Engineering Mathematics 1 Course
Our Engineering Mathematics course covers differential and integral calculus, partial differentiation, matrices and eigenvalues, ordinary differential equations, sequences and series, multiple integrals and an introduction to vector calculus. 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 first-year engineering students, 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
$13 – $33
per hour
Free demo class · pay only if you continue
What you will learn
Learning outcomes
- Apply algebraic and trigonometric concepts
- Solve calculus problems
- Work with matrices and determinants
- Solve differential equations
- Apply vectors to engineering problems
- Use numerical methods
- Develop mathematical problem-solving skills
Prerequisites
- Basic arithmetic
- Basic algebra
- Basic geometry
- High-school mathematics
Tags
Course structure
Syllabus(6 modules)
- nth order derivatives
- Leibniz's theorem
- Polar curves
- Angle between radius vector and tangent
- Curvature
What is Engineering Mathematics I?
In short: this course gives one-to-one online tutoring in first-year engineering mathematics. A verified tutor explains calculus, differential equations, matrices and linear algebra step by step, with practice on your own problem sheets and past papers.
Engineering Mathematics I is the first-semester mathematics module taken by engineering students, building the calculus, vector calculus, differential equations and linear algebra that later engineering subjects depend on. It focuses on techniques and applications rather than pure proof, with many worked problems.
This online course teaches Engineering Mathematics I 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 I course cover?
| Topic | Key content |
|---|---|
| Differential calculus I and polar curves | nth derivatives, Leibniz's theorem, polar curves, angle between radius vector and tangent, curvature |
| Differential calculus II | Taylor's and Maclaurin's series, indeterminate forms, partial derivatives, Euler's theorem, Jacobians |
| Vector calculus | Derivatives of vector functions, velocity and acceleration, gradient, divergence and curl, solenoidal and irrotational fields |
| Integral calculus | Reduction formulae, double and triple integrals, beta and gamma functions |
| Differential equations | Exact, reducible to exact and Bernoulli equations, orthogonal trajectories, applications |
| Linear algebra | Rank of a matrix, Gauss elimination, Gauss–Jordan and Gauss–Seidel methods, eigenvalues and eigenvectors |
How do you solve an exact differential equation?
For M dx + N dy = 0:
- Check exactness: ∂M/∂y = ∂N/∂x.
- Integrate M with respect to x, treating y as constant.
- Integrate the terms of N that do not contain x with respect to y.
- Add the two results and set the sum equal to a constant c.
- If it is not exact, look for an integrating factor first.
How do you find the rank of a matrix?
- Use elementary row operations to reduce the matrix to echelon form.
- Make zeros below each leading entry.
- Count the non-zero rows.
- That count is the rank.
- For a system Ax = b, compare the rank of A and the augmented matrix to decide whether solutions exist.
What does a worked matrix rank question look like?
Here is a typical question: find the rank of the matrix with rows (1, 2, 3), (2, 4, 6) and (1, 1, 1).
| Step | Working |
|---|---|
| R2 → R2 − 2R1 | Row 2 becomes (0, 0, 0) |
| R3 → R3 − R1 | Row 3 becomes (0, −1, −2) |
| Echelon form | Two non-zero rows remain |
| Rank | 2 |
Where do students lose marks in Engineering Mathematics I?
Students most often lose marks in Engineering Mathematics I through the habits below. Each is easy to fix with practice and feedback on your own work.
| Mark-loser | What to do instead |
|---|---|
| Arithmetic slips in row operations | Write each operation and check each row |
| Integration constants missing | Add + C to indefinite integrals |
| Wrong method for a differential equation | Classify the equation before solving |
| Units and notation dropped | Keep notation consistent |
| No checking | Substitute answers back where possible |
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 II, Engineering Physics and our Mathematics subject page.
Engineering Mathematics 1 for 1st semester: who this course is for, prerequisites and study plan
Engineering Mathematics 1 for 1st semester students is the first maths paper in most BTech and BE programmes, and this course covers its calculus, vector calculus, differential equations and matrices units with a 1-to-1 tutor and past papers.
