12 Calculus
Introduction to Calculus
 Radical expression Rationalizing Denominators
 The Slope of a Tangent
 Rates of Change
 Limit of Function
 Properties of Limits
 Continuity
Derivatives
 The Derivatives Function
 The Derivatives of Polynomial Functions
 The Product Rule
 The Quotient Rule
 The Derivatives of Composite Functions
 Higher Order Derivatives, Velocity and Acceleration
 Minimum and Maximum on an interval
Curve Sketching
 Increasing and Decreasing Functions
 Critical Points, Local Maxima and Local Minima
 Vertical and Horizontal Asymptotes
 Concavity and Points of Inflection
 An Algorithm for Curve Sketching
Derivatives of Exponential and Trigonometric Functions
 Derivatives of Exponential Functions, y = e×
 The Derivatives of the General Exponential Function, y = b×
 Optimization Problem Involving Exponential Functions
 The Derivatives of y = sin x and y = cos x
 The Derivatives of y = tan x
An Introduction to Vector
 Introduction to Vector
 Vector Addition
 Multiplication of a Vector by a Scalar
 Properties of Vectors
 Vectors in R² and R³
 Operations with Algebraic Vectors in R²
 Linear Combinations and Spanning Sets
Applications of Vectors
 Vectors as Forces
 Velocity
 The Dot Product of Two Geometric Vectors
 The Dot Product of Algebraic Vectors
 Scalar and Vector Projections
 The Cross Product of Two Vectors
 Applications of the Dot Product and Cross Product
Equations and Lines and Planes
 Vector and Parametric Equations of a line in R²
 Cartesian Equation of a Line
 Vector Parametric Equations of a Line in R³
Relationships between Points, Lines and Planes
 The Intersection of a Line with a Plane and the Intersection of Two Lines
 Systems of Equations
 The Intersection of Two Planes
