- Graphs of Equations
- Graphing Procedure and Symmetry of a Graph
- Intercepts
- Functions
- Concept of Domain and Range
- Even and Odd Functions
- Power Functions and Logarithmic Functions
- Sum, Difference, Product and Quotient
- Composite Functions
- Graphs of Sine and Cosine
- Models and Data
- Logarithmic and Exponential

- Limit
- Concept of Limit
- Evaluate Limits Graphically and Vertical Asymptotes
- Direct Substitution
- Properties of Limits
- One-Sided Limit Type
- Infinite Limit Type
- Basic Trigonometric Limits
- Limits of Polynomial and Rational Functions
- Limits Involving Radical Functions
- Continuity
- Continuity at a Point, Continuity Test, Types of Discontinuity
- Intermediate Value Theorem, Existence of Solutions

- Derivatives and Applications of Derivatives
- Definition of Derivative
- Slope of Tangent Line
- Average and Instantaneous Rates of Change
- Differentiability Implies Continuity
- Constant, Identity, and Power Rules
- Sum and Difference Differentiation Rules
- Products and Quotients Differentiation Rules
- Motion, Velocity, Speed, Acceleration and Jerk
- Derivatives of Trigonometric Functions
- Differentiation Rules and Multi-Step Differentiation
- Chain Rule
- Implicit Differentiation
- Higher Order Derivatives-Acceleration and Jerk
- Related Rates
- Derivatives of Exponential Functions
- Differentials and Approximations
- Tangent Line Approximation
- Approximation Errors
- Maxima and Minima, Mean Value Theorem, Rolle's Theorem
- Absolute versus Local Extrema
- First Derivative Test
- Concavity and Inflection
- Second Derivative Test
- Limits at Infinity
- Absolute Extrema and Optimization
- Newton's Method
- Analyzing the Graphs of Functions
- Graphing Functions Using Calculus

- Indefinite Integral and Integral Formulas
- Antiderivative
- Trigonometric Rules
- Area Computations
- Area Sums
- Area as Limit
- Probability and Probability Density Functions
- Definite Integrals and Finite Sum Estimation
- Properties of Definite Integrals
- Riemann Sum
- Using Finite Sums to Distance
- Fundamental Theorem of Calculus, Integration Techniques, Numerical Integration
- Mean Value Theorem
- Endpoint Approximations
- Trapezoidal and Midpoint Approximations
- Simpson's Rule
- Setting Up Integration Problems, Volumes, Volumes of Solids of Revolution
- Area Between Curves
- Cross Section Method
- Volumes by Disks
- Volumes by Washers
- Method of Cylindrical Shells
- Length of a Plane Curve
- Basic Formula of Areas of Surfaces of Revolution
- Moments and Centers of Mass, Work and Force, Fluid Forces
- Work by a Variable Force, Work by a Constant Force

- Exponential Function, a to the x power
- Derivatives and Integrals of Exponential Functions
- Inverse Functions
- Definition of Inverse Functions
- Reflective Property
- Existence (One-to-One, Monotonic)
- Finding Inverse Functions
- Continuity and Differentiability
- Derivative Rule for Inverses
- Natural Log
- Analysis of Logarithmic Graphs
- Logarithmic Differentiation
- Logarithmic Integration
- Other Exponential and Logarithmic Functions
- Indeterminate Forms
- Growth and Decay
- Exponential Change
- Compound Interest
- Compound Interest per Year
- Compound Interest per Period
- Continuous Interest
- APR and APY
- Annuities
- Annuities for Loans
- Relative Rates of Growth and Decay
- Properties of Inverse Trigonometric Functions
- Derivatives of Six Inverse Trigonometric Properties
- Analyzing Graphs of Inverse Trigonometric Functions
- Integration of Inverse Trigonometric Functions by Substitution
- Hyperbolic Functions
- Hyperbolic Functions (Definitions, Evaluation, Properties, Identities)
- Derivatives and Integrals of Hyperbolic Functions
- Inverse Hyperbolic Functions (Definitions, Evaluation, Properites)
- Derivatives and Integrals of Inverse Hyperbolic Functions

