MATH 101 is the University of Victoria's Calculus II, and the continuation of both MATH 100 and MATH 109 — either one gets you in. It is a different kind of difficulty from Calculus I. Differentiation is an algorithm: there is always a rule that applies. Integration is a search, and MATH 101 then adds series, where the question stops being "what is the answer" and becomes "does an answer exist at all". Students who were comfortable last term are often surprised by that shift, and the surprise is the normal starting point.
What is covered in UVic MATH 101?
UVic's calendar description is dense: volumes; arc length and surface area; techniques of integration with applications; polar coordinates and area; Taylor's formula; improper integrals; series and tests for convergence; power series and Taylor series; and complex numbers. Unpacked:
- Techniques of integration: substitution, integration by parts, trigonometric integrals and substitution, partial fractions
- Applications of the integral: volumes of revolution by discs, washers and shells; arc length; surface area
- Polar coordinates: curves in polar form, and area enclosed by them
- Improper integrals: infinite limits and infinite discontinuities, and deciding whether a value exists
- Sequences and series: convergence and divergence, and the full battery of tests
- Power series: radius and interval of convergence
- Taylor's formula and Taylor series: approximating a function near a point, with a bound on the error
- Complex numbers: arithmetic, the complex plane, and the link back to the exponential and trigonometric functions
1.5 units, listed as 3-0-1 — three lecture hours a week plus a tutorial.
Complex numbers at the end of Calculus II is not universal, and it is a topic students routinely under-prepare because it arrives when the term is nearly over.
Who MATH 101 is for, and where it leads
The prerequisite is MATH 100 or MATH 109, or permission of the department. Note what is not on that list: MATH 102 does not lead here. UVic says so directly, and it is the single most consequential fact about UVic's first-year calculus offering.
MATH 101 is then the gateway to the second year:
- MATH 200 Calculus III — vectors and vector functions, partial differentiation, Lagrange multipliers, multiple integration, cylindrical and spherical coordinates, line and surface integrals. Requires MATH 101.
- MATH 202 Intermediate Calculus for CSC and EOS — vectors, curves and surfaces in space, partial differentiation, Taylor's theorem in two variables, an introduction to differential equations. Also requires MATH 101, and credit is granted for only one of MATH 200, 202 and 205.
If you are heading toward mathematics, physics, computer science, engineering or the earth and ocean sciences, MATH 101 is the hinge the rest of the degree turns on.
Common challenges students face in MATH 101
There is no algorithm for choosing a technique
This is the central difficulty, and it is genuinely new. A product in Calculus I told you to use the product rule. A product in an integral might mean parts, might mean substitution, might mean a trigonometric identity first. Recognition is built by volume and reflection, not by reading worked examples.
Volumes fail on the picture, not the integral
Discs, washers and shells are three formulas, and the hard part is none of them: it is drawing the region, deciding which variable to integrate in, and getting the limits right. Students who set up the picture correctly almost always finish; students who guess almost never do.
Convergence tests become a memory game
There are eight or nine, each with conditions, and memorising the list without learning which shapes of series suggest which test leaves you comparing all of them under exam pressure. Exams reward the test that finishes in two lines.
Taylor series feel unmotivated
Writing a Taylor series is mechanical once you have the derivatives. Understanding that you are trading an intractable function for a polynomial you can actually compute, within a controllable error, is what makes the remainder term worth caring about — and what makes the topic stick.
Complex numbers arrive last and get skipped
They land in the final weeks, they look unconnected to everything else, and revision time is short by then. They are also on the exam.
Last term's derivatives have gone rusty
MATH 101 uses MATH 100's differentiation constantly, and a break between terms is enough for it to fade. Time spent re-deriving a trigonometric derivative is time not spent on the integral it sits inside.
How Learn4Less helps you succeed in MATH 101
We build a decision procedure for integrals
Rather than drilling each technique in isolation, we work on the first fifteen seconds: what to look at in an integrand, what each feature suggests, and how to recognise quickly that a chosen route is not working. That is the skill the exam tests.
We start volume problems with the drawing
Region, axis, slice, limits — then the integral. Doing it in that order turns the hardest questions on the paper into routine ones.
We turn convergence tests into a map
Each test tied to the shape of series it handles well. A factorial suggests one thing, an alternating sign another, a rational expression a third. Recognition replaces recall.
We repair the differential calculus in place
If the real sticking point is a derivative you have forgotten, we fix it inside the integration problem rather than sending you back a term.
MATH 101 exam and midterm preparation
Unseen integrals, on the clock
Your section's course outline is the authority on weighting. What is constant is that you will meet integrals you have not seen, with the technique choice left to you. That is what we practise.
Tutorial sheets first
MATH 101 is 3-0-1, and the tutorial is where problems closest to exam style get worked. We treat those sheets as primary material rather than as extra homework.
Writing a long solution so it can be marked
Integration answers run to half a page. A marker who cannot follow your substitution cannot award the marks for it. We work on stating the substitution, changing the limits, and keeping the write-up legible under pressure.
Checking your own work
Our free integral calculator works definite and indefinite integrals step by step, including improper integrals and divergence, so you can find where a long computation went wrong rather than only learning that it did.
Why choose Learn4Less for MATH 101 tutoring?
Integral calculus is a core subject for us
We tutor the Calculus II course at UBC, SFU, KPU and UVic. Seeing the same technique go wrong across four curricula is how you learn which explanations actually land.
Sessions built around your own problems
Bring the assignment that is due, the tutorial question you could not finish, or the midterm you want to understand rather than shelve.
Online across Canada and the US
UVic sessions run online, with screen sharing and live work on a shared page — for long integration write-ups this is often better than paper, because the whole session is saved for you. In-person tutoring is available in the Vancouver area only.
Free tools, no session required
The integral calculator, the derivative calculator and our concept reviews are open to anyone.
Frequently Asked Questions
Can I take MATH 101 after MATH 102?
No. MATH 101 requires MATH 100 or MATH 109. UVic is explicit that MATH 102 does not serve as a prerequisite for MATH 101 and does not prepare students for further study of calculus. If you have taken MATH 102 and now need MATH 101, speak to an academic advisor — you will most likely need MATH 100 or MATH 109 first, and credit is granted for only one of the three.
Does it matter whether I took MATH 100 or MATH 109?
No. They are equivalent Calculus I courses with the same learning objectives and textbook, and either one satisfies the prerequisite. You will be in the same MATH 101 room as everyone else.
Is MATH 101 harder than MATH 100?
Different, and harder in a specific way. The computations are longer and there is no rule telling you what to do first. Students who got through Calculus I by pattern matching usually find Calculus II harder; students who understood why the rules worked usually find it manageable.
Which courses need MATH 101?
MATH 200 Calculus III and MATH 202 Intermediate Calculus for CSC and EOS both require it, and it is the standard prerequisite for the second year of mathematics, physics, computer science and engineering pathways at UVic.
When should I get a tutor for MATH 101?
The techniques stack, so early — usually around integration by parts, which is where most students first notice that the method is no longer obvious. Waiting until series means tackling two problems at once, with less term left to do it in.
