags
Course structure
Syllabus(5 modules)
- Euler's formulae
- Discontinuous functions
- Even and odd functions
- Half-range series
- Harmonic analysis
What is Engineering Mathematics II?
In short: this course gives one-to-one online tutoring in second-level engineering mathematics. A verified tutor explains Laplace transforms, Fourier series, vector calculus and partial differential equations with step-by-step worked problems.
Engineering Mathematics II is the second-semester engineering maths module, covering the transform methods and differential equations used throughout electrical, mechanical and civil engineering. It includes Fourier series for periodic signals, Laplace transforms for solving differential equations, second-order and partial differential equations, and vector integral theorems.
This online course teaches Engineering Mathematics II one to one with a verified tutor who has studied or taught it at university level, at your pace and aligned with your own module.
Related subject: Engineering mathematics help.
What does the Engineering Mathematics II course cover?
| Topic | Key content |
|---|---|
| Fourier series | Euler's formulae, Fourier series of discontinuous, even and odd functions, half-range series, harmonic analysis |
| Laplace transforms | Transforms of elementary functions, properties, inverse transforms, convolution, solving ODEs |
| Second-order linear ODEs with variable coefficients | One integral known, removal of first derivative, change of independent variable, variation of parameters |
| Partial differential equations | Formation of PDEs, first-order linear and non-linear PDEs, Lagrange's method, Charpit's method |
| Vector calculus | Gradient, divergence and curl, line, surface and volume integrals, Green's, Stokes' and Gauss's divergence theorems |
How do you find a Fourier series?
For f(x) on (−π, π):
- a₀ = (1/π) ∫ f(x) dx over the interval.
- aₙ = (1/π) ∫ f(x) cos nx dx.
- bₙ = (1/π) ∫ f(x) sin nx dx.
- Use symmetry: even functions have bₙ = 0; odd functions have a₀ = aₙ = 0.
- Write f(x) = a₀/2 + Σ (aₙ cos nx + bₙ sin nx).
How do you solve an ODE with Laplace transforms?
- Take the Laplace transform of both sides.
- Use L{y′} = sY − y(0) and L{y″} = s²Y − sy(0) − y′(0).
- Substitute the initial conditions.
- Solve algebraically for Y(s).
- Use partial fractions.
- Take the inverse Laplace transform to find y(t).
What does a worked Laplace transform question look like?
Here is a typical question: solve y′ + 2y = 0 with y(0) = 3 using Laplace transforms.
| Step | Working |
|---|---|
| Transform | sY(s) − 3 + 2Y(s) = 0 |
| Solve for Y(s) | Y(s) = 3 ÷ (s + 2) |
| Inverse transform | y(t) = 3e^(−2t) |
| Check | y′ = −6e^(−2t) = −2y ✓ and y(0) = 3 ✓ |
Where do students lose marks in Engineering Mathematics II?
Students most often lose marks in Engineering Mathematics II through the habits below. Each is easy to fix with practice and feedback on your own work.
| Mark-loser | What to do instead |
|---|---|
| Initial conditions forgotten | Include them when transforming derivatives |
| Partial fractions errors | Check by recombining |
| Wrong Fourier coefficients | Use the correct interval and formulas |
| Vector identities misapplied | Check each operator carefully |
| No final check | Substitute back into the equation |
How is it assessed, and how can a tutor help?
Engineering mathematics modules are usually assessed by written exams with problem-solving questions and internal tests or assignments.
Tutors explain concepts, work through practice problems with you and give feedback on your approach. Graded work you submit must be your own, as set out in our academic integrity policy. For deadline-driven guidance, see assignment help.
How the lessons work
Lessons are live and one to one on video with screen sharing and a shared whiteboard. You can follow a full course or book sessions on the topics you find hardest before exams. See also Engineering Mathematics I, Fluid Mechanics and MATLAB.
Engineering maths tutor for Mathematics 2: who this course is for, prerequisites and study plan
An engineering maths tutor for Mathematics 2 helps you master Laplace transforms, Fourier series, differential equations and vector integration through live 1-to-1 lessons built around your own university syllabus and past papers.
