MH1802: pass the exams, not just read the notes
Your complete guide to Nanyang Technological University's calculus for the sciences course. See where the marks are, work real practice questions, and study with an AI tutor that knows MH1802.
Sia generates MH1802 practice questions, walks through types of numbers; functions and algebraic step by step, and quizzes you on the material the exam weights most heavily.
Worked example
You need to solve a first-order linear differential equation that is not separable. Why does multiplying through by an integrating factor work, and how do you know which factor to use?
Identify the obstacle. A first-order linear equation has a derivative term and an undifferentiated term with a variable coefficient. Neither side is the derivative of anything recognisable, so integrating both sides directly achieves nothing.
Derive the factor rather than recall it. Apply the product rule to the desired product and compare it term by term with the multiplied equation. Matching the two forces a condition on the multiplier, and that condition is a separable equation whose solution is the integrating factor.
Integrate and solve. With the left side now an exact derivative, integrating both sides gives the product directly, and dividing back out gives the solution with its constant. NTU places this in week 10 immediately after classification, because recognising the equation type is what selects the method.
The trap: Option C is the answer that feels safe and is wrong in a way that matters. The integrating factor is not a convenience multiplier; it is the unique family of functions that makes the left-hand side exact. Choosing arbitrarily leaves the equation exactly as intractable as before. ILO 22 asks you to apply the appropriate techniques, and the appropriateness is the assessed part. classic slip!
One exam decides 40% of your grade. Summative assessment. This whole page is built around that.
Overview
What MH1802 is, and where it sits
MH1802 is NTU's calculus course written for science students rather than for mathematics majors. The published aims are threefold and unusually explicit: to equip you with the analytical skills to apply calculus techniques to scientific problems, with the reading skills to understand mathematical content in basic scientific and engineering literature, and with the communication skills to present mathematical ideas rigorously to mathematicians, scientists and engineers.
The scope is wide. Twenty-five intended learning outcomes are published, running from the vocabulary of number types and functions through complex numbers and de Moivre's theorem, limits and continuity, differentiation and its applications, numerical approximation, integration and its techniques, first and second order ordinary differential equations, and finally the power series method.
That breadth is the defining feature and the main risk. Very few individual topics are difficult; there are simply a lot of them, and the thirteen-week schedule moves at roughly one major topic per week with no slack. Complex numbers in week 3 are explicitly noted as being conducted mainly as an online self-study topic.
Always treat your own course outline and the exam timetable as authoritative.
Difficulty & time commitment
Is MH1802 hard, and how much time does it take?
MH1802 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 pace week by week. Twenty-five ILOs across thirteen weeks means a missed week is a missed topic, not a topic you can catch up in the gaps.
- You do the week 3 complex numbers self-study properly. It is delivered mainly online and it is the foundation for the integration techniques in week 8.
- You attend lectures for the in-class quizzes. Ten percent is participation-based with no make-ups available.
- You treat the two common tests as the main event; together they outweigh the final examination.
You may struggle if
- You assume the lower exam weighting means a lower workload. The 40% final still assesses all twenty-five ILOs.
- You skip the online self-study on complex numbers because no lecture forces you to.
- You leave the differential equations block to the end. It arrives in weeks 10 to 12 and covers ILOs 19 to 25.
- You miss a common test. There are no make-ups, and 20% is a fifth of the grade.
- Keep a running index of the twenty-five ILOs and tick them off as they are taught; the breadth is easier to manage when it is visible.
- For each differential equation type, record the identifying test alongside the method. Classification is ILO 21 and it is what selects everything downstream.
- Do the homework on schedule even though it is auto-graded and only 10%. It is the only weekly forcing function in the course.
- Practise the scientific applications — kinematics, chemical kinetics, centre of mass. ILOs 12, 19 and 24 all ask you to move between a scientific description and a mathematical one in both directions.
Syllabus
The 13 topics, topic by topic
The exam-weight marker on each topic shows where the marks concentrate. The amber topics carry the highest exam weight.
