MH1811: pass the exams, not just read the notes
Your complete guide to Nanyang Technological University's mathematics 2 course. See where the marks are, work real practice questions, and study with an AI tutor that knows MH1811.
Sia generates MH1811 practice questions, walks through sequences and series step by step, and quizzes you on the material the exam weights most heavily.
Worked example
Determine whether the series with general term n / (n² + 1) converges.
Note that the terms tend to zero, so the divergence test is inconclusive (ruling out option D) and 'terms tend to zero' is never enough for convergence (ruling out option B).
By the limit comparison test the series behaves like the harmonic series, which diverges. So the series diverges.
The ratio test gives a limit of 1 here and is inconclusive, ruling out option C.
The trap: Concluding convergence from terms tending to zero. That condition is necessary, not sufficient — the harmonic series is the standard counterexample and this series is a disguised version of it. classic slip!
One exam decides 50% of your grade. Summative assessment. This whole page is built around that.
Overview
What MH1811 is, and where it sits
MH1811 Mathematics 2 is the second engineering mathematics course at NTU, following MH1810 as its co-requisite. The OBTL+ document, implemented from AY2025-2026, extends differentiation and integration to functions of several variables, adds sequences, series and Taylor expansions, and finishes with first- and second-order ordinary differential equations.
Sixteen intended learning outcomes structure the course: convergence of sequences and series and the full set of convergence tests; power series and Taylor's remainder theorem; limits, partial derivatives, gradients, tangent planes and directional derivatives of functions of two or three variables; classifying stationary points and Lagrange multipliers; double and triple integrals; and solving separable, linear, Bernoulli, exact and constant-coefficient second-order ODEs, then applying them to practical problems.
Assessment is three pieces: a take-home online assignment 25% with unlimited attempts, a one-hour mid-term test 25% and a two-hour final examination 50%. The course is 3 AU with 38 contact hours across lectures and twelve tutorials, offered in both semesters; the course author is Fedor Duzhin.
Always treat your own course outline and the exam timetable as authoritative.
Difficulty & time commitment
Is MH1811 hard, and how much time does it take?
MH1811 is manageable if you keep a weekly rhythm and treat the back half as the main event. The pattern is consistent: it starts gently and steepens, and the heaviest assessment is the part that separates grades.
The difficulty curve and the assessment weighting point the same way: the back half is harder and worth more. Front-loading effort there is the highest-return decision in the course.
Is this course for you
Who tends to do well, and who tends to struggle
You will likely do well if
- You keep going on the online assignment until it is 100%; the document says that is how it is designed.
- You can already differentiate and integrate fluently from MH1810.
- You like organising methods into decision trees — series tests and ODE types reward that.
- You sketch regions before setting up double integrals.
You may struggle if
- You treat the convergence tests as a list to memorise rather than a procedure to choose from.
- You skip the mid-term's compulsory status; it is 25% and zero if missed without a certificate.
- You cannot yet handle partial fractions and trigonometric integrals from MH1810.
- You leave ODEs, the last three weeks, for the final week.
- Build a one-page flowchart: which convergence test to try first for which kind of series.
- Practise Taylor's remainder bounds; they are the ILO most often skipped and most often examined.
- For every stationary point, compute the second-derivative test and state the classification in words.
- Classify an ODE by type before solving — separable, linear, Bernoulli, exact — and write the method name.
Syllabus
The 13 topics, week by week
The exam-weight marker on each topic shows where the marks concentrate. The amber topics carry the highest exam weight.
T1 · Sequences
Week 1; ILO 1General terms, limits, squeeze theorem, convergence and divergence.
T2 · Series
Week 2; ILO 2Geometric and telescoping series and their sums.
T3 · Convergence tests
Week 3; ILO 3Divergence, alternating, integral, comparison, limit comparison, ratio and root tests; absolute and conditional convergence.
T4 · Power series
Week 4; ILO 4Radius and interval of convergence; term-by-term differentiation and integration.
T5 · Taylor series
Week 5; ILO 5Maclaurin and Taylor series; remainder and estimation theorems.
T6 · Functions of several variables
Week 6; ILOs 6-7Domains, level curves, limits and continuity in two and three variables.
T7 · Partial derivatives and gradients
Week 7; ILOs 8-9Chain rule, gradient vectors, tangent planes, linear approximation, total differential.
T8 · Directional derivatives
Week 8; ILOs 9-10Rates of change in a given direction and applications.
T9 · Optimisation
Week 9; ILOs 11-12Classifying stationary points; Lagrange multipliers with an equality constraint.
T10 · Double integration
Week 10; ILO 13Sketching regions and evaluating double integrals; generalisation to triple integrals.
T11 · Double integrals and first-order ODEs
Week 11; ILOs 13-15Separable, homogeneous, linear, Bernoulli and exact equations.
T12 · Second-order ODEs
Week 12; ILOs 14-15Homogeneous constant-coefficient equations; undetermined coefficients and variation of parameters.
T13 · ODE applications
Week 13; ILOs 14-16Modelling and solving practical problems with ODEs.
