2017 - 2018 Calculus Syllabus
Great Online Graphing Calculator
Another Graphing Calculator
Calculus Prerequisites:
Calculus readiness test: (http://www.etown.edu/depts/math/files/PracticePreCalculus.pdf )
PreCalculus stuff to know cold
(Trig Cheat Sheet)
( Unit Circle)
( Algebra 2 & Trig Things to Remember )
Common Mistakes for Algebra/Calculus (https://www.math.hmc.edu/calculus/tutorials/algebrareview/)
Extra Problems for each section with solutions (https://www.math.ucdavis.edu/~kouba/ProblemsList.html)
** Calculus Topics Review / AP test Practice
Paul's Online Tutorial (Great resources) (http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx)
CalculusHelp.Com (http://www.calculus-help.com/tutorials)
Education Portal (http://education-portal.com/academy/course/ap-calculus.html)
AP Central (https://apstudent.collegeboard.org/apcourse/ap-calculus-ab/exam-practice)
Trig Rules (http://www2.clarku.edu/~djoyce/trig/identities.html)
**Unit 1: Limits
What is a Limit?
Piece-wise Functions and Limits [*HW / Key]
Finding Limits Graphically and Numerically. (Extra Problems , Extra Resource) [* HW1 /Key, HW2/ Key ]
Evaluating Limits Analytically/Algebraically. ( Extra Resources) [*HW/ Key] Algebraic Factoring Limits [*HW / Key ]
Properties of Limits [*HW / Key]
Continuity ( Extra Resource)and Intermediate Value Theorem ( Extra Resource 1, ER 2) [*HW/ Key]
Squeeze Theorem [*HW/Key]
Infinite Limits. ( Extra Resources) Limits at Infinity. ( Extra Resources) Notes [*HW / Key]
**Unit 2: Differentiation
What is Differentiation?
Limit Definition of the Derivative at a point [*HW /Key] Limit def. of Tan(x)
Derivative by the limit definition [*HW1 /Key] [*HW2 /Key]
Alternate form of the Derivative and Existence of Derivatives [*HW /Key]
The Derivative and the Tangent Line Problem. [ Limit def review *HW W/ Key]
Basic Differentiation Rules. (Extra Resources 1 / ER 2) [*HW/ Key]
Product and Quotient Rules [*HW/ Key] and Higher-Order Derivatives. [*HW/key] (Extra Resources)
Trig Function Derivatives with product and quotient rule [*HW/Key]
Horizontal Tangents [*HW /Key]
The Chain Rule. (Extra Resources) [*HW/Key][*HW/ Key2]
Derivatives Review [*HW/ Key] (Derivative Test)
Motion [*HW /Key] [*HW 2/ Key] (Motion Quiz)
Deriv. Review with motion [*HW]
Implicit Differentiation. (Khan Academy / Education Portal ) [*HW1/Key][*HW2/Key]
Related Rates. (Notes, Extra resources: YouTube Video) [*HW1/Key] [*HW2/Key][*HW3/Key]
***Unit 3: Applications of Differentiation
Extrema on an Interval (Root Math)[*HW / Key]
Rolle's Theorem and the Mean Value Theorem (Root Math)[*HW / Key]
Increasing and Decreasing Functions and the First Derivative Test (Root Math) [*HW / Key]
Review Extrama, Rolles, MVT, and Inc/Dec Fns [*HW / Key]
Concavity and the Second Derivative Test (Root Math) [*HW / Key]
A Summary of Curve Sketching (Note Sheet) [*HW / Key][*HW/Key 2]
Differentials (Resource) [*HW / Key]
Review/ Key Applications of Differentiation
[*Review / KEY]
***** Review for Semester One Exam*****
***Unit 4: Integration (Khan Integrals)
Sigma Notation (Resource) [*HW/ KEY, HW/ KEY]
Area Approximation with Rectangles [*HW / KEY]
Anti derivatives and Indefinite Integrals. Basic Deriv. and Integration Notes Sheet [*HW /KEY, HW/KEY]
Area. (Resource)[*HW/ KEY, KEY for extra 3 problems with limit]
Riemann Sums and Definite Integrals. (Resource 1, Resource 2)
