Math Analysis

Course Syllabus

Matrices:

• Matrix Operations
• Solving Systems with matrices

Function Families: General Topics

• Interval notation
• Increasing or decreasing intervals
• Find the maximum/minimum value of a function
• Identify if the function is odd, even, or neither
• Intercepts and the meaning of intercepts
• Find where the function equals to zero
• End-behavior
• Domain & Range

Function Families: Types & Properties of Families

• Linear
• Quadratic
• Polynomial
• Rational
• Exponential
• Logarithmic

Trigonometry Unit: 

• Trigonometric ratios
• Trigonometric identities
• Inverse trig functions
• Graphing trig functions
• Solving trig equations

Conic Sections Unit:

• Classifying conics
• Finding the center of a conic section
• Graphing conic sections

Polar Coordinates & Vectors:

• Graphing in the polar plane
• Converting between rectangular & polar
• Polar equations
• Vector operations
• Dot product
• Graphing vectors & vector properties

Sequences & Series Unit: Arithmetic & Geometric

• Sigma notation
• Finding the sum of a series
• Expanding a binomial
• Mathematical Induction

Limits & Continuity Unit:

• Describing the continuity of functions graphically and algebraically
• Finding limits as the variable approaches infinity or a specific value

Differentiation Unit:

• Tangent lines
• The derivative
• Product/Quotient and higher order rules
• The Chain Rule
• Implicit Differentiation
• Related Rates

Applications of Differentiation:

• Extrema of an interval
• Rolle’s Theorem and the Mean Value Theorem
• First Derivative Test – increasing & decreasing behaviors
• Second Derivative Test – concavity
• Curve Sketching
• Optimization
• Differentials