This Engineering Mathematics 2 course suits first-year BTech, BE and diploma students in their second semester, and students who need to clear a backlog in the second maths paper.
Prerequisites: Engineering Mathematics 1, especially calculus, matrices and determinants.
Course length: 40 one-hour lessons across 5 modules.
| Stage | Module | What you can do afterwards |
|---|---|---|
| 1 | Fourier series | Find full-range and half-range Fourier series |
| 2 | Laplace transform | Find transforms and inverse transforms and solve ODEs |
| 3 | Second-order linear differential equations | Solve constant-coefficient equations and use variation of parameters |
| 4 | Partial differential equations, vector calculus | Solve standard PDEs and apply Green's, Gauss's and Stokes' theorems |
Where it leads: revise the basics in our Engineering Mathematics 1 course, and use our MATLAB course to check Laplace and Fourier results.
Engineering Mathematics 2 Course: frequently asked questions
What is in Engineering Mathematics II?
Fourier series, Laplace transforms, second-order and partial differential equations, and vector integral theorems.
What is a Fourier series used for?
Representing periodic functions and signals as sums of sines and cosines.
Why are Laplace transforms useful?
They turn differential equations into algebraic equations, which are easier to solve.
What is a half-range Fourier series?
A sine or cosine series for a function defined on half the period.
What is Charpit's method?
A general method for solving non-linear first-order partial differential equations.
What does Stokes' theorem state?
The line integral around a closed curve equals the surface integral of the curl over any surface it bounds.
Which book is best for Engineering Mathematics 2?
Two widely used books are Higher Engineering Mathematics by B. S. Grewal and Advanced Engineering Mathematics by Erwin Kreyszig. Grewal is popular for its many solved examples, and Kreyszig for clear theory. Your tutor follows the book your university recommends and adds past-paper questions for each unit.
Can you help me prepare for my exam?
Yes. Tutors practise past-paper problems step by step.
How much does an Engineering Mathematics II tutor cost?
The price depends on the tutor and session length. You see the hourly rate before booking, with no subscription.
Can a tutor do my assignment for me?
No. Tutors explain, guide and give feedback so you can complete your own work, in line with our academic integrity policy.
How do I solve an ODE with Laplace transforms?
Transform the equation, solve for Y(s), then take the inverse transform.
What is the Laplace transform of e^(at)?
1 ÷ (s − a), for s > a.
What is the syllabus of Engineering Mathematics 2?
The syllabus varies by university, but Engineering Mathematics 2 usually covers higher-order linear differential equations, Laplace transforms and their inverses, Fourier series, partial differential equations and vector integration with Green's, Gauss's and Stokes' theorems. Some universities also include complex variables. Your tutor works from your own syllabus.
What is divergence?
A measure of how much a vector field spreads out from a point.
What is curl?
A measure of the rotation of a vector field.
What is Green's theorem?
It relates a line integral around a closed curve to a double integral over the region inside.
How do I find Fourier coefficients?
Integrate the function multiplied by sine or cosine terms over one period, using the standard formulas.
What is a PDE?
A partial differential equation, involving partial derivatives of a function of several variables.
Is Engineering Mathematics 2 hard?
Many students find Engineering Mathematics 2 harder than the first paper because topics such as higher-order differential equations, Laplace transforms, Fourier series and vector calculus build on earlier calculus. The exact topics vary by university. Regular practice with past questions makes it manageable, and your tutor focuses on the methods you find slowest.
Do you offer lessons in my time zone?
Yes. Lessons are online, so you can book times that suit your time zone.
Can an engineering maths tutor help me clear a backlog?
Yes. If you need to clear a backlog in Engineering Mathematics 2, a tutor starts with the units that carry the most marks in your university papers, usually Laplace transforms, Fourier series and differential equations. Lessons focus on repeatable question types and timed past papers, so you can pass the re-exam with confidence.
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