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More Helpful Tools for the Mathematics of Calculus

The chapter will introduce strategies, tools, and supplemental material that is helpful for the understanding of Calculus. This chapter is not required for the Calculus sequence, but will provide more background and access to extension problems later in the text.
The chapter begins with an introduction to formal and symbolic logic. This will introduce logical operators, definitions, and arguments. The second topic will be about proof. There are three main parts to this section: Direct Proof, Indirect Proof, and Proof by Induction. A brief historical note on applications of logic and proof will then be discussed before moving on the more algebraic supplements. A very quick introduction to Linear Algebra is provided to introduce matrices and basic operations. Finally, the chapter ends with Pascal’s Triangle and it’s applications.
By the end of this chapter, you should understand:

• The different Logical Operators
• The definitions of argument, valid, sound, and proposition
• How to write a logical argument using propositions
• What the main types of proof are and their strategies
• How to write a formal proof in mathematics or logic
• What equinumerous sets are and how they are described
• What a matrix is and how it can be used
• The basic matrix operations
• How to construct Pascal’s Triangle
• How to use Pascal’s Triangle to expand a binomial

List of Topics in this Chapter:

1. Logic
2. Proof
3. An Introduction to Linear Algebra
4. Pascal’s Triangle and Binomial Expansions
5. Summation

Unit Daily Plan

Practice Problems

1. Logic
2. Proof
3. An Introduction to Linear Algebra
4. Pascals Triangle and Binomial Expansions
5. Summation

Sample Assessments

1. Logic
2. Proof
3. An Introduction to Linear Algebra
4. Pascals Triangle and Binomial Expansions
5. Summation

Solution Sets

1. Logic
2. Proof
3. An Introduction to Linear Algebra
4. Pascals Triangle and Binomial Expansions
5. Summation