Welcome to the Spring 2024 semester! I am thrilled to have you in Calculus 2. This course is a pivotal step in your mathematical education, bridging the gap between the foundational concepts of differentiation and the complex applications of accumulation and infinite series.

Course Logistics and Essentials

To ensure a smooth start to the semester, please review the following critical information and set up your accounts immediately:

  • Class Syllabus: Please read the syllabus thoroughly. It contains the roadmap for the semester, grading policies, and the schedule of topics.
  • WebAssign Registration: Homework will be submitted via WebAssign. You can access the course using the Class Key below:
    • Class Key: TRCC.MOHEGAN 5801 7599
  • Hybrid/Remote Access: For those attending online, we utilize Google Meet. Note: Please email me in advance if you plan to join remotely so I can look out for your login request.
  • Class Notes: PDF copies of the lecture notes and whiteboard sessions are available for download.

What to Expect in Calculus 2

In Calculus 1, we spent a great deal of time mastering the derivative, $f'(x)$, and the basic concept of the definite integral. In this course, we expand our toolkit significantly.

1. Techniques of Integration
We will move beyond basic anti-derivatives and learn powerful techniques to solve complex integrals, such as Integration by Parts, which acts as the reverse Product Rule:

$$ \int u \, dv = uv - \int v \, du $$

2. Applications of Integration
We will apply integration to calculate volumes of revolution, arc lengths, and surface areas. You will learn how to visualize 3D shapes generated by rotating curves around an axis.

3. Sequences and Series
Perhaps the most distinct shift in Calc 2 is the study of infinite series. We will analyze convergence and divergence, culminating in Taylor Series, which allows us to approximate complex functions using polynomials:

$$ f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!} (x-a)^n $$

Keys to Success

Calculus 2 has a reputation for being challenging because it requires a strong command of Algebra and Trigonometry. Consistency is key. Make sure to keep up with the WebAssign homework and review your class notes daily. If you find yourself struggling with a concept, please reach out or join the Google Meet sessions.

I look forward to a great semester exploring the beauty of mathematics with you!