How it's assessed
Assessment structure
| Component | Weight | Format & timing |
|---|---|---|
| Continuous Assessment: take-home online assignment (multiple-choice online quiz with unlimited attempts) | 25% | Take-home online multiple-choice assignment with unlimited attempts. Across the semester. Continuous assessment. |
| Continuous Assessment: mid-term test (one hour, short-answer maths questions) | 25% | One-hour mid-term test, short-answer questions; compulsory, one make-up only with a medical certificate. Mid-semester. Continuous assessment. |
| Final exam (two-hour written examination, short-answer maths questions) | 50% | Two-hour written final examination, short-answer questions, all sixteen ILOs. Examination period. Summative assessment. |
- The three components sum to 100 and no examination hurdle is published. The mid-term test is compulsory: missing it without a valid reason scores zero, and only one make-up test is scheduled, requiring a Singapore-issued medical certificate.
- A two-hour short-answer examination worth 50% covers all sixteen ILOs. The one-hour mid-term is the same style on the first half, so it is the rehearsal; the online assignment is the practice bank.
This is an exam-cram course. With the exams at 50% of the grade and the final exam (two-hour written examination, short-answer maths questions) alone at 50%, your result is overwhelmingly decided by how well you perform under time pressure. Summative assessment.
Final exam timing: During the examination period. Confirm the exact date and venue on your exam timetable.
How to actually pass it
A weekly rhythm, two checklists, and the traps to avoid
The course rewards consistency over cramming, and practice over re-reading. Here is the loop that works, then what to have nailed before each exam.
The weekly loop
Before the mid-semester checklist
- Decide convergence of a series using the right test and justify it.
- Find the radius and interval of convergence of a power series.
- Write the Maclaurin series of a standard function and bound its error.
- Evaluate a two-variable limit or show it does not exist.
Before the final heaviest topics
- Find the tangent plane and use it for linear approximation.
- Classify stationary points and solve a constrained optimisation by Lagrange multipliers.
- Set up and evaluate a double integral over a sketched region.
- Solve first-order ODEs of each type and second-order constant-coefficient ODEs.
The mistakes that cost marks
Testing the wrong thing. The divergence test can only show divergence; using it to conclude convergence is the classic week-3 error.
Forgetting the constraint. In Lagrange problems the constraint equation is one of the equations to solve, not a footnote.
Wrong order of integration. Reversing limits without re-sketching the region produces the wrong integral every time.
Teaching team
Who teaches MH1811
The bios below are factual. We do not rate lecturers; any star ratings are submitted by students who have taken MH1811.
Teaching team as listed in the course materials reviewed. AskSia does not rate lecturers; star ratings are submitted by students who have taken MH1811.
Formula & concept sheet
The vocabulary and formulas you must own
- Convergent series
- A series whose partial sums approach a finite limit.
- Ratio test
- A convergence test comparing successive terms' ratio with 1.
- Power series
- A series in powers of (x − a) with a radius of convergence.
- Taylor series
- The power series of a function built from its derivatives at a point.
- Partial derivative
- The rate of change of a multivariable function with respect to one variable, others held fixed.
- Gradient
- The vector of partial derivatives, pointing in the direction of steepest ascent.
- Directional derivative
- The rate of change along a unit direction, the gradient dotted with that direction.
- Lagrange multiplier
- The method for optimising a function subject to an equality constraint.
- Double integral
- The integral of a two-variable function over a region in the plane.
- Integrating factor
- The multiplier that makes a first-order linear ODE exact.
- Variation of parameters
- A method for particular solutions of non-homogeneous second-order ODEs.
Set texts
The prescribed reading
The syllabus references map straight onto these.
Thomas' Calculus
.
Where it fits
Prerequisites, related courses & why it matters
Co-requisite MH1810. Mutually exclusive with MS2900, MH1100, MH1101 and MH1801. 3 AU; 38 contact hours; offered in Semester 1 and Semester 2.
Your MH1811 study toolkit
Study the course with Sia, not just read about it
Each tool already knows MH1811: your syllabus, your texts, and where the marks are. Grouped by how you study, from first contact to exam week.
FAQ
Frequently asked questions
Is MH1811 hard?
It rates moderate, at the harder end. The mathematics is the most demanding in the first-year engineering sequence, but 25% of the grade is an unlimited-attempt assignment and there is no exam hurdle.
What is the assessment breakdown?
Take-home online assignment 25%, one-hour mid-term test 25% and two-hour final examination 50%, per the OBTL+ document.
Is the assignment really unlimited attempts?
Yes. The document describes it as a multiple-choice online quiz with unlimited attempts and states that students willing to put in the effort will get 100%.
What happens if I miss the mid-term?
You score zero unless you have a valid reason; with a Singapore-issued medical certificate you can sit the single make-up test. Missing that too may lead to an incomplete grade if documented.
What is the textbook?
Thomas' Calculus, 13th edition, with Stewart's Calculus, 9th edition, as a reference.
Who wrote the course?
The OBTL+ document names Fedor Duzhin as course author.
Study MH1811 with Sia
Work through sequences, series, convergence tests and the rest of the course with a tutor that knows it and quizzes you on the topics the assessments weight most heavily.
Start studying with Sia
