Mr. Sutton Presents... Ap Calculus Bc

A clear, concise, no-nonsense guide to AP Calculus BC (includes full lessons for AB material)

What you'll learn

Evaluate limits and determine continuity

Find derivatives of functions

Apply derivatives to problems with extrema, motion, and related rates

Find integrals of functions and use the Fundamental Theorem of Calculus

Apply integrals to problems with differential equations, motion, accumulation and area/volume

Create series to model functions and determine convergence/divergence

Apply Calculus to vectors and polor functions

Requirements

A solid working knowledge of algebra, trigonometry, exponential and logarithmic functions, sequences and series, vectors, paremetrics and polar coordinates

Already having taken Calc AB is a plus, but not required

Description

Mr. Sutton Presents… AP Calculus BCLet's cut out the fluffy description and get right to the point.  You are looking for a convenient, self-paced way to learn some quality mathematics.  You want a teacher who speaks, writes and explains clearly and without rambling in his videos.  You want lots of practice problems with answers you can look up.  You want to pay as little as possible for all this!Here is what all of my courses offer:Clear, concise videos that get to the point quickly with just enough "back story" to provide context, just enough "application" to spice it up, and carefully chosen examples to model the process.PDF versions of each lesson if you get sick of my voice or want to look back without hunting through the video.  All lessons were recorded with PowerPoint slides, so you don't have to decipher my handwriting.A printable guided notes handout allowing you to fill-in-the-blanks while you watch each lesson.  Very helpful if you learn better by writing things down but want to avoid needless rewriting or a disorganized jumble!2-4 practice problem sets per lesson, including printable handouts AND both PDF and video solutions of every single practice problem – an extra 20-30 hours of video content!End-of-chapter practice quizzes (with handouts and PDF/video solutions) to review multiple concepts at once. Here is what this course covers:Limits and ContinuityIntuitive Limits - FiniteIntuitive Limits - InfiniteAlgebraic Limits - Polynomials and Rational FunctionsAlgebraic Limits - Piecewise FunctionsLimits at InfinityContinuityIntermediate Value Theorem (IVT)Rate of ChangeDerivativesThe Power RuleDifferentiabilityGraphing DerivativesProduct and Quotient RulesDerivatives of Trigonometric FunctionsChain RuleImplicit DifferentiationTangent Lines and Higher Order DerivativesDerivatives of Exponential FunctionsDerivatives of Logarithmic FunctionsDerivatives of Inverse Trigonometric FunctionsApplications of DerivativesExtreme Values of FunctionsIncreasing and Decreasing IntervalsLocal ExtremaConcavityPoints of InflectionGraphical AnalysisMean Value TheoremLinearizationDerivatives of InversesL'Hospital's RuleMotionRelated RatesIntegralsAntiderivativesDefinite Integrals - Geometric ApproachRectangular Approximation Method (RAM)Trapezoidal RuleProperties of Definite IntegralsFTC - Derivative of an IntegralFTC - Graphical AnalysisFTC - Integral Evaluation (Polynomials)FTC - Integral Evaluation (Non-Polynomials and Function Values)Average ValueIntegration by SubstitutionIntegration by Partial Fractions (BC only)Integration by Parts (BC only)Improper Integrals (BC only)Applications of IntegralsDifferential Equations in One VariableSeparable Differential EquationsSlope FieldsExponential Growth and DecayMotion and PositionTotal DistanceAccumulation ProblemsRate In Rate OutArea Between CurvesVolume - Solids of RevolutionVolume - Cross-SectionsIntegration With Respect to the Y-AxisEuler's Method (BC only)Logistic Growth (BC only)Sequences and Series (BC only)Derivatives and Integrals of SeriesMaclaurin SeriesTransforming Maclaurin SeriesTaylor SeriesAlternating Series Error BoundLagrange Error BoundGeometric, Nth Term and Ratio TestsInterval of ConvergenceIntegral and P-Series TestsAlternating Series TestDirect Comparison TestLimit Comparison TestParametric, Vector and Polar Functions (BC only)Parametric FunctionsArc LengthVectorsPolar Functions - Slope and Basic AreaPolar Functions - Advanced Area

Overview

Section 1: Limits and Continuity

Lecture 1 2.1 Intuitive Limits - Finite

Lecture 2 2.2 Intuitive Limits - Infinite

Lecture 3 2.3 Algebraic Limits - Polynomials and Rational Functions

Lecture 4 2.4 Algebraic Limits - Piecewise Functions

Lecture 5 2.5 Limits at Infinity

Lecture 6 2.6 Continuity

Lecture 7 2.7 Intermediate Value Theorem (IVT)

