SFU MATH 152 Calculus II: Syllabus, Topics and Practice

MATH 152 is Calculus II at Simon Fraser University, the course that follows MATH 150 or MATH 151. Since SFU's first course is all about derivatives, MATH 152 carries the full weight of integral calculus and then moves on to sequences and series. This guide maps each MATH 152 topic to free practice so you can build the skills one small problem at a time.

What SFU MATH 152 covers

The SFU calendar lists the MATH 152 topics as: Riemann sums, the Fundamental Theorem of Calculus, definite, indefinite and improper integrals, approximate integration, integration techniques, and applications of integration; first-order separable differential equations and growth models; and sequences and series, series tests, power series, convergence and applications of power series.

That is a combination of the second half of a typical Calculus 1 (definite integrals and the Fundamental Theorem) and most of a typical Calculus 2. Parametric and polar curves are not listed, because SFU already covers them in MATH 151.

MATH 152 topic map

Where MATH 152 sits at SFU

MATH 155 and MATH 158 are alternative second courses for other programs, and you cannot take MATH 152 for credit if you already have one of them.

Example problems at the MATH 152 level

1. The Fundamental Theorem. If F(x) = \int_0^{x^2} \cos t \, dt, then by the chain rule F'(x) = 2x\cos(x^2).

2. An improper integral.

3. A growth model. Solve \frac{dy}{dt} = 0.3y with y(0) = 50. Separating variables gives y = 50e^{0.3t}.

4. Radius of convergence. For \sum \frac{x^n}{n\,3^n}, the ratio test gives \frac{|x|}{3} < 1, so the radius is R = 3.

How to do well in MATH 152

• Learn to pick the method. Integration problems rarely say which technique to use. Practice mixed sets like choosing a strategy so you learn to recognise the shape of each integral.
• Keep derivatives sharp. Every antiderivative is a derivative read backwards, so weak derivative rules make integration slow.
• Write the test you are using. For each series, name the test and check its conditions before you conclude. Graders look for this.
• Practise little and often. Short, frequent sessions in practice beat long cramming sessions before midterms.

Tip: before choosing a convergence test, try the nth term test. If the terms do not go to zero, the series diverges and you are done.