Advance Math

Functions in general

Definition of a function (presented multiple ways including graphically: vertical line test)
Zeroes, roots, x-intercepts
Domain and range, maxima and minima
Properties of functions: increasing, decreasing, continuous, even, odd
Function operations, including composition
Inverse functions
Graphical transformations
Functions as mathematical models
Curve fitting using various kinds of regression
Parametric descriptions of curves

Polynomial and rational functions

Linear and quadratic functions
Higher-degree polynomials and powers
Theorems about real zeros and factors: Remainder Theorem, Factor Theorem, Rational Root Theorem
Theorems about complex zeros and factors: Fundamental Theorem of Algebra, Complex Conjugate Theorem
Rational functions including their discontinuities

Exponential and logarithmic functions

Exponential functions, including e^x
Logarithmic functions, including ln x
Properties of logarithms
Manipulating and solving exponential and logarithmic equations
Exponential models of growth and decay
Logarithmic models

Trigonometric functions

Angle measurement in radians, revolutions, and degrees
Right triangle trigonometry, with applications
Definitions of six trigonometric functions as circular functions
Graphs of six trigonometric functions
Modeling of sinusoidal waves using sine and cosine functions (amplitude, period, etc.)
Inverses of sine, cosine, and tangent functions
Basic trigonometric identities: reciprocals/quotients, Pythagorean, co-function, odd/even
Sum, difference, and double-angle identities
Solving trigonometric equations
Proving trigonometric identities
Law of Sines and Law of Cosines, with applications

Complex numbers, vectors, and polar equations

Complex number system and properties
Vectors in the plane, including magnitude, dot product, and projection operations
Polar coordinate system
Polar equations and their graphs
Complex numbers in polar form
Powers and roots of complex numbers (including DeMoivre�s Theorem)

Matrices and linear systems

�Solving linear systems in two variables using substitution, elimination, and graphs
�Review of basic matrix algebra, including identity and inverse matrices
�Solving linear systems using matrix row operations into reduced row echelon form
�Solving linear systems using multiplication by an inverse matrix
�Matrices of linear transformations

Analytic geometry

�Rectangular equations of conic sections
�Parametric equations of conic sections
�Focus and focus-directrix descriptions of conic sections
�b^2 - 4ac classification for conic sections

Discrete mathematics

Basic combinatorics: counting principles
Permutations and combinations
Binomial Theorem
Concept of probability�

Sequences and series

�Sequences, including arithmetic and geometric
�Series, finite and infinite, including algebraic and geometric

Limits

Limit concept; descriptions of graphs using limits
Limit properties and computations



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Mathematics

College Algebra Plane Geometry Solid Geometry Trigonometry Vector Analysis Calculus 1 Calculus 2 Physics 1 Physics 2 Physics 3 Physics 4 Statistics & Pobability Advance Math Numerical Analysis Mechanics Differential Equation Thermodynamics
		Advance Math Advance Math Functions in general Definition of a function (presented multiple ways including graphically: vertical line test) Zeroes, roots, x-intercepts Domain and range, maxima and minima Properties of functions: increasing, decreasing, continuous, even, odd Function operations, including composition Inverse functions Graphical transformations Functions as mathematical models Curve fitting using various kinds of regression Parametric descriptions of curves Polynomial and rational functions Linear and quadratic functions Higher-degree polynomials and powers Theorems about real zeros and factors: Remainder Theorem, Factor Theorem, Rational Root Theorem Theorems about complex zeros and factors: Fundamental Theorem of Algebra, Complex Conjugate Theorem Rational functions including their discontinuities Exponential and logarithmic functions Exponential functions, including e^x Logarithmic functions, including ln x Properties of logarithms Manipulating and solving exponential and logarithmic equations Exponential models of growth and decay Logarithmic models Trigonometric functions Angle measurement in radians, revolutions, and degrees Right triangle trigonometry, with applications Definitions of six trigonometric functions as circular functions Graphs of six trigonometric functions Modeling of sinusoidal waves using sine and cosine functions (amplitude, period, etc.) Inverses of sine, cosine, and tangent functions Basic trigonometric identities: reciprocals/quotients, Pythagorean, co-function, odd/even Sum, difference, and double-angle identities Solving trigonometric equations Proving trigonometric identities Law of Sines and Law of Cosines, with applications Complex numbers, vectors, and polar equations Complex number system and properties Vectors in the plane, including magnitude, dot product, and projection operations Polar coordinate system Polar equations and their graphs Complex numbers in polar form Powers and roots of complex numbers (including DeMoivre�s Theorem) Matrices and linear systems �Solving linear systems in two variables using substitution, elimination, and graphs �Review of basic matrix algebra, including identity and inverse matrices �Solving linear systems using matrix row operations into reduced row echelon form �Solving linear systems using multiplication by an inverse matrix �Matrices of linear transformations Analytic geometry �Rectangular equations of conic sections �Parametric equations of conic sections �Focus and focus-directrix descriptions of conic sections �b^2 - 4ac classification for conic sections Discrete mathematics Basic combinatorics: counting principles Permutations and combinations Binomial Theorem Concept of probability� Sequences and series �Sequences, including arithmetic and geometric �Series, finite and infinite, including algebraic and geometric Limits Limit concept; descriptions of graphs using limits Limit properties and computations Hosted by www.Geocities.ws