Marianopolis College · 201-SNY-MS

Marianopolis 201-SNY-MS tutoring

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Course overview

The official Fall 2024–Winter 2026 listing describes Marianopolis 201-SNY-MS as applying calculus, series and linear algebra to finance and economics. It does not verify a Fall 2026 offering.

Optional course listed in the catalogue. It may not run every term. Ask us whether we can tutor you in it.

From an income rate to an amount

This original example practises an integration application. A sequence of separate payments and a matrix model call for different setups; use your current chapter to choose the branch.

In a simplified model, a stall receives income continuously at a rate $r(t)=120+30t$ CAD per hour for $0\le t\le4$ , where $t$ is the numerical time in hours after opening. Its receipts ledger already contains 200 CAD at $t=0$ . Let $R(t)$ be the cumulative amount recorded in that ledger, in CAD. No money leaves this ledger. How much income is received during the first two hours, and what does the ledger show at two hours? Before calculating, decide whether using the final rate for both hours will overestimate or underestimate the new income.

Show a hint

A rate times a short time interval gives an approximate amount. Integrate over the requested interval to add those amounts, then decide whether the question asks for the new income or the ledger total.

Show the reasoning

1. Choose the interval and quantity. The new income is $R(2)-R(0)$ , not $R(2)$ . Since the rate is continuous in this model,

$R(2)-R(0)=\int_0^2(120+30t)\,dt.$

2. Find and check a primitive. An antiderivative is $F(t)=120t+15t^2$ . Differentiating with respect to $t$ gives $F^\prime(t)=120+30t=r(t)$ . Thus the new income is $F(2)-F(0)=240+60=300$ CAD. Multiplying CAD per hour by hours gives CAD.

3. Add the known starting amount only for the total. The ledger shows $R(2)=200+300=500$ CAD. The 200 CAD is not additional income earned during the two-hour interval.

4. Check without an antiderivative. The rate rises linearly from $120$ to $180$ CAD per hour. Its average over these two hours is $(120+180)/2=150$ CAD per hour, giving $150(2)=300$ CAD. Using the final rate throughout would give $180(2)=360$ CAD, an overestimate. The ledger records receipts; no cost information was given to calculate profit.

Your turn: a falling rate and a later interval

A new model has income rate $s(t)=180-20t$ CAD per hour for $0\le t\le4$ . Its ledger starts with the same 200 CAD at opening, and no money leaves it. Find the income received from hour 1 to hour 3, then find the ledger total at hour 3. Predict whether multiplying the rate at hour 1 by the two-hour duration overestimates the interval’s income.

Check the interval and the total

An antiderivative is $G(t)=180t-10t^2$ , with $G^\prime=s$ . Income from hour 1 to hour 3 is $G(3)-G(1)=450-170=280$ CAD. The rate falls from 160 to 120 CAD per hour, so its average is 140; over two hours that again gives 280 CAD. Using the starting rate would give $160(2)=320$ CAD, which is too high.

The ledger total at hour 3 includes income from opening: $200+\int_0^3s(t)\,dt=200+450=650$ CAD. Adding 200 to the 1-to-3-hour income would omit the first hour. Check another way: the ledger has $200+170=370$ CAD at hour 1, then receives 280 CAD, reaching 650 CAD.

Review exact changes and starting values The linked model accumulates cost over production quantity rather than income over time. Identify its units and bounds afresh.

Bring the line where you chose the bounds. A tutor can ask what each amount includes before checking the integration.

201-SNY-MS topics to review

Series and summations in financial modelsDifferentiation and integration in applicationsMatrix and vector methodsInvestment, repayment and portfolio modelsGame theory and linear programmingLeontief economic models

Common difficulties

Translating a financial or economic situation into variables and constraints
Choosing between a series, calculus or matrix method
Interpreting a result within the model’s assumptions

How tutoring can help

Lessons follow your course materials and focus on what you want help with. Your tutor adapts to your needs and pace, explaining difficult ideas patiently, step by step. There’s time to ask questions, revisit unclear steps and practise together to build understanding and confidence.

Exam preparation for 201-SNY-MS

Use your section’s outline to select applications. Define the variables, justify the mathematical model, then check whether the result answers the financial or economic question.

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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201-SNY-MS · official course reference