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Honors Calculus 2: Course Structure, Content, and Study Guide

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Introduction to Definite Integrals

  • Guided course
    Basic Rules for Definite Integrals
    06:07
  • Guided course
    Definition of the Definite Integral
    05:43

Estimating Area with Finite Sums

  • Guided course
    Estimating the Area Under a Curve with Right Endpoints & Midpoint
    05:59
  • Guided course
    Estimating the Area Under a Curve with Right Endpoints & Midpoint Example 1
    09:17
  • Guided course
    Estimating the Area Under a Curve Using Left Endpoints
    07:59

Riemann Sums

  • Guided course
    Sigma Notation
    04:22
  • Guided course
    Introduction to Riemann Sums
    06:11
  • Guided course
    Sigma Notation Example 1
    03:05

Fundamental Theorem of Calculus

  • Guided course
    Fundamental Theorem of Calculus Part 2
    05:22
  • Guided course
    Fundamental Theorem of Calculus Part 1
    06:11
  • Guided course
    Fundamental Theorem of Calculus Part 1 Example1
    03:25

Substitution

  • Indefinite Integrals Example 1
    04:40
  • Substitution With an Extra Variable
    04:27
  • Definite Integrals
    06:36

Sequences

  • Recursive Formulas
    5:59
  • Arithmetic Sequences - General Formula Example 2
    7:00
  • Geometric Sequences - Recursive Formula
    04:18

Series

  • Guided course
    Intro to Series: Partial Sums
    06:45
  • Guided course
    Intro to Series: Partial Sums Example 1
    04:33
  • Guided course
    Geometric Series
    06:00

Convergence Tests

  • Guided course
    Ratio Test
    05:35
  • Guided course
    Direct Comparison Test
    09:25
  • Guided course
    Ratio Test Example 1
    10:07

Taylor Series & Taylor Polynomials

  • Taylor Polynomials
    07:00
  • Taylor Series
    08:42
  • Convergence of Taylor & Maclaurin Series
    08:26

Parametric Equations

  • Parameterizing Equations
    08:02
  • Eliminate Parameter: Equations with Trig
    04:11
  • Eliminate Parameter: Equations with Trig Example 3
    04:39

Calculus with Parametric Curves

  • Guided course
    Differentiation of Parametric Curves Example 2
    06:38
  • Guided course
    Higher Order Derivatives of Parametric Curves
    06:40
  • Guided course
    Arc Length of Parametric Curves
    06:29

Polar Coordinates

  • Convert Points from Polar to Rectangular
    06:17
  • Convert Points from Rectangular to Polar Example 1
    2:21
  • Convert Equations from Polar to Rectangular Example 2
    3:03

Calculus in Polar Coordinates

  • Guided course
    Area of Polar Regions Example 2
    12:18
  • Guided course
    Slope of Polar Curves
    09:04
  • Guided course
    Slope of Polar Curves Example 1
    05:58