Unit 7 Differential Eqap Calculus

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Unit 7 Differential Eqap Calculus

Unit 7 Differential Eqap Calculus Equation

Calculus

Version #1
​The course below follows CollegeBoard's Course and Exam Description. Lessons will begin to appear starting summer 2020.
BC Topics are listed, but there will be no lessons available for SY 2020-2021

Unit 0 - Calc Prerequisites (Summer Work)
0.1 Summer Packet
Unit 1 - Limits and Continuity
1.1 Can Change Occur at an Instant?
1.2 Defining Limits and Using Limit Notation
1.3 Estimating Limit Values from Graphs
1.4 Estimating Limit Values from Tables
1.5 Determining Limits Using Algebraic Properties
(1.5 includes piecewise functions involving limits)
1.6 Determining Limits Using Algebraic Manipulation
1.7 Selecting Procedures for Determining Limits
(1.7 includes rationalization, complex fractions, and absolute value)
1.8 Determining Limits Using the Squeeze Theorem
1.9 Connecting Multiple Representations of Limits
Mid-Unit Review - Unit 1
1.10 Exploring Types of Discontinuities
1.11 Defining Continuity at a Point
1.12 Confirming Continuity Over an Interval
1.13 Removing Discontinuities
1.14 Infinite Limits and Vertical Asymptotes
1.15 Limits at Infinity and Horizontal Asymptotes
1.16 Intermediate Value Theorem (IVT)
Review - Unit 1
Unit 2 - Differentiation: Definition and Fundamental Properties
2.1 Defining Average and Instantaneous Rate of
Change at a Point
2.2 Defining the Derivative of a Function and Using
Derivative Notation
(2.2 includes equation of the tangent line)
2.3 Estimating Derivatives of a Function at a Point
2.4 Connecting Differentiability and Continuity
2.5 Applying the Power Rule
2.6 Derivative Rules: Constant, Sum, Difference, and
Constant Multiple
(2.6 includes horizontal tangent lines, equation of the
normal line, and differentiability of piecewise)
2.7 Derivatives of cos(x), sin(x), e^x, and ln(x)
2.8 The Product Rule
2.9 The Quotient Rule
2.10 Derivatives of tan(x), cot(x), sec(x), and csc(x)
Review - Unit 2
Unit 3 - Differentiation: Composite, Implicit, and Inverse Functions
3.1 The Chain Rule
3.2 Implicit Differentiation
3.3 Differentiating Inverse Functions
3.4 Differentiating Inverse Trigonometric Functions
3.5 Selecting Procedures for Calculating Derivatives
3.6 Calculating Higher-Order Derivatives
Review - Unit 3
Unit 4 - Contextual Applications of Differentiation
4.1 Interpreting the Meaning of the Derivative in Context
4.2 Straight-Line Motion: Connecting Position, Velocity,
and Acceleration
4.3 Rates of Change in Applied Contexts Other Than
Motion
4.4 Introduction to Related Rates
4.5 Solving Related Rates Problems
4.6 Approximating Values of a Function Using Local
Linearity and Linearization
4.7 Using L'Hopital's Rule for Determining Limits of
Indeterminate Forms
Review - Unit 4
Unit 5 - Analytical Applications of Differentiation
5.1 Using the Mean Value Theorem
5.2 Extreme Value Theorem, Global Versus Local
Extrema, and Critical Points
5.3 Determining Intervals on Which a Function is
Increasing or Decreasing
5.4 Using the First Derivative Test to Determine Relative
Local Extrema
5.5 Using the Candidates Test to Determine Absolute
(Global) Extrema
5.6 Determining Concavity of Functions over Their
Domains
5.7 Using the Second Derivative Test to Determine
Extrema
Mid-Unit Review - Unit 5
5.8 Sketching Graphs of Functions and Their Derivatives
5.9 Connecting a Function, Its First Derivative, and Its
Second Derivative
(5.9 includes a revisit of particle motion and
determining if a particle is speeding up/down.)
5.10 Introduction to Optimization Problems
5.11 Solving Optimization Problems
5.12 Exploring Behaviors of Implicit Relations
