# Purdue MA 16600 Calculus II: Topics, Study Guide and Practice

> A study guide for Purdue MA 16600 (Analytic Geometry and Calculus II): vectors, integration techniques, infinite series and polar coordinates, with practice.

Source: https://practicecalculus.com/courses/purdue-ma-16600
Updated: 2026-11-03

## At a glance

- **Course code:** MA 16600 (Indiana transfer course IMA 1603, Calculus - Long II)
- **Credit hours:** 4
- **Prerequisites:** C- or better in MA 16500 or MA 16100, among other accepted courses
- **Covers:** Vectors in two and three dimensions, techniques of integration, infinite series, polar coordinates, surfaces in three dimensions
- **Restrictions:** Not open to students with credit in MA 16200
- **Next course:** MA 26100 (Multivariate Calculus)
- **Practice here:** [Calculus 2](/learn/calculus-2)

## Key takeaways

- MA 16600 is Purdue's 4-credit Calculus II course and the continuation of MA 16500.
- It opens with vectors and the dot and cross products, then covers integration techniques and applications.
- The second half covers infinite series, power and Taylor series, parametric curves and polar coordinates.
- A C- or better in MA 16600 is one of the accepted prerequisites for MA 26100.

**Purdue MA 16600**, Analytic Geometry And Calculus II, is the second course in Purdue's main calculus sequence. It is a 4-credit continuation of MA 16500 that adds vectors, integration techniques, infinite series and polar coordinates. This guide maps every MA 16600 topic to practice problems with instant feedback.

## What Purdue MA 16600 covers

The math department lists vectors in two and three dimensions, techniques of integration, infinite series, polar coordinates and surfaces in three dimensions. A Purdue Engineering course outline gives the weekly order: 3D coordinates, vectors, dot and cross products; areas between curves, volumes, shells and average value; integration by parts, trig integrals, trig substitution, partial fractions, tables and approximate integration; improper integrals, arc length, surface area and physics applications; then sequences, series, the integral, comparison, alternating, ratio and root tests, power series, Taylor and Maclaurin series, and finally parametric curves and polar coordinates.

This is a standard **Calculus 2** course with an early vector unit borrowed from Calculus 3.

## MA 16600 topic map

| MA 16600 topic | Practice | Read |
| --- | --- | --- |
| Vectors, dot and cross products | [The dot product](/learn/calculus-3/vectors-and-space/dot-product) | [Dot and cross product](/blog/vectors-dot-and-cross-product) |
| Areas, volumes and shells | [Volumes with washers](/learn/calculus-1/applications-of-integrals/volumes-washers) | [Volumes of revolution](/blog/volumes-of-revolution), [area between curves](/blog/area-between-curves) |
| Average value | [Average value](/learn/calculus-1/applications-of-integrals/average-value) | [Mean value theorem for integrals](/theorems/mean-value-theorem-for-integrals) |
| Integration by parts | [Integration by parts](/learn/calculus-2/integration-techniques/integration-by-parts) | [Integration by parts](/blog/integration-by-parts) |
| Trig integrals and substitution | [Trig substitution](/learn/calculus-2/integration-techniques/trig-substitution) | [Trig substitution](/blog/trig-substitution) |
| Partial fractions | [Partial fractions](/learn/calculus-2/integration-techniques/partial-fractions) | [Partial fractions](/blog/partial-fractions) |
| Approximate integration | [Area with rectangles](/learn/calculus-1/integrals/riemann-sums) | [Riemann sums](/blog/riemann-sums) |
| Improper integrals | [Integrating to infinity](/learn/calculus-2/improper-integrals-and-applications/infinite-limits-of-integration) | [Improper integrals](/blog/improper-integrals) |
| Arc length, surface area, physics | [Arc length and surface area](/learn/calculus-2/improper-integrals-and-applications/arc-length-and-surface-area) | [Center of mass](/learn/calculus-2/improper-integrals-and-applications/center-of-mass) |
| Integral and comparison tests | [Comparison tests](/learn/calculus-2/sequences-and-series/comparison-tests) | [Convergence tests](/blog/convergence-tests) |
| Alternating series, ratio and root tests | [Alternating series](/learn/calculus-2/sequences-and-series/alternating-series) | [Alternating series test](/rules/alternating-series-test), [ratio test](/rules/ratio-test) |
| Power series | [Power series and radius of convergence](/learn/calculus-2/power-series-parametric-polar/power-series-and-radius) | [Power series](/blog/power-series) |
| Taylor and Maclaurin series | [Common Maclaurin series](/learn/calculus-2/power-series-parametric-polar/maclaurin-series) | [Taylor series](/blog/taylor-series) |
| Parametric curves and polar coordinates | [Polar coordinates](/learn/calculus-2/power-series-parametric-polar/polar-coordinates) | [Parametric curves](/learn/calculus-2/power-series-parametric-polar/parametric-curves) |