T1 · Types of numbers; functions and graphs
Week 1; ILO1-2The vocabulary of number types and the function families the course runs on.
T2 · Algebraic, trigonometric and logarithmic functions
Week 2; ILO2-4Identities and their use in proof, including the binomial theorem.
T3 · Exponential functions, identities and basic complex numbers
Week 3; ILO4-5Euler's formula and de Moivre's theorem, delivered largely as online self-study.
T4 · Limits and continuity
Week 4; ILO6-8Types of limits, their evaluation, and the intermediate value theorem as a root estimator.
T5 · Derivatives and techniques of differentiation
Week 5; ILO8-9Deriving the derivative formulas, then applying the standard techniques.
T6 · Applications of differentiation; numerical approximation
Week 6; ILO9-12Curve sketching, optimisation, mean value problems, Newton's method and differentials.
T7 · Indefinite and definite integrals, Fundamental Theorem of Calculus, integration techniques I
Week 7; ILO13-14Riemann sums, the theorem that links the two operations, and the first techniques.
T8 · Integration techniques II; applications of integration
Week 8; ILO15Substitution, parts, partial fractions and complex methods, then area, arc length and volume.
T9 · Applications of integration in science; numerical approximation of integrals
Week 9; ILO16-18Kinematics and centre of mass, plus numerical methods where no closed form exists.
T10 · Introduction to differential equations; first order ordinary differential equations
Week 10; ILO19-20Classification, then separation of variables and integrating factors.
T11 · Second order linear differential equations with constant coefficients
Week 11; ILO21-22Homogeneous and non-homogeneous cases, the workhorse of applied modelling.
T12 · Power series method
Week 12; ILO23-24Solving differential equations where elementary methods do not reach.
T13 · Revision
Week 13; ILO1-25Consolidation across all twenty-five outcomes.
How it's assessed
Assessment structure
| Component | Weight | Format & timing |
|---|---|---|
| Final Examination | 40% | Graded in-class final examination assessed against all twenty-five ILOs, point-based marking. Examination period. Summative assessment. |
| Common Test 1 | 20% | Graded mid-semester test assessed in class, covering ILOs 1 to 8, point-based marking. First half of semester. Continuous assessment. |
| Common Test 2 | 20% | Graded mid-semester test assessed in class, covering ILOs 7 to 18, point-based marking. Second half of semester. Continuous assessment. |
| Graded take-home homework | 10% | Weekly and biweekly homework, mostly multiple choice or short answer, auto-graded through an online homework platform. Self-organised study groups are permitted. Weekly and biweekly. Continuous assessment. |
| In-class quizzes and discussions | 10% | In-class quick quizzes during some lectures, assessed on participation and attendance. No make-ups are offered for missed in-class participation components. Across the semester. Continuous assessment. |
- The five components sum to 100. NTU publishes no separate hurdle on the final examination. The outline states there are no make-up tests for the midterms and no make-ups for missed in-class participation components.
- Only 40% rests on the final examination, which is the lowest exam weighting of any NTU course in this network. The two common tests are 20% each, and their published ILO coverage divides the course cleanly: Common Test 1 spans ILOs 1 to 8 — numbers, functions, complex numbers and limits — while Common Test 2 spans ILOs 7 to 18, the differentiation and integration block. The final assesses all twenty-five.
This is an exam-cram course. With the exams at 80% of the grade and the final examination alone at 40%, your result is overwhelmingly decided by how well you perform under time pressure. Summative assessment.
Final exam timing: In-class final examination 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
- Explain the terms used for number types and functions, and identify the functions that describe given scientific phenomena.
- Apply algebraic, trigonometric, logarithmic and exponential identities, including the binomial theorem, to prove identities.
- Apply complex numbers, Euler's formula and de Moivre's theorem to related problems.
- Explain and evaluate limits, apply continuity and the intermediate value theorem, and derive the derivative formulas from limits.
Before the final heaviest topics
- Apply differentiation techniques, classify critical points, sketch curves and solve optimisation and mean value problems.
- Apply Taylor series, numerical approximation, L'Hospital's rule and numerical derivatives.
