# Vectors and Calculus Notes and Handouts

Vectors

Chapter 6

Chapter 6.1     An Introduction to Vectors

Chapter 6.3     Multiplication of a Vector by a Scalar

Chapter 6.4     Properties of Vectors

Chapter 6.5     Vectors in R2 and R3

Chapter 6.6 and 6.7     Operations with Algebraic Vectors in R2 and R3

Chapter 6.8     Linear Combinations and Spanning Sets

Chapter 7

Chapter 7.1     Vectors as Forces

Chapter 7.2     Velocity

Chapter 7.3     The Dot Product of Two Geometric Vectors

Chapter 7.4     The Dot Product of Two Algebraic Vectors

Chapter 7.5     Scalar and Vector and Projections

Chapter 7.6     The Cross Product of Two Vectors

Chapter 7.7     Applications of the Dot Product and Cross Product

Chapter 8

Chapter 8.1     Vectors and Parametric Equations of a Line in R2

Chapter 8.2     Cartesian Equation of a Line

Chapter 8.3     Vector, Parametric and Symmetric Equations of a line in R3

Chapter 8.4     Vector and Parametric Equations of a Plane

Chapter 8.5     The Cartesian Equation of a Plane

Chapter 8.6     Sketching Planes in R3

Chapter 9

Chapter 9.1     The Introduction of a Line with a Plane and the Intersection of Two Lines

Chapter 9.2     Systems of Equations

Chapter 9.3     The Intersection of Two Planes

Chapter 9.4     The Intersection of Three Planes

Chapter 9.5     The Distance from a Point to a Line in R2 and R3

Chapter 9.6     The Distance from a Point to a Plane

Calculus

Chapter 1

* - Please note that we do Chapter 1 a little bit differently than your textbook, so there is not a direct link between handout numbers
and your text for the handouts related to Chapter 1.

Chapter 1.1     Radical Expressions:  Rationalizing Denominators

Initial Limits Worksheet

Note on Algebraic Techniques for Evaluating Limits

Note on One-Sided Limits and Continuity

Chapter 1.6     Continuity

Chapter 2

Chapter 2.1     The Derivative Function

Chapter 2.2     The Derivatives of Polynomial Functions

Chapter 2.3     The Product Rule

Chapter 2.4     The Quotient Rule

Chapter 2.5     The Derivatives of Composite Functions

Chapter 3

Chapter 3.1     Higher Order Derivatives, Velocity and Acceleration

Chapter 3.2     Minimum and Maximum on an Interval (Extreme Values)

Chapter 3.3 and 3.4     Optimization Problems, including Optimization Problems in Economics and Science

Chapter 4

Chapter 4.1     Increasing and Decreasing Functions

Chapter 4.2     Critical Points, Local Maxima, and Local Minima

Chapter 4.3     Vertical and Horizontal Asymptotes

Chapter 4.4     Concavity and Points of Inflection

Chapter 5

Chapter 5.1, 5.2 and 5.3     Derivatives of Exponential Functions with Base e; Derivatives of Exponential Functions with More General Bases; Optimization Problems Involving Exponential Functions

Appendices

Handouts with Problems

Logarithm Method of Solving Exponential Equations

3D Optimization Problems

Exam Review