Lecture 8 2.8 Rate of Change

Lecture 9 Practice Quizzes

Section 2: Derivatives

Lecture 10 3.1 The Power Rule

Lecture 11 3.2 Differentiability - Part 1

Lecture 12 3.3 Differentiability - Part 2

Lecture 13 3.4 Graphing Derivatives

Lecture 14 3.5 Product and Quotient Rules

Lecture 15 3.6 Derivatives of Trigonometric Functions

Lecture 16 3.7 Chain Rule

Lecture 17 3.8 Implicit Differentiation

Lecture 18 3.9 Tangent Lines and Higher Order Derivatives

Lecture 19 3.10 Derivatives of Exponential Functions

Lecture 20 3.11 Derivatives of Logarithmic Functions

Lecture 21 3.12 Derivatives of Inverse Trigonometric Functions

Lecture 22 Derivative Practice

Lecture 23 Practice Quizzes

Section 3: Applications of Derivatives

Lecture 24 4.1 Extreme Values of Functions

Lecture 25 4.2 Increasing and Decreasing Intervals

Lecture 26 4.3 Local Extrema

Lecture 27 4.4 Concavity

Lecture 28 4.5 Points of Inflection

Lecture 29 4.6 Graphical Analysis

Lecture 30 4.8 Mean Value Theorem

Lecture 31 4.9 Linearization

Lecture 32 4.10 Derivatives of Inverses

Lecture 33 4.11 L'Hospital's Rule

Lecture 34 4.12 Motion

Lecture 35 4.13 Motion Practice

Lecture 36 4.14 Related Rates (Basic)

Lecture 37 4.15 Related Rates (Advanced)

Lecture 38 Practice Quizzes

Section 4: Integrals

Lecture 39 5.1 Antiderivatives Part 1

Lecture 40 5.2 Antiderivatives Part 2

Lecture 41 5.3 Definite Integrals - Geometric Approach

Lecture 42 5.4 Rectangular Approximation Method (RAM) (Part 1)

Lecture 43 5.5 Rectangular Approximation Method (RAM) (Part 2)

Lecture 44 5.6 Trapezoidal Rule

Lecture 45 5.7 Properties of Definite Integrals

Lecture 46 5.8 FTC - Derivative of an Integral

Lecture 47 5.9 FTC - Graphical Analysis

Lecture 48 5.10 FTC - Integral Evaluation (Polynomials)

Lecture 49 5.11 FTC - Integral Evaluation (Non-Polynomials)

Lecture 50 5.12 FTC Free Response Practice

Lecture 51 5.13 Average Value

Lecture 52 5.14 Integration by Substitution (Indefinite)

Lecture 53 5.15 Integration by Substitution (Definite)

Lecture 54 5.16 Integration by Partial Fractions (BC only)

Lecture 55 5.17 Integration by Parts (BC only)

Lecture 56 5.18 Improper Integrals (BC only)

Lecture 57 Practice Quizzes

Section 5: Applications of Integrals

Lecture 58 6.1 Differential Equations in One Variable

Lecture 59 6.2 Separable Differential Equations

Lecture 60 6.3 Slope Fields

Lecture 61 6.4 Differential Equation Free Response Practice

Lecture 62 6.5 Exponential Growth and Decay

Lecture 63 6.6 Motion and Position

Lecture 64 6.7 Total Distance

Lecture 65 6.8 Motion Free Response Practice

Lecture 66 6.9 Accumulation Problems

Lecture 67 6.10 Rate In Rate Out

Lecture 68 6.11 Accumulation Free Response Practice

Lecture 69 6.12 Area Between Curves

Lecture 70 6.13 Volume - Solids of Revolution

Lecture 71 6.14 Volume - Cross-Sections

Lecture 72 6.15 Integration With Respect to the Y-Axis

Lecture 73 6.16 Area and Volume Free Response Practice

Lecture 74 6.17 Euler's Method

Lecture 75 6.18 Logistic Growth

Lecture 76 Practice Quizzes

Section 6: Sequences and Series

Lecture 77 7.1 Derivatives and Integrals of Series

Lecture 78 7.2 Maclaurin Series

Lecture 79 7.3 Transforming Maclaurin Series

Lecture 80 7.4 Taylor Series

Lecture 81 7.5 Alternating Series Error Bound

Lecture 82 7.6 Lagrange Error Bound

Lecture 83 Series Free Response Practice

Lecture 84 7.7 Geometric, Nth Term and Ratio Tests

Lecture 85 7.8 Interval of Convergence

Lecture 86 7.9 Integral and P-Series Tests

Lecture 87 7.10 Alternating Series Test

Lecture 88 Convergence Free Response Practice

Lecture 89 7.11 Direct Comparison Test

Lecture 90 7.12 Limit Comparison Test

Lecture 91 Practice Quizzes

Section 7: Parametric, Vector and Polar Functions

Lecture 92 8.1 Parametric Functions

Lecture 93 8.2 Arc Length

Lecture 94 8.3 Vectors

Lecture 95 8.4 Vector Free Response Practice

Lecture 96 8.5 Polar Functions - Slope and Basic Area

Lecture 97 8.6 Polar Functions - Advanced Area

Lecture 98 Polar Free Response Practice

Lecture 99 Practice Quizzes

Students preparing for the AP Exam in BC Calculus or high school/college students just looking for a challenging Calculus course