Rules of Integration and U-Substitution packet for 2/11-2/14 week [Packet/Key]
The Fundamental Theorem of Calculus. (Resource)[*HW/ KEY]
Integration by Substitution.(Khan, Resource, More Practice) (*HW1/ Key , HW2 / Key)
***Review (integration) 1 /KEY Extra Review for Unit 4 (Integration) test /KEY
Second Fundamental Theorem of Calculus Notes [*HW/Key]
Mean Value Theorem (Finds the X value) and Absolute Value Theorem (average height, Finds Y value) Notes / Notes2 [*HW/Key]
Net Change and Substitution with an extra Variable (Video Notes) [*HW/Key]
Motion Notes[HW1 , HW2]
Hard Integration Practice(Great Practice Webpage) Great Source
Review for Integration Test / Key
***Unit 5: Logarithmic, Exponential, and Other Transcendental Functions
The Natural Logarithmic Function: Differentiation and Integration Notes [*integration and Ln HW]
Inverse Trigonometric Functions: Differentiation and Integration
Exponential Functions: Differentiation and Integration
Chain Rule with Natural Log and Exponential Functions
Review of all above [*HW 2/23 w/Key]
Bases Other than e and Applications Derivatives and Integrals [*HW and Key]
***Unit 6: Differential Equations
Slope Fields (Resource 1, Resource 2, Resource 3) [*HW / Key]
Differential Equations /Hyperbolic Functions[*HW / Key]
Book Page 377-378 # 5,9,15,19,23,25,33,34,39,41 [*HW /Key]
Differential Equations: Growth and Decay [*HW/Key]
Separation of Variables and Logistic Equations [*HW + book P.414/61-66] Extra Orthogonal Trajectories Examples
Homogeneous Differential Equations [*HW Problem 3 Only/Key]
[*Review / KEY] for Differential Equations Test
***Unit 7: Applications of Integration
Area of a Region Between Two Curves (Resource) [*HW/ KEY] [*HW2/KEY]
Volume: The Disk and Washer Method [*HW/KEY1][*HW/KEY2]
Arc Length and Surfaces of Revolution [*HW/KEY]
Review Test/ KEY
Final Project Description/Rubric
Year End Review/ Key
L'Hospitals Rule
Final Exam Review Topics
Great Online Graphing Calculator
Another Graphing Calculator
Calculus Prerequisites:
Calculus readiness test: (http://www.etown.edu/depts/math/files/PracticePreCalculus.pdf )
PreCalculus stuff to know cold
(Trig Cheat Sheet)
( Unit Circle)
( Algebra 2 & Trig Things to Remember )
Common Mistakes for Algebra/Calculus (https://www.math.hmc.edu/calculus/tutorials/algebrareview/)
Extra Problems for each section with solutions (https://www.math.ucdavis.edu/~kouba/ProblemsList.html)
** Calculus Topics Review / AP test Practice
Paul's Online Tutorial (Great resources) (http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx)
CalculusHelp.Com (http://www.calculus-help.com/tutorials)
Education Portal (http://education-portal.com/academy/course/ap-calculus.html)
AP Central (https://apstudent.collegeboard.org/apcourse/ap-calculus-ab/exam-practice)
Trig Rules (http://www2.clarku.edu/~djoyce/trig/identities.html)
**Unit 1: Limits
What is a Limit?
Piece-wise Functions and Limits [*HW / Key]
Finding Limits Graphically and Numerically. (Extra Problems , Extra Resource) [* HW1 /Key, HW2/ Key ]
Evaluating Limits Analytically/Algebraically. ( Extra Resources) [*HW/ Key] Algebraic Factoring Limits [*HW / Key ]
Properties of Limits [*HW / Key]
Continuity ( Extra Resource)and Intermediate Value Theorem ( Extra Resource 1, ER 2) [*HW/ Key]
Squeeze Theorem [*HW/Key]
Infinite Limits. ( Extra Resources) Limits at Infinity. ( Extra Resources) Notes [*HW / Key]
**Unit 2: Differentiation
What is Differentiation?
