Vectors
Chapter 6
Chapter 6.1 An Introduction to Vectors
Chapter 6.2 Vector Addition
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 8.1 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 9.1 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.
Note on Algebraic Techniques for Evaluating Limits
Note on One-Sided Limits and Continuity
Note on Limits as x approaches Infinity
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
Appendix - Implicit Differentiation
Appendix - Related Rates
Proofs
Proof of Derivative of y = sin x
Proof of Derivatives of Exponential (and Related) Functions
Handouts with Problems
Logarithm Method of Solving Exponential Equations
Exam Review
Calculus and Vectors Exam Review