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


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