Calculus Tuition in Singapore

Calculus

I'm happy to help with both single and multi-variable calculus.

Limits, continuity, differentiation, rates of change, stationary points, tangent and normal lines, Taylor series, integration and its key techniques, areas and volumes, arc lengths and surface areas, fundamental theorem of calculus
Partial derivatives, gradients, Jacobians, total derivatives, exact differentials, homogeneous functions, curvilinear coordinates, the envelope theorem
Multiple integrals, change of variables, infinite series
Vector calculus: line and surface integrals, divergence and curl, Green's, Stokes', and Gauss' Theorems
Fourier series and Fourier integrals
Ordinary differential equations, Laplace transforms, partial differential equations

Where calculus usually trips students up

Most students reach me able to differentiate and integrate, yet still lose marks. In my experience the trouble sits in a handful of predictable places.

Treating limits as a formality. Once a course defines continuity, differentiability and convergence through limits, a rough intuition stops being enough and the marks move to the precise argument.
The jump to several variables. Partial derivatives, the multivariable chain rule, and the difference between a partial and a total derivative catch out almost everyone the first time.
Vector calculus bookkeeping. Green's, Stokes' and the divergence theorem are not hard to state, but choosing the right one, and orienting the curve or surface correctly, is where solutions fall apart.
Setting up before solving. With a multiple integral, an arc length, or a volume of revolution, the integral is often the easy part. Drawing the region and choosing the order or coordinate system is what decides the answer.
Differential equations by pattern-matching. Reaching for a method before identifying the type of equation, or confusing initial-value with boundary-value conditions, quietly costs accuracy.
Small sign and substitution slips. A missing Jacobian in a change of variables, or a dropped limit when an integral is improper, turns a sound method into a wrong number.

Before you start: a calculus prerequisites checklist

Calculus rarely fails on the calculus itself. It fails on the algebra and pre-calculus underneath. Before week one, it is worth checking you are comfortable with the following. If any feel shaky, that is exactly the kind of gap a few targeted sessions can close quickly.

What to be comfortable with before week one
Be comfortable with	Why it matters for calculus
Algebra	Rearranging, factoring and partial fractions underpin almost every integration technique and most simplification.
Functions	Domain, range, composition and inverses are the language of a subject that studies how functions change.
Exponentials and logarithms	Their derivatives and integrals appear constantly, and they model growth and decay throughout the course.
Trigonometry	Identities and radian measure are needed for differentiating and integrating trig functions and for many substitutions.
Coordinate geometry	You will read slopes, areas and turning points straight off a graph, so confident curve sketching pays off early.
Vectors	A little comfort with vectors helps once you reach partial derivatives, gradients and vector calculus.

A one-semester self-study plan for independent learners

Not everyone wants weekly lessons. Some of the people I hear from are adult learners, or students whose main degree is in another field, who simply need to teach themselves calculus to a solid standard over a semester. If that is you, here is a thirteen-week route map built around texts that explain themselves well. Adjust the pace to your background, and message me if you would like a few sessions to unblock the parts that resist self-study.

Texts I often point self-study students to
Text	Author	Best for
Calculus: Early Transcendentals	James Stewart	A clear, applications-led first course; the mainstream choice
Thomas' Calculus	Thomas, Hass, Heil & Weir	A solid alternative single text, strong on engineering applications
Calculus	Michael Spivak	A rigorous, proof-first treatment for those who want the why, not just the how
Vector Calculus	Marsden & Tromba	The multivariable and vector-calculus half of the plan
Elementary Differential Equations	Boyce & DiPrima	A gentle, thorough start on ordinary differential equations

A thirteen-week plan
Week	Focus	Suggested reading	Checkpoint
1–2	Limits and continuity	Stewart or Thomas, the limits chapters	Evaluate limits confidently and state continuity precisely
3	Differentiation	Stewart or Thomas, rules of differentiation	Differentiate standard functions, including the chain and implicit rules
4	Using the derivative	Stewart or Thomas, applications	Optimisation, related rates and curve sketching
5	The definite integral	Stewart or Thomas, integration and the FTC	State and use the Fundamental Theorem of Calculus
6	Techniques of integration	Stewart or Thomas, integration techniques	Substitution, integration by parts and partial fractions
7	Applications of integration	Stewart or Thomas, applications	Areas, volumes of revolution and arc length
8	Sequences and series	Stewart or Thomas, infinite series	Apply the standard convergence tests
9	Power and Taylor series	Stewart or Thomas, power series	Find and use a Taylor expansion
10	Functions of several variables	Marsden & Tromba, partial derivatives	Partial derivatives, gradients and the multivariable chain rule
11	Multiple integrals	Marsden & Tromba	Double and triple integrals, and change of variables
12	Vector calculus	Marsden & Tromba	Line and surface integrals, and the Green, Stokes and divergence theorems
13	First-order differential equations and review	Boyce & DiPrima, the opening chapters	Solve separable and linear first-order equations

Frequently Asked Questions (FAQ) - Calculus Tuition

Which calculus topics and modules do you cover?

Single-variable and multivariable calculus, vector calculus, sequences and series, and differential equations, including Laplace transforms and Fourier series. In practice that covers the first- and second-year calculus and engineering-mathematics modules at NUS, NTU, SUTD, SIT and the other local universities, as well as polytechnic students working at degree level. Send me your module outline and I will confirm the fit.

I can do the calculations but lose marks on proofs and harder problems. Can you help?

Yes, and that is the most common reason students come to me. We work on reading the definitions precisely, justifying each step the way a marker expects, and setting a problem up before rushing to compute. The aim is that the method becomes reliable, not just the arithmetic.

Can you help with the calculus inside an engineering, physics or economics module?

Often, yes. A good deal of applied calculus, such as optimisation, differential equations, and line and surface integrals, appears inside modules with other names. Share the module and the specific problems you are stuck on, and I will tell you honestly whether it is something I cover well.

Do you also cover differential equations, Laplace transforms and Fourier series?

Yes. Ordinary and partial differential equations, Laplace transforms, and Fourier series and integrals are all part of the calculus work I teach, and they sit on this same page rather than a separate one.

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