McGill University · AEMA 102

McGill AEMA 102 tutoring

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Course overview

AEMA 102 at Macdonald Campus develops integral calculus and applications, including numerical integration, improper integrals and series. The example below starts by deciding what a signed rate accumulates. Send your chapter or a question, even if you haven’t started it, so we can confirm support before booking.

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AEMA 102 topics to review

Indefinite and definite integralsTrapezoidal and Simpson approximationsAreas, volumes, work and average valuesImproper integrals and infinite series

Common difficulties

Selecting an integration technique
Choosing a convergence test
Managing long calculations without losing the goal

Net change and total exchanged volume are different

A tank initially contains $V(0)=10$ litres. In this original model, one reversible pipe has signed flow $q(t)=4-2t$ L/min for $0\le t\le4$ , with $t$ in minutes. Positive flow enters the tank; negative flow leaves it. There are no other flows. Find the net volume change and the total volume that passes through the pipe in either direction during these four minutes. Predict whether equal starting and ending volumes would mean no flow occurred.

Hint: find where the rate changes sign

The net change integrates $q$ . The total volume exchanged integrates $|q|$ . Split at a sign change before removing the absolute value.

Separate direction from amount

The rate is zero at $t=2$ , positive before and negative after. With antiderivative $Q(t)=4t-t^2$ , the net change is

\Delta V=\int_0^4q(t)\,dt=Q(4)-Q(0)=0\,\mathrm L.

From 0 to 2 minutes, $Q(2)-Q(0)=4$ L enters. From 2 to 4, the signed change is $Q(4)-Q(2)=-4$ L, so 4 L leaves. The total volume exchanged is $4+4=8$ L, and the final tank volume is still 10 L. The tank stays nonempty: $V(t)=10+4t-t^2\ge10$ on this interval.

Calling the integral of the signed rate “the total amount moved” loses the direction distinction. Here total inflow is 4 L, total outflow is 4 L, and total exchange is 8 L.

Retry: start counting at minute 1

For the same physical model, now consider only $[1,4]$ . Find the net change, total inflow, total outflow and total exchanged volume. Check against the volumes at the two endpoints.

Check the changed interval

Since $Q(1)=3$ , $Q(2)=4$ and $Q(4)=0$ , net change is $0-3=-3$ L. Inflow on $[1,2]$ is $4-3=1$ L; outflow on $[2,4]$ is 4 L. Thus total exchange is 5 L. The endpoint volumes are $V(1)=13$ L and $V(4)=10$ L, agreeing with the net decrease of 3 L.

Continue with integration methods and area practice when the quantity is clear but the integral is not. This is a topic exercise for AEMA 102, not a claim about a current exam.

For numerical integration, compare trapezoidal and Simpson estimates. The official AEMA 102 listing names both methods and lists Winter 2027; this is topic practice, not a Fall 2026 exam claim. Ask us to confirm tutoring for your topic.

How tutoring can help

Send the rate and time interval; you can work on the integral with your tutor even if you haven’t started it. If support is confirmed, your tutor can check what positive and negative values mean, locate sign changes and distinguish a net change from a total amount before choosing an integration method.

Exam preparation for AEMA 102

Exam preparation can use mixed sets that require choosing the integration or convergence method before calculating.

Use your section’s outline to choose the chapters to review. We work through permitted practice and comparable problems, without completing graded assignments or exams on your behalf.

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AEMA 102 · official course reference