Welcome to Calculus II (MAT K256)

Welcome back to class! I am thrilled to kick off this semester with you. Calculus II is a fascinating journey where we take the foundational tools you learned in Calculus I—limits, derivatives, and basic integrals—and apply them to solve much more complex and interesting problems. It is often considered the bridge between basic calculus and the multidimensional world of Calculus III and Differential Equations.

Course Overview & Key Concepts

This semester, we will be diving deep into the textbook Calculus, Early Transcendentals by James Stewart (8th Edition). Our focus will be split into several major mathematical pillars:

  • Advanced Techniques of Integration: We move beyond simple substitution. You will master methods like Integration by Parts ($$ \int u \, dv = uv - \int v \, du $$), partial fractions, and trigonometric substitution to handle complex integrals.
  • Applications of Integration: We won't just solve equations; we will visualize them. We will calculate the volumes of revolution using disks, washers, and cylindrical shells, and analyze the work required to move objects against force.
  • Parametric Equations & Polar Coordinates: We will break away from standard Cartesian coordinates ($x, y$) to explore curves defined by parameters and polar systems, which are essential for describing curved motion and complex shapes.
  • Sequences and Series: Perhaps the most abstract and powerful part of the course. We will determine if infinite lists of numbers converge to a limit or diverge. You will learn to represent functions as infinite polynomials known as Taylor and Maclaurin Series: $$ f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!} (x-a)^n $$

Course Logistics and Grading

Success in this course relies heavily on consistency. According to the attached syllabus, attendance is vital to your success. Here is a quick breakdown of how your performance will be measured:

  • Participation: 10%
  • Three Tests: 20% each (60% total)
  • Final Exam: 30%

Additionally, remember that all students are required to maintain an online learning portfolio in Digication to monitor your growth throughout the semester.

New This Semester: Question Form

To make our time in the classroom as efficient as possible, I am introducing a new system this semester. I have created a "Questions for Next Week's Class" form. If you are stuck on a homework problem or a specific concept (like the Ratio Test or Improper Integrals), please fill this out before we meet.

I will be reviewing these submissions to tailor our in-class discussions and ensure we are tackling the exact hurdles you are facing. I will explain exactly how to use this tool during class tonight.

Please download the full syllabus below to review the schedule, office hours (Room D205), and academic policies. Let's make this a great semester!