Link for Calculus Math:

https://github.com/lyffski/PDF/blob/main/calculus_script-pt1_compressed.pdf‍

Link for Pre-Calculus Math:

https://github.com/lyffski/PDF/blob/main/precalculus_script_compressed.pdf

Link for German Math Abitur:

https://github.com/lyffski/PDF/blob/main/Math-FOS_compressed.pdf

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Table of Content (Calculus Math)

• Graphs and Limits
• When Limits Fail to Exist
• Limit Laws
• The Squeeze Theorem
• Limits using Algebraic Tricks
• When the Limit of the Denominotor
• Limits at Infinity and Graphs
• Limits at Infinity and Algebraic Tricks
• Continuity at a Point
• Continuity on Intervals
• Intermediate Value
• Derivatives and Tangent Lines
• Computing Derivatives from the Definition
• Interpreting Derivatives
• Derivatives as Functions and Graphs of Derivatives
• Proof that Differentiable Functions are Continuous
• Power Rule and Other Rules for De
• Higher Order Derivatives and Notation
• Derivative of e^x
• Proof of the Power Rule and Other Derivative Rules
• Product Rule and Quotient Rule
• Proof of Product Rule and Quotient Rule
• Special Trigonometr
• Derivatives of Trig Functions
• Proof of Trigonometric Limits and Derivatives
• Rectilinear Motion
• Marginal Cost
• The Chain Rule
• More Chain Rule Examples and Justification
• Justification of the Chain Rule
• Implicit Differentiation
• Derivatives of Exponential Functions
• Derivatives of Log Functions
• Logarithmic Differ
• Inverse Trig Functions
• Derivatives of Inverse Trigonometric Functions
• Related Rates - Distances
• Related Rates - Volume and Flow
• Related Rates - Angle and
• Maximums and Minimums
• First Derivative Test and Second Derivative Test
• Extreme Value Examples
• Mean Value Theorem
• Proof of Mean Value
• Derivatives and the Shape of the Graph
• Linear Approximation
• The Differential
• L'Hospital's Rule
• L'Hospital's Rule on Other Indeterminate Forms
• Newtons Method
• Antiderivatives
• Finding Antiderivatives Using Initial Conditions
• Any Two Antiderivatives Differ by a Constant
• Summation Notation
• Approximating Area
• The Fundamental Theorem of Calculus, Part 1
• The Fundamental Theorem of Calculus, Part 2
• Proof of the Fundamental Theorem of Calculus
• The Substitution Method
• Why U-Substitution Works
• Average Value of a Function
• Proof of the Mean Value Theorem for Integrals
• Exponent Rules

• Simplifying using Exponent Rules
• Simplifying Radicals
• Factoring
• Factoring - Additional Examples
• Rational Expressions
• Solving Quadratic Equations
• Rational Equations
• Solving Radical Equations
• Absolute Value Equations
• Interval Notation
• Absolute Value Inequalities
• Compound Linear Inequalities
• Polynomial and Rational Inequalities
• Distance Formula
• Midpoint Formula
• Circles: Graphs and Equations
• Lines: Graphs and Equations
• Parallel and Perpendicular Lines
• Functions
• Toolkit Functions
• Transformations of Functions
• Introduction to Quadratic Functions
• Graphing Quadratic Functions
• Standard Form and Vertex Form for Quadratic Functions
• Justification of the Vertex Formula
• Polynomials
• Exponential Functions
• Exponential Function Applications
• Exponential Functions Interpretations
• Compound Interest
• Logarithms: Introduction
• Log Functions and Their Graphs
• Combining Logs and Exponents
• Log Rules
• Solving Exponential Equations Using Logs
• Solving Log Equations
• Doubling Time and Half Life
• Systems of Linear Equations
• Distance, Rate, and Time Problems
• Mixture Problems
• Rational Functions and Graphs
• Combining Functions
• Composition of Functions
• Inverse Functions
• Increasing and Decreasing Functions
• Maximums and minimums on graphs
• Even and Odd Functions
• Piecewise Functions
• Angles and Their Measures
• Arclength and Areas of Sectors
• Linear and Radial Speed
• Right Angle Trigonometry
• Sine and Cosine of Special Angles
• Unit Circle Definition of Sine and Cosine
• Properties of Trig Functions
• Graphs of Sine and Cosine
• Graphs of Sinusoidal Functions
• Graphs of Tan, Sec, Cot, Csc
• Graphs of Transformations of Tan, Sec, Cot, Csc
• Inverse Trig Functions
• Solving Basic Trig Equations
• Solving Trig Equations that Require a Calculator
• Trig Identities
• Pythagorean Identities
• Angle Sum and Difference Formulas
• Proof of the Angle Sum Formulas
• Double Angle Formulas
• Half Angle Formulas
• Solving Right Triangles
• Law of Cosines
• Law of Cosines - old version
• Law of Sines
• Parabolas - Vertex, Focus, Directrix
• Ellipses
• Hyperbolas
• Polar Coordinates
• Parametric Equations
• Difference Quotient

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