Review - Unit 5
Unit 6 - Integration and Accumulation of Change
6.1 Exploring Accumulation of Change
6.2 Approximating Areas with Riemann Sums
6.3 Riemann Sums, Summation Notation, and Definite
Integral Notation
6.4 The Fundamental Theorem of Calculus and
Accumulation Functions
6.5 Interpreting the Behavior of Accumulation Functions
​ Involving Area
Mid-Unit Review - Unit 6
6.6 Applying Properties of Definite Integrals
6.7 The Fundamental Theorem of Calculus and Definite
Integrals
6.8 Finding Antiderivatives and Indefinite Integrals:
Basic Rules and Notation
6.9 Integrating Using Substitution
6.10 Integrating Functions Using Long Division
​ and Completing the Square
6.11 Integrating Using Integration by Parts (BC topic)
6.12 Integrating Using Linear Partial Fractions (BC topic)
6.13 Evaluating Improper Integrals (BC topic)
6.14 Selecting Techniques for Antidifferentiation
Review - Unit 6
Unit 7 - Differential Equations
7.1 Modeling Situations with Differential Equations
7.2 Verifying Solutions for Differential Equations
7.3 Sketching Slope Fields
7.4 Reasoning Using Slope Fields
7.5 Euler's Method (BC topic)
7.6 General Solutions Using Separation of Variables
7.7 Particular Solutions using Initial Conditions and
Separation of Variables
7.8 Exponential Models with Differential Equations
7.9 Logistic Models with Differential Equations (BC topic)
Review - Unit 7
Unit 8 - Applications of Integration
8.1 Average Value of a Function on an Interval
8.2 Position, Velocity, and Acceleration Using Integrals
8.3 Using Accumulation Functions and Definite Integrals
in Applied Contexts
8.4 Area Between Curves (with respect to x)
8.5 Area Between Curves (with respect to y)
8.6 Area Between Curves - More than Two Intersections
Mid-Unit Review - Unit 8
8.7 Cross Sections: Squares and Rectangles
8.8 Cross Sections: Triangles and Semicircles
8.9 Disc Method: Revolving Around the x- or y- Axis
8.10 Disc Method: Revolving Around Other Axes
8.11 Washer Method: Revolving Around the x- or y- Axis
8.12 Washer Method: Revolving Around Other Axes
8.13 The Arc Length of a Smooth, Planar Curve and
Distance Traveled (BC topic)
Review - Unit 8
Unit 9 - Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC topics)
9.1 Defining and Differentiating Parametric Equations
9.2 Second Derivatives of Parametric Equations
9.3 Arc Lengths of Curves (Parametric Equations)
9.4 Defining and Differentiating Vector-Valued Functions
9.5 Integrating Vector-Valued Functions
9.6 Solving Motion Problems Using Parametric and
Vector-Valued Functions
9.7 Defining Polar Coordinates and Differentiating in
Polar Form
9.8 Find the Area of a Polar Region or the Area Bounded
by a Single Polar Curve
9.9 Finding the Area of the Region Bounded by Two
Polar Curves
Review - Unit 9
Unit 10 - Infinite Sequences and Series (BC topics)
10.1 Defining Convergent and Divergent Infinite Series
10.2 Working with Geometric Series
10.3 The nth Term Test for Divergence
10.4 Integral Test for Convergence
10.5 Harmonic Series and p-Series
10.6 Comparison Tests for Convergence
10.7 Alternating Series Test for Convergence
10.8 Ratio Test for Convergence
10.9 Determining Absolute or Conditional Convergence
10.10 Alternating Series Error Bound
10.11 Finding Taylor Polynomial Approximations of
Functions
10.12 Lagrange Error Bound
10.13 Radius and Interval of Convergence of Power
Series
10.14 Finding Taylor Maclaurin Series for a Function
10.15 Representing Functions as a Power Series
Review - Unit 8

Version #2
​The course below covers all topics for the AP Calculus AB exam, but was built for a 90-minute class that meets every other day.
Lessons and packets are longer because they cover more material.