## MA 16600 in the Purdue sequence

| Course | Credit hours | Role |
| --- | --- | --- |
| MA 16500 | 4 | Prerequisite: Calculus I |
| MA 16600 | 4 | Calculus II, continuation of MA 16500 |
| MA 16200 | 5 | Calculus II, continuation of MA 16100 |
| MA 26100 | 4 | Next: Multivariate Calculus |

Review the first course in the [MA 16500 guide](/courses/purdue-ma-16500), and see what comes next in the [MA 26100 guide](/courses/purdue-ma-26100).

## Example problems at the MA 16600 level

**1. Volume by shells.** Rotate the region under $y = x^2$, $0 \le x \le 1$, about the $y$-axis:

$$V = 2\pi \int_0^1 x \cdot x^2\,dx = 2\pi \left[\frac{x^4}{4}\right]_0^1 = \frac{\pi}{2}$$

**2. Radius of convergence.** For $\sum_{n=0}^{\infty} \frac{x^n}{3^n}$, the ratio test gives $\left|\frac{x}{3}\right| < 1$, so the radius of convergence is $R = 3$.

**3. A cross product.** For $\mathbf{a} = \langle 1, 2, 0 \rangle$ and $\mathbf{b} = \langle 0, 1, 1 \rangle$:

$$\mathbf{a} \times \mathbf{b} = \langle 2 \cdot 1 - 0 \cdot 1,\ 0 \cdot 0 - 1 \cdot 1,\ 1 \cdot 1 - 2 \cdot 0 \rangle = \langle 2, -1, 1 \rangle$$

## How to do well in Purdue MA 16600

- **Start vectors strong.** They come first and return in MA 26100. The [cross product lesson](/learn/calculus-3/vectors-and-space/cross-product) is a quick refresher.
- **Practice picking a technique.** Mixed problems in [choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy) mirror exam questions.
- **Build a series checklist.** Try the [nth-term test](/rules/nth-term-test) first, then compare to geometric or p-series, then reach for the ratio test.
- **Keep the [formula sheet](/formulas) handy** for Maclaurin series and trig identities, and take timed [practice exams](/practice).
- **Review** [common calculus mistakes](/blog/common-calculus-mistakes) before every exam.

> **Tip:** for interval of convergence, the ratio test gives the open interval. Always check the two endpoints separately.

## Frequently asked questions

### What is MA 16600 at Purdue?

MA 16600, Analytic Geometry And Calculus II, is the continuation of MA 16500. It covers vectors in two and three dimensions, techniques of integration, infinite series, polar coordinates and surfaces in three dimensions.

### What do I need before MA 16600?

A Purdue course outline lists a C- or better in MA 16500 or MA 16100 among the accepted prerequisites, along with several other course combinations. Check the current catalog for your situation.

### What is the difference between MA 16600 and MA 16200?

MA 16200 is the 5-credit continuation of MA 16100, and MA 16600 is the 4-credit continuation of MA 16500. They cover similar topics, and MA 16600 is not open to students with credit in MA 16200.

### Is MA 16600 hard?

Many students find Calculus II the toughest course of the sequence, because integration requires choosing a technique and series need a new kind of reasoning. Daily mixed practice helps the most.

### What comes after MA 16600?

MA 26100, Multivariate Calculus, which covers lines, planes and curves in three dimensions, differential calculus of several variables, multiple integrals and an introduction to vector calculus.