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Calculus (BC)
1. Review: Functions/Pre-Calculus
1.1.
Interval Notation vs. Set Notation
1.2.
Domain & Range
1.3.
Operations with Functions
1.4.
Even and Odd Functions
1.5.
Transformations of Functions
1.6.
Polynomials
1.7.
Factoring
1.8.
Dividing Polynomials
1.9.
Rational Functions
1.10.
Radical Functions
1.11.
Piecewise Functions
1.12.
Absolute Value Functions
1.13.
Inverse Functions
1.14.
Exponential Functions
1.15.
Logarithmic Functions
1.16.
Trigonometric Functions
1.17.
Inverse Trigonometric Functions
2. Limits & Continuity
2.1.
Basics
2.2.
Limit Laws
2.3.
One-Sided Limits
2.4.
Infinite Limits
2.5.
Limits at Infinity
2.6.
Indeterminate Forms
2.7.
Computing Limits by Factoring
2.8.
Computing Limits by Multiplying by the Conjugate
2.9.
Computing Limits by Getting a Common Denominator
2.10.
The Fundamental Trig Limit
2.11.
The Squeeze Theorem
2.12.
Continuity
2.13.
The Intermediate Value Theorem
2.14.
The Epsilon Delta Definition of a Limit
2.15.
Exam-Like Practice Questions
3. Differentiation 1: Basics & Fundamental Properties
3.1.
Average Rate of Change & the Secant Line
3.2.
Instantaneous Rate of Change & the Tangent Line
3.3.
Derivatives as a Rate of Change
3.4.
The Limit Definition of a Derivative
3.5.
Differentiation Laws
3.6.
The Power Rule (Derivative of Polynomials)
3.7.
The Product Rule
3.8.
The Quotient Rule
3.9.
Derivatives of Trig Functions
3.10.
Derivatives of Exponential Functions
3.11.
Exam-Like Practice Questions
4. Differentiation 2: Composite, Implicit, & Inverse Functions
4.1.
The Chain Rule
4.2.
Implicit Differentiation
4.3.
Derivatives of Inverse Functions
4.4.
Derivatives of Logarithmic Functions
4.5.
Derivatives of Inverse Trig Functions
4.6.
Higher Order Derivatives
4.7.
Bonus: Logarithmic Differentiation (Important technique in calculus but not usually covered in AP Calculus AB or BC)
5. Applications of Differentiation: Contextual
6. Applications of Differentiation: Analytical
7. Integration & Accumulation of Change
7.1.
Finite Sums
7.2.
Approximating Areas & Riemann Sums
7.3.
The Definite Integral
7.4.
Properties of Definite Integrals
7.5.
Computing Definite Integrals Geometrically
7.6.
Antiderivatives & The Indefinite Integrals
7.7.
Antiderivatives of Trig Functions
7.8.
Antiderivatives of Inverse Trig Functions
7.9.
Antiderivatives of Exponential Functions
7.10.
Antiderivatives of
7.11.
Initial Conditions
7.12.
The Fundamental Theorem of Calculus - Part 1
7.13.
The Fundamental Theorem of Calculus - Part 2
7.14.
Integrating Even and Odd Functions
7.15.
Integration by Substitution (U-Substitution)
7.16.
Exam-Like Practice Questions
8. Integration Techniques
9. Improper Integrals
10. Differential Equations
11. Applications of Integration
12. Parametric & Polar Curves
13. Sequences and Series
Calculus (AB)
1. Review: Functions/Pre-Calculus
1.1.
Interval Notation vs. Set Notation
1.2.
Domain & Range
1.3.
Operations with Functions
1.4.
Even and Odd Functions
1.5.
Transformations of Functions
1.6.
Polynomials
1.7.
Factoring
1.8.
Dividing Polynomials
1.9.
Rational Functions
1.10.
Radical Functions
1.11.
Piecewise Functions
1.12.
Absolute Value Functions
1.13.
Inverse Functions
1.14.
Exponential Functions
1.15.
Logarithmic Functions
1.16.
Trigonometric Functions
1.17.
Inverse Trigonometric Functions
2. Limits & Continuity
2.1.
Basics
2.2.
Limit Laws
2.3.
One-Sided Limits
2.4.
Infinite Limits
2.5.
Limits at Infinity
2.6.
Indeterminate Forms
2.7.
Computing Limits by Factoring
2.8.
Computing Limits by Multiplying by the Conjugate
2.9.
Computing Limits by Getting a Common Denominator
2.10.
The Fundamental Trig Limit
2.11.
The Squeeze Theorem
2.12.
Continuity
2.13.
The Intermediate Value Theorem
2.14.
The Epsilon Delta Definition of a Limit
2.15.
Exam-Like Practice Questions
3. Differentiation 1: Basics & Fundamental Properties
3.1.
Average Rate of Change & the Secant Line
3.2.
Instantaneous Rate of Change & the Tangent Line
3.3.
Derivatives as a Rate of Change
3.4.
The Limit Definition of a Derivative
3.5.
Differentiation Laws
3.6.
The Power Rule (Derivative of Polynomials)
3.7.
The Product Rule
3.8.
The Quotient Rule
3.9.
Derivatives of Trig Functions
3.10.
Derivatives of Exponential Functions
3.11.
Exam-Like Practice Questions
4. Differentiation 2: Composite, Implicit, & Inverse Functions
4.1.
The Chain Rule
4.2.
Implicit Differentiation
4.3.
Derivatives of Inverse Functions
4.4.
Derivatives of Logarithmic Functions
4.5.
Derivatives of Inverse Trig Functions
4.6.
Higher Order Derivatives
4.7.
Bonus: Logarithmic Differentiation (Important technique in calculus but not usually covered in AP Calculus AB or BC)
5. Applications of Differentiation: Contextual
6. Applications of Differentiation: Analytical
7. Integration & Accumulation of Change
7.1.
Finite Sums
7.2.
Approximating Areas & Riemann Sums
7.3.
The Definite Integral
7.4.
Properties of Definite Integrals
7.5.
Computing Definite Integrals Geometrically
7.6.
Antiderivatives & The Indefinite Integrals
7.7.
Antiderivatives of Trig Functions
7.8.
Antiderivatives of Inverse Trig Functions
7.9.
Antiderivatives of Exponential Functions
7.10.
Antiderivatives of
7.11.
Initial Conditions
7.12.
The Fundamental Theorem of Calculus - Part 1
7.13.
The Fundamental Theorem of Calculus - Part 2
7.14.
Integrating Even and Odd Functions
7.15.
Integration by Substitution (U-Substitution)
7.16.
Exam-Like Practice Questions
8. Differential Equations
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