Unit 0 - Calc Prerequisites (Summer Work)
0.1 Things to Know for Calc
0.2 Summer Packet
0.3 Calculator Skillz
Unit 1 - Limits
1.1 Limits Graphically
1.2 Limits Analytically
1.3 Asymptotes
1.4 Continuity
Review - Unit 1
Unit 2 - The Derivative
2.1 Average Rate of Change
2.2 Definition of the Derivative
2.3 Differentiability [Calculator Required]
​ Review - Unit 2
Unit 3 - Basic Differentiation
3.1 Power Rule
3.2 Product and Quotient Rules
3.3 Velocity and other Rates of Change
3.4 Chain Rule
3.5 Trig Derivatives
Review - Unit 3
Unit 4 - More Deriviatvies
4.1 Derivatives of Exp. and Logs
4.2 Inverse Trig Derivatives
4.3 L'Hopital's Rule
Review - Unit 4
Unit 5 - Curve Sketching
5.1 Extrema on an Interval
5.2 First Derivative Test
5.3 Second Derivative Test
Review - Unit 5
Unit 6 - Implicit Differentiation
6.1 Implicit Differentiation
6.2 Related Rates
6.3 Optimization
​ Review - Unit 6
Unit 7 - Approximation Methods
7.1 Rectangular Approximation Method
7.2 Trapezoidal Approximation Method
Review - Unit 7
Unit 8 - Integration
8.1 Definite Integral
8.2 Fundamental Theorem of Calculus (part 1)
8.3 Antiderivatives (and specific solutions)
Review - Unit 8
Unit 9 - The 2nd Fundamental Theorem of Calculus
9.1 The 2nd FTC
9.2 Trig Integrals
9.3 Average Value (of a function)
9.4 Net Change
Review - Unit 9
Unit 10 - More Integrals
10.1 Slope Fields
10.2 u-Substitution (indefinite integrals)
10.3 u-Substitution (definite integrals)
10.4 Separation of Variables
Review - Unit 10
Unit 11 - Area and Volume
11.1 Area Between Two Curves
11.2 Volume - Disc Method
11.3 Volume - Washer Method
​ 11.4 Perpendicular Cross Sections
Review - Unit 11
Solver
AP Calculus AB - 1st Semester
Unit 1 - Limits and Continuity
Week 0
Zoom Meetings on 8/12, 8/13, and 8/14 at 10:45 AM
Meeting ID: 315 776 7806 Password: mryaton
Video on Introduction to Limits (Due on 8/12)
Introduction to Limits Self-Assessment (Due on 8/12)
Video on Finding Limits Graphically (Due on 8/13)
Finding Limits Graphically Self-Assessment (Due on 8/13)
Week 1
Video on Estimating Limits from Tables (Due on 8/16)
Estimating Limits from Tables Self-Assessment(Due 8/16)
Video on Finding Limits Algebraically(Due on 8/17)
Finding Limits Algebraically Self-Assessment(Due 8/17)
Associating Limits w/ Graphical Behavior (8/19 in class)
Kuta - Limits at Removable Discontinuities (8/19 in class)
Selecting Procedures for Evaluating Limits (8/20 in class)
Kuta - Limits at Jump Discontinuities (8/20 in class)
Week 1 - Unit 1 Limits Quiz (8/21)
Week 2
Video on Types of Discontinuities(Due on 8/23)
Types of Discontinuities Self-Assessment (Due on 8/23)
Video on Defining Continuity at a Point(Due on 8/24)
Defining Continuity at a Point Self-Assessment(Due 8/24)
Video on Continuity over an Interval(Due on 8/25)
Continuity over an Interval Self-Assessment(Due 8/25)
Continuity Practice Set (8/26 in class)
Establishing Continuity for EVT and IVT (8/27 in class)
Week 2 - Unit 1 - Limits Quiz (8/28)
Week 3
Limits at Infinity of Graphs Video (Due on 8/30)
Limits at Infinity of Graphs Self-Assessment (Due on 8/30)
Limits at Infinity of Quotients Video (Due on 8/31)
Limits at Infinity of Quotients Self-Assessment (Due 8/31)