- Trigonometric Integration
- Strategies for Fitting Integrands to Basic Forms
- Integration by Parts
- Rule for Integration by Parts
- Guidelines for Integration by Parts
- Recursive Integration by Parts
- Trigonometric Integrals
- Powers of Sines and Cosines
- Powers of Secants and Tangents
- Products of Sines and Cosines of Different Angles
- Definite Integrals of Even and Odd Functions
- Trigonometric Substitution
- Partial Fractions
- Partial Fraction Decomposition
- General Method
- Convergence and Divergence of Integrals
- Improper Integrals and Infinite Discontinuities
- Domination Test
- Limit Comparison Test
- General and Particular Solutions
- Euler's Numerical Methods (Improved Euler, Runge-Kutta)
- Slope Fields and Isoclines
- Differential Equations and Integration
- Solving Separable First-Order Differential Equations
- Exponential and Logistic Growth

- Sequences in Calculus
- Definition of a Sequence
- Limit of a Sequence
- Convergence and Divergence of Sequences
- L'Hopital's Rule
- Rules, Sandwich/Squeeze
- Picard's Method
- Infinite Series
- Infinite Polynomials
- Sequence of Partial Sums
- Geometric Series
- Alternating Series
- Convergence Tests
- nth-Term Test
- Ratio Test
- Root Test
- Integral Test
- Limit Comparison Test, Simplified Limit Comparison Test
- Alternating Series Test
- Alternating Series Remainder
- Absolute and Conditional Convergence
- Rearrangement
- Summary and Comparison of Procedures for Determining Convergence
- Power Series and Convergence
- Term-By-Term Integration of Power Series
- Series Multiplication of Power Series
- Taylor and Maclaurin Series
- Taylor and Maclaurin Polynomials
- Convergence of Taylor and Maclaurin Polynomials
- Maclaurin Series Truncation Error
- Calculations with Series
- Binomial Series for Powers
- Choosing Centers
- Evaluating Non-Elementary Integrals
- Finding and Identifying Maclaurin Series

- Properties of Ellipses
- Properties of Hyperbolas
- Quadratic Equations and the Conic
- Rotation to Eliminate XY-Term
- Parametric Equations and Plane Curves
- Parametric Equations
- Eliminating the Parameter (Domain, Curve Sketching)
- Finding Parametric Equations (Parabola, Cycloids)
- Evaluating Parametric Equations
- Parametric-Inverses
- Parametric Equations and Calculus
- Differentiation and Parametric Form
- Parametric Formula for Length of a Curve
- Parametric Formulas for Area of a Surface of Revolution
- Parametric Formula for Area in the Plane
- Polar Axis and Polar Coordinates
- Special Polar Equations and Graphs
- Polar Equations and Conics
- Polar Equations of Conics in Calculus
- Kepler's Laws
- Polar Equations and Calculus
- Polar Formula for Area in the Plane
- Polar Formula for Length of a Curve
- Polar Formulas for Area of a Surface of Revolution
- Polar Formulas for Mass, Moments, and Centers

- Vectors in the Plane and Calculus
- Directed Line Segment
- Sum, Difference, Product of Vector and Scalar
- Position Vector
- Unit Vector
- Slopes, Tangents, and Normals
- Dot Products in Calculus
- Dot Product (Scalar Product, Inner Product, Tail to Tail)
- Angle Between Vectors
- Scalar Projection
- Vector Projection in Calculus
- Lines in the Plane, Distance From Points to Lines
- Vector-Valued Functions in the Plane
- Derivative of a Vector-Valued Function
- Properties of the Derivative
- Indefinite Integral of a Vector-Valued Function
- Position, Velocity, and Acceleration Along a Plane Curve (Differentiation)
- Acceleration, Velocity, and Position Along a Plane Curve (Integration)
- Arc Length of a Plane Curve
- Curvature Formulas (Circle of Curvature)
- Tangential and Normal Components of Acceleration

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