# Rutgers Math 152 (01:640:152) Calculus II: Study Guide and Practice

> A study guide for Rutgers Math 152, Calculus II for the Mathematical and Physical Sciences: integration, series, power series, polar and complex numbers.

Source: https://practicecalculus.com/courses/rutgers-01-640-152
Updated: 2026-11-03

## At a glance

- **Course code:** 01:640:152 (Math 152)
- **Credits:** 4
- **Offered:** Fall, spring and summer
- **Prerequisites:** Calculus I: Math 135 or Math 151 (not Math 130)
- **Covers:** Integral calculus and its applications, infinite series and power series, parametric curves, polar coordinates, complex numbers
- **Next course:** 01:640:251 Multivariable Calculus
- **Practice here:** [Calculus 2](/learn/calculus-2)

## Key takeaways

- Math 152 continues Math 151 and is the second course in the Rutgers New Brunswick calculus sequence for the mathematical and physical sciences.
- It is a 4-credit course offered in fall, spring and summer.
- It covers integral calculus and applications, infinite series and power series, parametric curves, polar coordinates and complex numbers.
- Math 152 is the prerequisite for Math 251 Multivariable Calculus.

**Rutgers Math 152** (01:640:152, Calculus II for the Mathematical and Physical Sciences) is the second semester of the Rutgers New Brunswick calculus sequence for math, science and engineering majors. It follows Math 151 (or Math 135) and leads to Math 251 Multivariable Calculus. This guide maps every Math 152 topic to a lesson you can practice with instant feedback.

## What Rutgers Math 152 covers

The Rutgers math department lists integral calculus and its applications, the theory of infinite series and power series, parametric curves, polar coordinates, and complex numbers. Its learning goals include using integrals to find volumes, arc lengths and surfaces of revolution; finding antiderivatives with u-substitution, integration by parts and trigonometric substitution; and deciding whether a series converges, then finding and using Taylor series.

Like Math 151, it meets for two lectures and one workshop each week (other than asynchronous online sections).

That is a full **Calculus 2**, with complex numbers as an extra. It lines up with all four units of the Calculus 2 path on PracticeCalculus.

## Math 152 topic map

| Math 152 topic | Practice | Read |
| --- | --- | --- |
| u-substitution | [U-substitution refresher](/learn/calculus-2/integration-techniques/u-substitution-refresher) | [U-substitution](/blog/u-substitution), [the rule](/rules/u-substitution-rule) |
| Integration by parts | [Repeated parts and LIATE](/learn/calculus-2/integration-techniques/repeated-parts-and-liate) | [Integration by parts](/blog/integration-by-parts) |
| Trig substitution | [Trig substitution](/learn/calculus-2/integration-techniques/trig-substitution) | [Trig substitution](/blog/trig-substitution) |
| Volumes | [Volumes with washers](/learn/calculus-1/applications-of-integrals/volumes-washers) | [Volumes of revolution](/blog/volumes-of-revolution) |
| Arc length and surfaces of revolution | [Arc length and surface area](/learn/calculus-2/improper-integrals-and-applications/arc-length-and-surface-area) | [Improper integrals](/blog/improper-integrals) |
| Infinite series | [Series and partial sums](/learn/calculus-2/sequences-and-series/series-and-partial-sums) | [Geometric series](/blog/geometric-series) |
| Convergence tests | [Comparison tests](/learn/calculus-2/sequences-and-series/comparison-tests) | [Convergence tests](/blog/convergence-tests), [ratio test](/rules/ratio-test) |
| Power and Taylor series | [Taylor polynomials](/learn/calculus-2/power-series-parametric-polar/taylor-polynomials) | [Power series](/blog/power-series), [Taylor series](/blog/taylor-series) |
| Parametric curves | [Arc length of parametric curves](/learn/calculus-2/power-series-parametric-polar/parametric-arc-length) | [Implicit differentiation](/blog/implicit-differentiation) |
| Polar coordinates | [Polar coordinates](/learn/calculus-2/power-series-parametric-polar/polar-coordinates) | [Area between curves](/blog/area-between-curves) |
| Complex numbers | [Common Maclaurin series](/learn/calculus-2/power-series-parametric-polar/maclaurin-series) | [Taylor series](/blog/taylor-series) |

We do not have a dedicated complex numbers lesson. The Maclaurin series lesson is the closest match, since Euler's formula $e^{i\theta} = \cos\theta + i\sin\theta$ comes from comparing the series for $e^x$, $\sin x$ and $\cos x$.

