Lectures

Below are note-taking guides for each lesson (for both Calculus AB and Calculus BC)

UNIT 1: LIMITS AND THEIR PROPERTIES

• Finding Limits Graphically and Numerically, Part 1.

• Finding Limits Graphically and Numerically, Part 2.

• Evaluating Limits Analytically, Pt 1.

• Evaluating Limits Analytically, Pt 2.

• Infinite Limits.

• Limits at Infinity.

• Formal Definition of the Limit.**

• Continuity and the Intermediate Value Theorem.

UNIT 2: DIFFERENTIATION

• Derivatives: Rate of Change.

• Derivatives and the Tangent Line Problem.

• Derivatives and Differentiability.

• More on Derivatives.*

• More on Derivatives (Part 2).*

• Derivatives Using Data.*

• Basic Differentiation Rules.

• Product and Quotient Rules.

• Particle Motion, Part 1.

• Particle Motion, Part 2.*

• The Chain Rule.

• Derivative Examples.*

• Implicit Differentiation.

• Related Rates.

UNIT 3: APPLICATIONS OF DIFFERENTIATION

• Extrema on an Interval.

• Rolle's Theorem and the Mean Value Theorem.

• Discovery Activity: First Derivative Test.

• Increasing and Decreasing Functions and the First Derivative Test.

• Concavity and the Second Derivative Test.

• Sketching Curves.*

• Graphing Rational Functions.*

• Graphs of f, f', and f".

• Optimization, Part 1.

• Optimization, Part 2.

• Newton's Method.

• Differentials.

UNIT 4: Integration

• Antiderivatives and Indefinite Integration.

• Area.

• Riemann Sums and Definite Integrals.

• The First Fundamental Theorem of Calculus, Part 1.

• The First Fundamental Theorem of Calculus, Part 2.

• The First Fundamental Theorem of Calculus, Part 3.*

• Average Value.

• The Second Fundamental Theorem of Calculus and Functions Defined by Integrals.

• Integration by U-Substitution, Pt. 1.

• Integration by U-Substitution, Pt. 2.

• Integration by U-Substitution, Pt. 3.

• Integration with Data.

UNIT 5: Exponential, Logarithmic, and Other Transcendental Functions

• The Natural Logarithmic Function: Differentiation.

• The Natural Logarithmic Function: Integration.

• Inverse Functions.

• Exponential Functions: Differentiation.

• Exponential Functions: Integration.

• Bases Other Than e and Applications.

• Inverse Trigonometric Functions: Differentiation.

• Inverse Trigonometric Functions: Integration.

UNIT 6: DIFFERENTIAL EQUATIONS

• Solving Differential Equations.

• Applications of Differential Equations.

• Slope Fields.

• Euler's Method.

UNIt 7: Applications of Integration

• Area Between Two Curves.

• Volume by Cross Sections.

• Volume by Disk and Washer Methods.

• Volume by Shell Method.

• Arc Length.

• Accumulation and Population Density.**

Unit 8: Integration Techniques, L'Hopital'S Rule, and Improper Integrals

• Review of Basic Integration Rules.

• Integration by Parts.

• Trigonometric Integrals, Part 1. (Calculus BC only)

• Trigonometric Integrals, Part 2. (Calculus BC only)

• Trigonometric Substitution. (Calculus BC only)

• Integration by Partial Fractions.

• Logistic Growth. (Calculus BC only)

• L'Hopital's Rule Introductory Activity.

• Indeterminate Forms and L'Hopital's Rule.

• Improper Integrals. (Calculus BC only)

Unit 9: Infinite Series (Calculus BC only)

• Sequences.

• Convergence and Divergence of Series.

• Geometric Series, nth-Term Test, and Telescoping Series.

• Integral Test and p-Series.

• Comparison of Series.

• Alternating Series.

• Ratio and Root Tests.

• Taylor Polynomials and Approximations.

• Power Series.

• Taylor Series.

• Representation of Functions by Power Series.

• Differentiating and Integrating Power Series.

• Lagrange Error Bound.

• More on Error.*

Unit 10: Parametric Equations and Polar Coordinates (CALCULUS BC ONLY)

• Graphing Parametric Equations and Eliminating the Parameter.

• Parametric Equations and Calculus.

• Parametric Equations, Vectors, and Calculus - Terms and Formulas to Know.

• Vectors - Motion Along a Curve (Part 1).

• Vectors - Motion Along a Curve (Part 2).

• Polar Coordinates and Graphs.

• Area Within a Polar Curve (Part 1).

• Area Within a Polar Curve (Part 2).