Limits Practice Set 1 (9/1 in class)
Intermediate Value Theorem Video (Due on 9/1)
Intermediate Value Theorem Self-Assessment (Due 9/1)
Unit 1 - Limits Test (9/4)
Unit 2 - Differentiation: Definition and Basic Derivative Rules
Week 4
Average Rate of Change Video (Due on 9/7)
Average Rate of Change Self-Assessment (Due on 9/7)
Estimating the Rate of Change Video (Due on 9/8)
Estimating the Rate of Change Self-Assessment (Due 9/8)
Instantaneous RoC Using Limits Video (Due 9/9)
Instant. RoC Using Limits Self-Assessment (Due 9/9)
Week 4 - Unit 2 - Differentiation Quiz (9/11)
Week 5
Defining the Derivative of a Function Video (Due on 9/13)
Defining the Derivative Self-Assessment (Due on 9/13)
Differentiability & Continuity Video (Due on 9/13)
Differentiability & Continuity Self-Assessment (Due 9/13)
Derivatives & the Power Rule Video (Due on 9/13)
Derivatives & the Power Rule Self-Assessment (Due 9/13)
Derivatives at a Point Video (Due on 9/14)
Derivatives at a Point Self-Assessment (Due on 9/14)
Manipulating Before Differentiating Video (Due on 9/15)
Manip Before Differentiating Self-Assessment (Due 9/15)
Derivatives of sin x, cos x, e^x, ln x Video (Due on 9/16)
Deriv of sin x, cos x, e^x, ln x Self-Assessment (Due 9/16)
Week 5 - Unit 2 - Differentiation Quiz (9/18)
Week 6
The Product Rule Video (Due on 9/20)
The Product Rule Self-Assessment (Due on 9/20)
The Quotient Rule Video (Due on 9/21)
The Quotient Rule Self-Assessment(Due on 9/21)
Differentiation Rules with Tables (9/23 in class)
Going Off on a Tangent (9/24 in class)
Week 6 - Unit 2 - Differentiation Quiz (9/25)
Week 7
Finding Derivatives of tan, cot, sec, cot Video (Due 9/27)
Finding Deriv of tan, cot, sec, cot Self-Assess (Due 9/27)
Unit 2 - Differentiation Test (10/2)
Unit 3 - Differentiation: Composite, Implicit, and Inverse Functions
Week 8
The Chain Rule Video (Due 10/4)
The Chain Rule Self-Assessment (Due 10/4)
The Chain Rule with Tables Video (Due 10/5)
The Chain Rule with Tables Self-Assessment (Due 10/5)
Implicit Differentiation Video (Due 10/6)
Implicit Differentiation Self-Assessment(Due 10/6)
Kuta Chain Rule Practice (10/6 in class)
Kuta Chain Rule with Trig Practice (10/6 in class)
Week 9
Differentiating Inverse Functions Video (Due on 10/11)
Differentiating Inverse Funct Self-Assessment (Due 10/11)
Differentiating Inverse Trig Functions Video (Due 10/12)
Differentiating Inverse Trig Self-Assessment (Due 10/12)
Calculating Higher-Order Deriv Video (Due on 10/13)
Calculating Higher-Order Deriv Self-Assess (Due 10/13)
Implicit Differentiation Practice (10/13 in class)
Unit 3 - Differentiation Test (10/16)
​Unit 4 - Contextual Applications of Differentiation
Week 10
Contextual Meaning of Derivatives Video (Due on 10/18)
Contextual Meaning of Deriv Self-Assess (Due on 10/18)
Straight-Line Motion Video (Due on 10/19)
Straight-Line Motion Self-Assessment (Due on 10/19)
Related Rates Video (Due on 10/20)
Related Rates Self-Assessment (Due on 10/20)
Week 11
Local Linearity and Linearization Video (Due on 10/25)
Local Linearity & Linearization Self-Assess (Due on 10/25)
L'Hospital's Rule Video (Due on 10/26)
L'Hospital's Rule Self-Assessment (Due on 10/26)
Unit 4 - Contextual Applications Test (10/30)