- Apply the Riemann sum and the Fundamental Theorem of Calculus, and integrate by substitution, parts, partial fractions and complex methods.
- Classify differential equations and solve first order and second order linear equations, including by the power series method.
The mistakes that cost marks
Breadth underestimated. Twenty-five ILOs is roughly two per week. The individual topics are approachable; the pace is what catches people.
Complex numbers skipped. Week 3 is largely self-study, which makes it the easiest week to lose and one of the more costly, since complex methods reappear in the integration techniques.
Differential equations classified by guesswork. ILO 21 is classification for a reason: the type determines the method, and applying a method to the wrong type produces confident wrong answers.
Common test missed. No make-ups are offered. Two tests at 20% each are 40% of the grade, the same as the final examination.
Teaching team
Who teaches MH1802
The bios below are factual. We do not rate lecturers; any star ratings are submitted by students who have taken MH1802.
Teaching team as listed in public course information. AskSia does not rate lecturers; star ratings are submitted by students who have taken MH1802.
Formula & concept sheet
The vocabulary and formulas you must own
- Binomial theorem
- The expansion of a binomial raised to a power, with coefficients given by binomial coefficients.
- Euler's formula
- The identity linking the complex exponential to sine and cosine.
- de Moivre's theorem
- A rule for powers and roots of complex numbers in polar form.
- Intermediate value theorem
- A continuous function on an interval takes every value between its endpoint values; used here to estimate roots.
- L'Hospital's rule
- A method for evaluating indeterminate limits using derivatives of numerator and denominator.
- Newton's method
- An iterative root-finder built from the tangent line approximation.
- Differential
- The linear approximation to a change in a function, used for error estimation.
- Riemann sum
- A finite approximation to a definite integral by summing rectangle areas.
- Integration by parts
- The integration rule obtained by reversing the product rule.
- Arc length
- The length of a curve, computed as an integral of the local rate of change.
- Ordinary differential equation
- An equation relating a function of one variable to its derivatives.
- Separation of variables
- A method for first order equations whose variables can be collected on opposite sides.
- Integrating factor
- The multiplier that turns a first order linear equation into an exact derivative.
- Power series method
- Solving a differential equation by assuming a series solution and matching coefficients.
Common acronyms: AU · ILO · ODE.
Where it fits
Prerequisites, related courses & why it matters
No prerequisite is published in the OBTL+ document for MH1802. The course carries 4 Academic Units and 52 contact hours, delivered as 39 hours of lectures and 13 hours of tutorials, and is offered in Semester 1. Published texts are Thomas' Calculus, 13th edition in SI units (Pearson-Addison-Wesley, 2016) and Stewart's Calculus, 7th edition metric (Cengage), with Riley, Hobson and Bence, Lang, Trim and Apostol listed as further references.
Your MH1802 study toolkit
Study the course with Sia, not just read about it
Each tool already knows MH1802: 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 MH1802 hard?
It rates as moderate and has the gentlest assessment structure of the NTU mathematics courses covered here — 40% on the final rather than 60%, with two common tests at 20% each. The pressure comes from breadth: twenty-five ILOs in thirteen weeks.
What is the assessment breakdown?
A 40% final examination, two common tests at 20% each, 10% graded take-home homework and 10% in-class participation.
What does each common test cover?
The published ILO mapping puts Common Test 1 across ILOs 1 to 8 and Common Test 2 across ILOs 7 to 18. The final examination is mapped to all twenty-five.
Can I get a make-up if I miss a test?
No. The outline states plainly that there are no make-up tests for the midterms, and no make-ups for missed in-class participation components. A medical certificate should still be submitted.
How is the homework marked?
Most questions are multiple choice or short answer and are graded automatically through an online homework platform. Working in self-organised study groups is explicitly permitted.
How does MH1802 differ from MH1100 and MH1101?
MH1802 covers in one semester roughly what MH1100 and MH1101 cover in two, at less depth and with differential equations added. It is written for science students, and it is mutually exclusive with the MH1100 and MH1101 route on the mathematics course listing.
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