Welcome to Calculus II (Fall 2017)

Welcome to the start of the semester! I am looking forward to a productive term exploring advanced integration, series, and vector calculus. This website will serve as your central hub for all class materials, including PowerPoints, review sheets, and important announcements.

Administrative Essentials

Before we dive into the mathematics, please ensure you complete the following housekeeping items to ensure you stay connected and informed:

  • Course Syllabus: Please review the Class Syllabus attached to this post carefully. It outlines the grading policy, attendance requirements, and our full schedule. Note that office hours are held Tuesdays and Thursdays from 4:00 pm to 6:00 pm in Room D205.
  • Contact Form: Please complete the Contact Form immediately. This allows me to contact you if I need to cancel class due to weather or send out urgent information to the group.
  • Textbook: We will be using Calculus, Early Transcendentals by James Stewart (8th Edition).

Tonight's Lesson: The Definite Integral (Section 5.2)

We are hitting the ground running by picking up where Calculus I left off. Tonight's lesson focuses on Section 5.2.

In this section, we transition from approximating areas using finite rectangles to finding exact areas using limits. The fundamental definition we are exploring is the Definite Integral, defined as the limit of Riemann sums:

$$ \int_a^b f(x) \, dx = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i^*) \Delta x $$

Key Concepts to Master:

  • Geometric Interpretation: The definite integral $\int_a^b f(x) \, dx$ represents the net signed area between the graph of $f(x)$ and the x-axis from $x=a$ to $x=b$.
  • Notation: $f(x)$ is the integrand, $a$ and $b$ are the limits of integration, and $dx$ indicates the variable of integration.
  • Properties: We will also discuss properties of the integral, such as splitting the interval: $\int_a^c f(x) \, dx + \int_c^b f(x) \, dx = \int_a^b f(x) \, dx$.

Homework & Preparation

According to the course outline, the suggested practice problems for Section 5.2 involve odd numbers (e.g., pg 389 / 17-19, 33, 47-53). Consistent practice is essential to your success in this course. Let's have a great semester!