## The Rutgers math and physical sciences sequence

| Course | Credits | Covers |
| --- | --- | --- |
| [Math 151 Calculus I](/courses/rutgers-01-640-151) | 4 | Derivatives, Mean Value Theorem, intro to integrals |
| Math 152 Calculus II | 4 | Integration, series, parametric, polar, complex numbers |
| [Math 251 Multivariable Calculus](/courses/rutgers-01-640-251) | 4 | Three-dimensional geometry, partials, multiple integrals, vector analysis |

Students who started with [Math 135](/courses/rutgers-01-640-135) may also take Math 152, although the department recommends the Math 151 route.

## Example problems at the Math 152 level

**1. Integration by parts with a log.** With $u = \ln x$ and $dv = x^2\,dx$:

$$\int x^2 \ln x\,dx = \frac{x^3}{3}\ln x - \int \frac{x^3}{3} \cdot \frac{1}{x}\,dx = \frac{x^3}{3}\ln x - \frac{x^3}{9} + C$$

**2. A parametric slope.** For $x = t^2$, $y = t^3$:

$$\frac{dy}{dx} = \frac{3t^2}{2t} = \frac{3t}{2}, \qquad \text{so at } t = 2, \ \frac{dy}{dx} = 3$$

**3. Complex numbers in polar form.** Since $1 + i = \sqrt{2}\,e^{i\pi/4}$,

$$(1 + i)^8 = (\sqrt{2})^8 e^{2\pi i} = 16$$

## How to do well in Math 152

- **Make LIATE a habit.** Choosing $u$ well is most of integration by parts. The [repeated parts and LIATE](/learn/calculus-2/integration-techniques/repeated-parts-and-liate) lesson drills it.
- **Work series problems in mixed sets.** Exams rarely tell you which test to use. Practice [choosing a test](/learn/calculus-2/sequences-and-series/choosing-a-test).
- **Connect polar and complex numbers.** Both use $r$ and $\theta$, and multiplying complex numbers in polar form is just multiplying lengths and adding angles.
- **Keep the [formula sheet](/formulas) close**, review [common calculus mistakes](/blog/common-calculus-mistakes), and take timed [practice exams](/practice).

> **Tip:** if the terms of a series do not go to zero, it diverges. Check the [nth-term test](/rules/nth-term-test) before anything else.

## Frequently asked questions

### What is Rutgers Math 152?

Math 152 (01:640:152) is Calculus II for the Mathematical and Physical Sciences at Rutgers New Brunswick. It covers integral calculus and its applications, the theory of infinite series and power series, parametric curves, polar coordinates and complex numbers.

### Can I take Math 152 after Math 135?

Yes. The prerequisite is Math 135 or Math 151 (not Math 130). The department says taking Math 152 after Math 135 is possible but not a recommended sequence, and suggests Math 151 for students who will need Math 152.

### What comes after Math 152?

Math 251 Multivariable Calculus, which lists Calculus II as its prerequisite.

### Is Rutgers Calc 2 hard?

Calculus II is often the hardest course in the sequence, because integration techniques and series tests require choosing a method. The department offers Math 158, a 1-credit practicum in the first weeks of the term, for students who are more likely to struggle.

### What should I review before Math 152?

Antiderivatives, u-substitution and the Fundamental Theorem from Calculus I. Comfort with trig identities also helps a lot once trigonometric substitution starts.