This Engineering Mathematics 1 course suits first-year BTech, BE and diploma students in any branch, and students repeating a first-semester maths paper who need a clear, exam-focused route.
Prerequisites: school-level algebra, trigonometry, geometry and basic calculus.
Course length: 40 one-hour lessons across 6 modules.
| Stage | Modules | What you can do afterwards |
|---|---|---|
| 1 | Differential calculus I and polar curves, differential calculus II | Use Leibniz's theorem, Taylor series and partial derivatives |
| 2 | Vector calculus | Find gradient, divergence and curl |
| 3 | Integral calculus | Evaluate double and triple integrals and change the order of integration |
| 4 | Differential equations, linear algebra | Solve first-order ODEs, find the rank of a matrix and eigenvalues |
Where it leads: continue with our Engineering Mathematics II course in the next semester, and see Engineering Physics for the first-year physics paper.
Engineering Mathematics 1 Course: frequently asked questions
What is in Engineering Mathematics I?
Differential calculus, polar curves, partial derivatives, vector calculus, integral calculus, differential equations and linear algebra.
What is Leibniz's theorem?
A formula for the nth derivative of a product of two functions.
What are gradient, divergence and curl?
Vector calculus operators measuring the rate of change of scalar fields, and the outflow and rotation of vector fields.
What is an exact differential equation?
One of the form M dx + N dy = 0 where ∂M/∂y = ∂N/∂x.
What is Gauss elimination?
A method for solving linear systems by reducing the matrix to upper triangular form.
Is engineering maths hard?
It is technique-heavy; regular practice with worked examples makes it manageable.
Do you follow my university's syllabus?
Yes. Tutors follow your university's syllabus and past papers.
Can you help me prepare for my exam?
Yes. Tutors practise past-paper problems step by step.
How much does an Engineering Mathematics 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 find the rank of a matrix?
Reduce it to echelon form with row operations; the rank is the number of non-zero rows.
What are eigenvalues?
Values λ for which Av = λv has a non-zero solution v.
How do I find eigenvalues?
Solve det(A − λI) = 0.
What is a Taylor series?
A representation of a function as an infinite sum of terms from its derivatives at a point.
What is a partial derivative?
The derivative of a multivariable function with respect to one variable, holding the others constant.
What is the Cayley–Hamilton theorem?
Every square matrix satisfies its own characteristic equation.
What is the difference between Engineering Mathematics 1 and 2?
Engineering Mathematics 1 is usually the first-semester paper on differential and integral calculus, matrices and first-order differential equations. Engineering Mathematics 2 builds on it with higher-order differential equations, Laplace transforms, Fourier series, vector integration and partial differential equations. The exact split varies by university.
What is the syllabus of Engineering Mathematics 1?
The syllabus varies by university, but Engineering Mathematics 1 usually covers differential calculus, partial differentiation, matrices with rank, eigenvalues and eigenvectors, sequences and series, multiple integrals and first-order differential equations. Always check your own university syllabus, because topics move between the first and second papers. Your tutor works from your syllabus and past papers.
Do you offer lessons in my time zone?
Yes. Lessons are online, so you can book times that suit your time zone.
Which book is best for Engineering Mathematics 1?
Two widely used books are Higher Engineering Mathematics by B. S. Grewal and Advanced Engineering Mathematics by Erwin Kreyszig. Many universities also recommend their own textbook or notes that follow the syllabus exactly. Your tutor uses the book your university sets and adds past-paper questions for each unit.
How do I pass Engineering Mathematics 1 in the 1st semester?
Learn the standard methods in each unit, such as rank of a matrix, eigenvalues, Taylor series and exact differential equations, and practise them with past papers from your own university. Most marks come from repeatable question types. Your tutor identifies those types early and drills them until you can solve them under time pressure.
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