Calculus II
The second semester of 1st year Calculus is the preparatory course for all of the 2nd year courses (Multivariable Calculus, Differential Equations, Linear Algebra). Often referred to as "the first course on integral calculus", Calculus II focuses on a more practical, computational command of the integral, which is only introduced as a concept in Calculus I.Calculus II is comprised of two distinct parts:
- Techniques of Integration
When you (or a computer) can algebraically integrate a function, how is that accomplished? Essentially, the Rules of Differentiation are "inverted" to the integral, providing the main strategies for attacking the algebraic integral - when possible. - When Algebraic Integration Just Can't Be Done
The vast majority of functions cannot be algebraically integrated - there just is no algebraic antiderivative for such functions. The development of "Plan B" for attacking these types of algebraic integrals comes in the form of expanding the way we describe functions, not just with the elementary class of functions including such friends as sin(x), ex, x1/2, etc. but with a more generalized description based upon infinite polynomials. This raises all kinds of questions that have to be studied, but once accomplished, we are able to conquer these algebraic integrals.
Curriculum: Calculus&LiveMath™
The curriculum for Calculus II is the e-textbook Calculus&LiveMath™, which is converted from the original Calculus&Mathematica™ courseware series by Davis/Porta/Uhl (published by MathEverywhere, Inc.To accompany these LiveMath™ notebooks from this e-text, we also present Video Commentary Lectures on the Basics and Tutorials notebooks in the Calculus&LiveMath™ e-text. These videos demonstrate how to use LiveMath™ as well as discuss the Calculus topics, as if reading and exploring along with the professor (which is exactly what you are doing!).
Examples of the Curriculum
Below are some PDF "print outs" of a few of the LiveMath™ notebooks from Calculus&LiveMath™ by Davis/Porta/Uhl. Included as well is an example homework notebook completed by a student in the course, demonstrating how the homework notebooks become the "common blackboards" that the students and instructor both write on in their "conversation" about the notebook.- Basics Notebook Example: 2.03.B1 - Measurements based on slicing and accumulating: Area and Volume
- Basics Notebook Commentary Movie: iTunes or VLC
- Homework Notebook Example: 2.03.G1 - Using the tools: Measurements of accumulation
Course Catalog Listing
Course Description: Further study of the integral, volume of a solid of revolution, length of a curve, area of a surface of revolution, work, moments, and centroids. Applications of differential and integral calculus to improper integrals, infinite series, polynomial approximations of functions, Taylor's Theorem, conics, polar coordinates, and vector analysis.
Prerequisite: Calculus I
Detailed Course Syllabus in PDF