Unit 5 - Analytical Applications of Differentiation
Week 12
Mean Value Theorem Video (Due on 11/1)
Mean Value Theorem Self-Assessment (Due on 11/1)
Extreme Value Theorem Video (Due on 11/1)
Extreme Value Theorem Self-Assessment (Due on 11/1)
First Derivative Test Video (Due on 11/2)
First Derivative Test Self-Assessment (Due on 11/2)
Unit 5 - Analytical Applications Quiz (11/6)
Week 13
Second Derivative Test Video (Due on 11/8)
Second Derivative Test Self-Assessment (Due on 11/8)
Sketching Graphs and Their Derivatives Video (Due on 11/9)
Sketching Graphs and Their Derivatives Self-Assessment (Due on 11/9)
Week 14
Optimization Problems Video (Due on 11/15)
Optimization Problems Self-Assessment (Due on 11/15)
Unit 5 - Analytical Applications Test (11/19)
Thanksgiving Break
Week 15
​Week 15 HW - 2018 AP Calculus AB MC (Due on 12/3)
Week 16
Week 16 HW - 2019 AP Calculus AB MC (Due on 12/10)
Week 17
AP Calculus AB Midterm
Christmas Break
Lifesize AP Calculus AB Meeting Code: 4918470
AP Calculus AB Cheat Sheet
AP Calculus AB - 2nd Semester
Unit 6 - Integration and the Accumulation of Change
Week 18
Accumulation of Change Video (Due on 1/4)
Accumulation of Change Self-Assessment (Due on 1/4)
Left & Right Riemann Sums Video (Due on 1/4)
Left & Right Riemann Sums Self-Assessment (Due on 1/4)
Midpoint & Trapezoidal Riemann Sums Video (Due on 1/5)
Midpoint & Trapezoidal Sums Self-Assess (Due on 1/5)
Unit 6 Integration Quiz (1/8)
Week 19
Integration Rules Video (Due on 1/10)
Integration Rules Self-Assessment (Due on 1/10)
Integration of Trig (& Other Functions) Video (Due 1/11)
Int of Trig (& Other Funct) Self-Assessment (Due 1/11)
Fundamental Theorem of Calculus Video (Due on 1/12)
Fundamental Theorem Calc Self-Assessment (Due 1/12)
Week 20
Definite Integral as Limit of Riemann Sum Video (Due 1/18)
Definite Integral as Limit of RS Self-Assess (Due 1/18)
Definite Integral Video (Due on 1/18)
Definite Integral Self-Assessment (Due on 1/18)
Integration by u-substitution Video (Due on 1/19)
Integration by u-substitution Self-Assessment (Due 1/19)
Week 21
Definite Integration using u-substitution Video (Due 1/24)
Definite Int using u-substitution Self-Assess (Due 1/24)
Unit 6 Integration Test (1/29)
Unit 7 - Differential Equations
Week 22
Writing Differential Equations Video (Due on 1/31)
Writing Differential Eq Self-Assessment (Due on 1/31)
Verifying Solutions of Diff Eq Video (Due on 2/1)
Verifying Solutions to Diff Eq Self-Assessment (Due 2/1)
Sketching Slope Fields Video (Due on 2/2)
Sketching Slope Fields Self-Assessment (Due on 2/2)
Unit 7 Differential Equations Quiz (2/5)
Week 23
Separable Differential Equations Video (Due on 2/7)
Separable Differential Eq Self-Assessment (Due on 2/7)
Finding Particular Solutions of Diff Eq Video (Due 2/8)
Finding Particular Solutions Self-Assessment (Due 2/8)
Unit 7 Differential Equations Quiz (2/12)
Week 24
Exponential Models with Diff Eq Video (Due 2/14)
Exponential Models with Diff Eq Self-Assess (Due 2/14)
Unit 7 Differential Equations Test (2/19)
Unit 8 - Applications of Integration
Week 25
Average Value of a Function Video (Due on 2/21)
Average Value of a Function Self-Assess (Due 2/21)
