- 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

- Definition of Derivative
- Average and Instantaneous Rates of Change
- Differentiability Implies Continuity
- Motion, Velocity, Speed, Acceleration and Jerk
- Derivatives of Trigonometric Functions
- Differentiation Rules and Multi-Step Differentiation
- Chain Rule
- Implicit Differentiation
- Related Rates
- Differentials and Approximations
- Tangent Line Approximation
- Approximation Errors
- Maxima and Minima, Mean Value Theorem, Rolle's Theorem
- First Derivative Test
- Limits at Infinity
- Newton's Method
- Graphing Functions Using Calculus

- Indefinite Integral and Integral Formulas
- Trigonometric Rules
- Area Computations
- Area as Limit
- Properties of Definite Integrals
- Using Finite Sums to Distance
- Endpoint Approximations
- Setting Up Integration Problems, Volumes, Volumes of Solids of Revolution
- Moments and Centers of Mass, Work and Force, Fluid Forces

- Exponential Function, a to the x power
- Derivatives and Integrals of Exponential Functions
- 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
- Continuous Interest
- APR and APY
- Analyzing Graphs of Inverse Trigonometric Functions

- Trigonometric Integration
- Integration by Parts
- Recursive Integration by Parts
- Trigonometric Integrals
- Powers of Sines and Cosines
- Powers of Secants and Tangents
- Definite Integrals of Even and Odd Functions
- Trigonometric Substitution
- Partial Fractions
- Partial Fraction Decomposition
- General Method
- 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
- Geometric Series
- Alternating Series
- Limit Comparison Test, Simplified Limit Comparison Test
- Alternating Series Test
- Alternating Series Remainder
- Absolute and Conditional Convergence
- Rearrangement
- 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
- Calculations with Series
- 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
- Finding Parametric Equations (Parabola, Cycloids)
- Parametric Equations and Calculus
- Polar Equations and Conics
- Kepler's Laws
- Polar Equations and Calculus
- Polar Formula for Area in the Plane
- 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

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