Limit Definition of the Derivative at a point [*HW /Key] Limit def. of Tan(x)
Derivative by the limit definition [*HW1 /Key] [*HW2 /Key]
Alternate form of the Derivative and Existence of Derivatives [*HW /Key]
The Derivative and the Tangent Line Problem. [ Limit def review *HW W/ Key]
Basic Differentiation Rules. (Extra Resources 1 / ER 2) [*HW/ Key]
Product and Quotient Rules [*HW/ Key] and Higher-Order Derivatives. [*HW/key] (Extra Resources)
Trig Function Derivatives with product and quotient rule [*HW/Key]
Horizontal Tangents [*HW /Key]
The Chain Rule. (Extra Resources) [*HW/Key][*HW/ Key2]
Derivatives Review [*HW/ Key] (Derivative Test)
Motion [*HW /Key] [*HW 2/ Key] (Motion Quiz)
Deriv. Review with motion [*HW]
Implicit Differentiation. (Khan Academy / Education Portal ) [*HW1/Key][*HW2/Key]
Related Rates. (Notes, Extra resources: YouTube Video) [*HW1/Key] [*HW2/Key][*HW3/Key]
***Unit 3: Applications of Differentiation
Extrema on an Interval (Root Math)[*HW / Key]
Rolle's Theorem and the Mean Value Theorem (Root Math)[*HW / Key]
Increasing and Decreasing Functions and the First Derivative Test (Root Math) [*HW / Key]
Review Extrama, Rolles, MVT, and Inc/Dec Fns [*HW / Key]
Concavity and the Second Derivative Test (Root Math) [*HW / Key]
A Summary of Curve Sketching (Note Sheet) [*HW / Key][*HW/Key 2]
Differentials (Resource) [*HW / Key]
Review/ Key Applications of Differentiation
[*Review / KEY]
***** Review for Semester One Exam*****
***Unit 4: Integration (Khan Integrals)
Sigma Notation (Resource) [*HW/ KEY, HW/ KEY]
Area Approximation with Rectangles [*HW / KEY]
Anti derivatives and Indefinite Integrals. Basic Deriv. and Integration Notes Sheet [*HW /KEY, HW/KEY]
Area. (Resource)[*HW/ KEY, KEY for extra 3 problems with limit]
Riemann Sums and Definite Integrals. (Resource 1, Resource 2)
Rules of Integration and U-Substitution packet for 2/11-2/14 week [Packet/Key]
The Fundamental Theorem of Calculus. (Resource)[*HW/ KEY]
Integration by Substitution.(Khan, Resource, More Practice) (*HW1/ Key , HW2 / Key)
***Review (integration) 1 /KEY Extra Review for Unit 4 (Integration) test /KEY
Second Fundamental Theorem of Calculus Notes [*HW/Key]
Mean Value Theorem (Finds the X value) and Absolute Value Theorem (average height, Finds Y value) Notes / Notes2 [*HW/Key]
Net Change and Substitution with an extra Variable (Video Notes) [*HW/Key]
Motion Notes[HW1 , HW2]
Hard Integration Practice(Great Practice Webpage) Great Source
Review for Integration Test / Key
***Unit 5: Logarithmic, Exponential, and Other Transcendental Functions
The Natural Logarithmic Function: Differentiation and Integration Notes [*integration and Ln HW]
Inverse Trigonometric Functions: Differentiation and Integration
Exponential Functions: Differentiation and Integration
Chain Rule with Natural Log and Exponential Functions
Review of all above [*HW 2/23 w/Key]
Bases Other than e and Applications Derivatives and Integrals [*HW and Key]
***Unit 6: Differential Equations
Slope Fields (Resource 1, Resource 2, Resource 3) [*HW / Key]
Differential Equations /Hyperbolic Functions[*HW / Key]
Book Page 377-378 # 5,9,15,19,23,25,33,34,39,41 [*HW /Key]
Differential Equations: Growth and Decay [*HW/Key]
Separation of Variables and Logistic Equations [*HW + book P.414/61-66] Extra Orthogonal Trajectories Examples
Homogeneous Differential Equations [*HW Problem 3 Only/Key]
[*Review / KEY] for Differential Equations Test
***Unit 7: Applications of Integration
Area of a Region Between Two Curves (Resource) [*HW/ KEY] [*HW2/KEY]
Volume: The Disk and Washer Method [*HW/KEY1][*HW/KEY2]
Arc Length and Surfaces of Revolution [*HW/KEY]
Review Test/ KEY
Final Project Description/Rubric
Year End Review/ Key
L'Hospitals Rule
Final Exam Review Topics