Motion with Integration Video (Due on 2/22)
Motion with Integration Self-Assess (Due 2/22)
Integrals in Context Video (Due on 2/23)
Integrals in Context Self-Assessment (Due on 2/23)
Unit 8 Applications of Integration Quiz (2/26)
Week 26
Area Between a Curve and x-axis Video (Due on 2/28)
Area Between a Curve and x-axis Self-Assessment (Due on 2/28)
Area Between Two Curves Video (Due 3/1)
Area Between Two Curves Self-Assessment (Due 3/1)
Horizontal Area Between Curves (Due 3/2)
Horizontal Area Between Curves Self-Assessment (Due 3/2)
Unit 8 Applications of Integration Quiz (3/5)
Week 27
Volume by Disc Method Video (Due on 3/7)
Volume by Disc Method Self-Assess (Due on 3/7)
Volume by Washer Method Video (Due on 3/8)
Volume by Washer Method Self-Assess (Due on 3/8)
Volume Around Other Axes Video (Due on 3/9)
Volume Around Other Axes Self-Assess (Due on 3/9)
Unit 8 Applications of Integration Quiz (3/12)
Spring Break
Week 28
Volumes with Cross-Sections (Squares and Rectangles) Video (Due on 3/22)
Volumes with Cross-Sections (Squares and Rectangles) Self-Assess (Due on 3/22)
Volumes with Cross-Sections (Triangles and Semicircles) Video (Due on 3/23)
Volumes with Cross-Sections (Triangles and Semicircles) Self-Assess (Due on 3/23)
Unit 8 Applications of Integration Test (3/26)
AP Calculus AB Review
Unit 1 Review - Limits and Continuity
Unit 2 Review - Differentiation: Definition and Basic Derivative Rules
Unit 3 Review - Differentiation: Composite, Implicit, and Inverse Functions
Unit 4 Review - Contextual Applications of Differentiation
Unit 5 Review - Analytical Apps of Differentiation
Unit 5 Calculus Review Video
Unit 5 Calculus Sample AP Problems Video
Unit 6 Review - Integration & Accum of Change
Unit 6 Calculus Review Video
Unit 6 Calculus Sample AP Problems Video
​Unit 7 Review - Differential Equations
Unit 7 Calculus Review & Sample AP Problems Video
Unit 8 Review - Applications of Integration
Unit 8 Calculus Review & Sample AP Problems Video
2019 AP Calculus AB #1 (15 min)
2019 AP Calculus AB #1 Video
2019 AP Calculus AB #2 (15 min)
2019 AP Calculus AB #2 Video
2019 AP Calculus AB #3 (15 min)
2019 AP Calculus AB #3 Video
2019 AP Calculus AB #4 (15 min)
2019 AP Calculus AB #4 Video
2019 AP Calculus AB #6 (15 min)
2019 AP Calculus AB #6 Video

Unit 7 Differential Eqap Calculus Solver

My AP Calculus AB and BC Ultimate Review Packets: AB: BC: Before you watch this video all about Unit 7 of A.

Unit 7 Differential Eqap Calculus Calculator

  • Day 4: Quiz (7.1-7.4) Day 5: Finding General Solutions using Separation of Variables. Day 6: Finding Particular Solutions Using Initial Conditions and Separation of Variables. Day 7: Review of Separation of Variables. Day 8: Exponential Models with Differential Equations. Day 9: Review Chapter 7. Day 10: Review Chapter 7. Day 11: Chapter 7 Test.
  • 7.2 and differential equations review solutions viso.pdf. (1130k) Jeff Viso.
  • Unit 1 Pre-calculus review. Unit 7 Integration. Unit 8 Integration and Differential Equations. Unit 9 Area and Volume.
  • Welcome; AP Calculus. AP Calculus FAQ's, Exam Results, & College Credit Equivalents; AP Calculus AB. Unit 1: Limits & Continuity; Unit 2: Derivatives; Unit 3: Curve.