Math Genius - Math Genius Curriculum lyrics

The mathematics topics below cover the scope of most middle-school, high-school, and college-level math cla**es. They're divided in the way they're usually taught in American curricula. Prealgebra Operations Order of Operations Operation Properties Inverse Operations Whole Numbers Place Value in the Decimal System Divisibility Factors Prime Numbers Prime Factorization Decimals Comparing Rounding Operations Fractions Reducing Fractions Adding and Subtracting Fractions Multiplying and Dividing Fractions Improper Fracions, Mixed Numbers, and Decimals Percents Conversions Operations Integers and Rationals The Number Line Types of Numbers and Properties Negative Numbers Absolute Value Powers, Exponents, and Roots Squares & Cubes Powers of Negative Numbers, Decimals, and Fractions Negative Exponents Square Roots, Other Roots, and Fractional Exponents Approximating Roots Operations with Exponents and Roots Perimeter and Area Perimeter Area Circles: Area and Circumference Variables Intro to Variables Evaluating/Simplifying Solving for Variables Geometry Building Blocks of Geometry Constructions Polygons Circles Surfaces Geometric Measurements 3-D Measurements Special Triangles Triangle Congruence Corresponding Parts Proving Congruence Similarity Proving Similarity Geometric Theorems Inductive and Deductive Reasoning Logic Statements Axioms and Postulates Geometric Proofs Algebra I Expressions and Equations Solving equations with one variable Applications of Solving Equations Inequalities Compound Inequalities Absolute Value Probability Graphing Data Graphing Equations Writing Equations Systems of Equations Variation Exponents Scientific Notation Polynomials Quadratics Parabolas Factoring The Quadratic Formula Graphing Quadratic Functions Difference of Squares Algebra II Binomial Expansion Factoring Matrices Rational Expressions Complex Numbers Imaginary Numbers Complex Numbers Complex Conjugates/Dividing Complex Numbers Functions Operations on Functions Discrete Functions Inequalities Operations with Functions Special Graphs Exponential Functions Logarithmic Functions Polynomials Systems of Three Equations Trigonometry Angles Graphs Trigonometric Equations Trigonometric Functions Trigonometric Identities Solving Oblique Triangles Oblique Triangles Law of Sines Ambiguous Case Law of Cosines Area of an Oblique Triangle Solving Right Triangles More Trigonometric Identities Precalculus Complex Numbers Conic Sections Continuity and Limits Functions Trigonometric Functions Polynomial Functions Parametric Equations and Polar Coordinates Exponential and Logarithmic Functions Sequences and Series Calculus AB (Calculus I) Functions, Limits, and Continuity Overview of Functions Limits Continuity Introduction to Derivatives Derivatives Differentiation Techniques Applications of the Derivative (AB) Rates of Change and Kinematics Related Rates Absolute and Local Extrema The Mean Value Theorem First Derivative an*lysis Second Derivative an*lysis Asymptotes Curve Sketching and Graphing Optimization Introduction to Integrals Indefinite Integrals Area as a Sum Definite Integrals Average Value, Second Fundamental Theorem Integration Techniques Inverse, Exponential, and Logarithmic Functions Inverse Functions Number e and the Natural Log Derivatives of ex and Natural Logs Exponential Growth and Decay Calculus BC (Calculus II) Functions, Limits, and Continuity Functions Limits and Continuity The Derivative Geometric Definition Limit Definition The Derivative Function Second Derivative Computing Derivatives Derivatives of Elementary Functions Differentiation Techniques Applications of the Derivative (BC) Kinematics (Velocity and Acceleration) Graph an*lysis Optimization Related Rates Definite Integral Overview of the Definite Integral Properties of the Definite Integral Antiderivatives, First Fundamental Theorem of Calculus Computing Integrals Addition and Multiplication by a Constant Change of Variables Integration by Parts Partial Fraction Decomposition Applications of the Integral Areas in a Plane Volumes of Solids Average Value of a Function Length of a Graph Distance Travelled Series Convergence of Series The Comparison Test Geometric Series The Ratio Test The Integral Test Series with Positive and Negative Terms Power Series The Taylor Series Approximating Functions with Polynomials The Remainder Term Common Taylor Series Differentiation and Integration of Power Series Parametric and Polar Curves Velocity, Acceleration, and Parametric Curves Length of a Parametric Curve The Area Below a Polar Curve Multivariable Calculus (Calculus III) Three Dimensional Space The 3-D Coordinate System Equations of Lines Equations of Planes Quadric Surfaces Functions of Several Variables Vector Functions Calculus with Vector Functions Tangent, Normal and Binormal Vectors Arc Length with Vector Functions Curvature Velocity and Acceleration Cylindrical Coordinates Spherical Coordinates Partial Derivatives Limits Partial Derivatives Interpretations of Partial Derivatives Higher Order Partial Derivatives Differentials Chain Rule Directional Derivatives Applications of Partial Derivatives Tangent Planes and Linear Approximations Gradient Vector, Tangent Planes and Normal Lines Relative Minimums and Maximums Absolute Minimums and Maximums Lagrange Multipliers Multiple Integrals Double Integrals Iterated Integrals Double Integrals over General Regions Double Integrals in Polar Coordinates Triple Integrals Triple Integrals in Cylindrical Coordinates Triple Integrals in Spherical Coordinates Change of Variables Surface Area Area and Volume Revisited Line Integrals Vector Fields Line Integrals Line Integrals of Vector Fields Fundamental Theorem for Line Integrals Conservative Vector Fields Green's Theorem Curl and Divergence Surface Integrals Parametric Surfaces Surface Integrals Surface Integrals of Vector Fields Stokes' Theorem Divergence Theorem Differential Equations (Calculus IV) Basic Concepts Definitions Direction Fields First Order Differential Equations Linear Equations Separable Equations Exact Equations Bernoulli Differential Equations Substitutions Intervals of Validity Modeling with First Order Differential Equations Equilibrium Solutions Euler's Method Second Order Differential Equations Basic Concepts Real Roots Complex Roots Repeated Roots Reduction of Order Fundamental Sets of Solutions More on the Wronskian Nonh*mogeneous Differential Equations Undetermined Coefficients Variation of Parameters Mechanical Vibrations Laplace Transforms The Definition Laplace Transforms Inverse Laplace Transforms Step Functions Solving IVP's with Laplace Transforms Nonconstant Coefficient IVP's IVP's with Step Functions Dirac Delta Function Convolution Integral Table of Laplace Transforms Systems of Differential Equations Systems of Differential Equations Solutions to Systems Phase Plane Real Eigenvalues Complex Eigenvalues Repeated Eigenvalues Nonh*mogeneous Systems Laplace Transforms Modeling Series Solutions Series Solutions Euler Equations Higher Order Differential Equations Basic Concepts for nth Order Linear Equations Linear h*mogeneous Differential Equations Undetermined Coefficients Variation of Parameters Laplace Transforms Systems of Differential Equations Series Solutions Boundary Value Problems & Fourier Series Boundary Value Problems Eigenvalues and Eigenfunctions Periodic Functions and Orthogonal Functions Fourier Sine Series Fourier Cosine Series Fourier Series Convergence of Fourier Series Partial Differential Equations The Heat Equation The Wave Equation Terminology Separation of Variables Solving the Heat Equation Heat Equation with Non-Zero Temperature Boundaries Laplace's Equation Vibrating String Summary of Separation of Variables Statistics Linear Algebra Discrete/Finite Mathematics Number Theory Topology