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MATH231

MATH231 (Calculus II) is a four credit hour calculus course, typically required for most engineering majors at UIUC, and is slightly more difficult than MATH221 (Calculus I).

Content Covered

  • Integration by parts
  • Trigonometric integrals and substitution
  • Partial fraction integration and advanced integration (approximate, improper, etc.)
  • Arc length and surfaces of revolution, and engineering applications
  • Series and sequences (tests, power series, Taylor and Maclaurin)
  • Parametric curves
  • Polar coordinates and applications

This class continues MATH220 (Calculus) and MATH221, with the beginning of the class dedicated to integrals covered at the end of previous courses. MATH221 next covers more advanced integration techniques which can require some memorization. Afterwards, MATH231 covers sequencies and series, which are difficult topics that are the source of MATH231's reputation for being difficult.

The majority of the content covered in this course is similar to AP Calculus BC, with most deviations in covering additional applications.

Prerequisites

There are two possible paths to take MATH231:

It is important to be comfortable with integration concepts covered in whichever previous course you take.

When to Take It

To graduate on time and get to ECE courses, MATH231 should be skipped (i.e. via AP Credit) if possible, and if not, taken during freshman year. MATH231 is offered during both the fall and spring semesters.

Typically, the fall offering of this course is called “Engineering Calculus II”. Taking the regular version instead of the engineering one makes no difference on requirement fulfillment, though the engineering one has been said to be more difficult.

Course Structure

Like other introductory math courses, homework is submitted online through Cengage WebAssign, which requires purchasing an access code. MATH231's homework assignments are typically more time-consuming than previous calculus courses in the Illinois Math curriculum.

Exams in MATH231 are offered either through the CBTF or on paper, depending on the instructor.

Instructors

The professors teaching this course change pretty much every semester, and professor names typically aren’t released until just before the semester begins. The only name that commonly appears is Professor Guzman.

Course Tips

While MATH231 is sometimes called a "weed out" course, this is not entirely true, and the course is manageable with good study and exam strategies:

  • utilize office hours frequently
  • spend time to study every day and make sure to memorize important concepts
  • show as much work as possible on paper exams

Life After

Series skills from MATH231 will be useful in ECE210.

After completing MATH231, most students take MATH241 (Calculus III) and/or MATH257 (Linear Algebra). If taking MATH231 during a spring semester, it is recommended to take MATH241 over the summer to get to postrequisite courses faster.

Infamous Topics

  • Series and sequences: Considered by many to be the worst part of MATH231. A lot of different tests for convergence and divergence can overwhelm the student.
  • Parametric curves: Can be somewhat unintuitive. Make sure you put in the time to understand this.
  • Polar coordinates: Many students have not seen polar coordinates before this class, and being asked to do calculus using them may seem confusing.

Resources

  • Professor Leonard has a fantastic lecture series for this class (and most math classes required for the ECE curriculum)
  • 3blue1brown has a great video series going over the fundamental ideas behind calculus, which is good for building intuition beyond computations