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MATH221

MATH221 (Calculus I) is an introductory, four credit hour calculus course intended for freshman students with some previous exposure to calculus concepts.

Content Covered

  • Limits & Continuity
  • Derivatives of Polynomials and Exponential Functions
  • Derivative Rules (Product, Quotient, Chain)
  • Application of Derivatives (Optimization, Newton’s Method, Related Rates, etc.)
  • Integration (Both Definite & Indefinite)
  • Integration Rules (Substitution)
  • Application of Integration (Area, Volume, Solids of Revolution, Work, etc.)

MATH221 begins with late pre-calculus and early calculus topics such as limits and continuity, and then continues onto differentiation, integration, and their applications. Previous experience with calculus is beneficial, but not required, and the rigor of MATH221 compared to AP Calculus AB may be a bit of a jump.

Prerequisites

There are three possible paths to take MATH221:

  • One year of highschool calculus
  • A score of at least 2 on the AP Calculus BC exam
  • An adequate ALEKS placement score

The course is computation-heavy, so it is important to have a strong algebra and pre-calculus base.

When to Take It

Nearly every course in the ECE curriculum directly or indirectly depends on MATH221, so it should be completed as soon as possible, ideally during fall of freshman year. If possible, it is recommended to skip this course with an AP Exam, proficiency exam, or via dual enrollment in high school.

Course Structure

As with most courses meant for first-semester freshman, the workload of MATH221 is not extreme. Homework assignments are offered through Cengage WebAssign (which you'll have to pay for), and can be completed relatively quickly with a thorough understanding of the material.

Since this course is an introductory course, the instructors change frequently, and with this, so do the exam and homework formats. As a rule of thumb, expect at least one homework assignment per week, three midterms, and a final exam.

Exams will typically consist of new problems, which are similar to homework problems but have a lower difficulty.

Instructors

The instructors for this course change frequently, although Professor Whittlesey and Professor Placzek are both frequent instructors and have the most experience teaching the course.

Course Tips

MATH221 is often described as the "calm before the storm" of MATH231 (Calculus II), so it is important to fully understand all the topics covered in MATH221 to make future courses easier. Since MATH221 requires previous exposure to calculus, most students will not attend office hours because they already (sometimes incorrectly) feel confident with material - this makes office hours a great opportunity to solidify any gaps in your knowledge since you'll have lots of time to ask questions.

Since the exam and homework format may change drastically semester by semester, use the generic advice of:

  • showing all your work on paper exams (if any) to ensure partial credit
  • starting the homework early to ensure you have time to seek help
  • attend lectures even if you feel confident about the topics being taught about (Math @ Illinois likes adding some special twists to what they teach, which you probably haven’t seen before)

Life After

The fundamentals of calculus are a vital skill in an engineer’s toolbox, with classes like ECE210 and ECE330 heavily relying on understanding of derivatives and their properties. After completing this class, a lot more doors will open for future coursework. MATH231 and MATH257 (Linear Algebra with Computational Applications) can both be taken immediately after MATH221.

Infamous Topics

  • Epsilon-Delta: Defining limits in this way is often unintuitive and much more mathematically rigorous than other parts of the course.
  • Optimization: Another topic that not all students have seen in high school level calculus classes, which can be difficult without a solid understanding of derivatives
  • Solids of Revolution: Typically introduced as one of the first applications of integration. These can be difficult to visualize and/or compute without a solid understanding of integration.

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