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MATH241

MATH241 (Calculus III) is a 4-credit-hour class that is a important prerequisite for later courses, and is required for the Math and Sciences requirement for both EE and CE students. It is offered in the Fall, Spring, and Summer.

Content Covered

  • Euclidean space
  • Partial Differentiation
  • Multiple Integrals
  • Line Integrals
  • Surface Integrals
  • Integral Theorems of Vector Calculus

Calculus III continues where Calculus II left off, introducing the cross and dot product of vectors within the Euclidean (x,y,z) space, cylindrical (r,θ,z) space, and the spherical (r, θ, Φ) space for Midterm 1. This is followed by the gradient (∇) function, as well as partial differentiation and multiple integrals for Midterm 2. In the later portion of the course, the Jacobian matrix, change of variables, and Lagrange multipliers are covered for Midterm 3. For Midterm 4 and beyond, line integrals, surface integrals, as well as Green's, Stokes', and the divergence theorems are taught.

Prerequisites

Students are required to have completed MATH231 (Calculus II) or received at least a 4 on AP Calculus BC.

When to Take it

This course should be taken in either semester freshman year assuming you have previously taken Calculus AB or BC, or as soon as possible. Many other courses (PHYS213/214, MATH285, ECE210) later within the EE/CE courseflow require Calculus III as prerequisites. PHYS212 allows for concurrent registration.

Course Structure

Students who have taken Calculus II at UIUC can expect more of the same, but those who take this course as an incoming student may be in for a shock. Expect to rely on office hours to learn confusing material, with weekly discussions and homeworks being most of the workload. Homeworks are autograded through WebAssign, which requires a expensive and required license. Discussions used to be graded by completion, but have recently switched to being graded by correctness and completion (One of the two problems is randomly picked to be graded).

This course has a total of four 50-minute midterms, which cover approximately the previous 3-4 weeks of material. There is also a 3-hour final exam, which also replaces the lowest midterm if higher. All exams are eligible for curves, but rarely are. Expect your gradescope score to be close to, if not exactly your exam grade. The grading distribution is as follows:

  • WebAssign Homeworks (15%)
  • Discussion sections and participation (10%)
  • Best three midterms (45% total, 15% each)
  • Final examination (30%)

Instructors

Instructors for this course vary based on student demand and registration. For this current semester (Fall 2023), the instructor list includes Professors Matthew Russell, Jeremiah Heller, and Ian Cavey, with Charles Rezk teaching the honors section. Professors Iftikhar Ahmed and Aldo Manfroi have previously taught the course.

Course Tips

Many previous criticisms of this course have been partially resolved; discussion worksheets used to be on content that had not even been taught for some sections. Ask your TAs questions, and attend office hours whenever you are confused. Online course resources will be very useful, as Calculus III is taught the same way at Illinois as it is at many other colleges. Since exams comprise such a significant portion of your grade, look to using former exams from other universities for excellent practice materials.

Life After

Calculus III is an important prerequisite for many courses, as previously mentioned. Expect to use information learned in this course in later classes. Topics such as cross and dot products appear almost everywhere throughout the physics courses, and more advanced theorems appear in classes like ECE329.

Infamous Topics

Much of Calculus III's topics are fairly moderate in difficulty, but Green's and the divergence theorem are quite challenging. Save your midterm drop for Midterm 4, as you are given a very small amount of time to learn difficult material.

Resources

  • Paul's Online Math Notes is a crucial set of notes which covers every topic in class, and even includes practice problems with walkthrough solutions.