Leonard Euler (1707-1783)
- Leonard Euler, the dominant mathematical figure of his century and the most prolific mathematician ever, was also an astronomer, physicist, botanist, and chemist, and an expert in oriental languages. His work was the first to give the function concept the prominence that it has in mathematics today. Euler's collected books and papers fill 72 volumes. This doesn't count his enormous correspondence to approximately 300 addresses. His introductory Algebra text, written originally in German (Euler was Swiss), is still available in English translation.
Calculus resources:
1. Online MIT Calculus resources:
https://www.edx.org/course/calculus-1a-differentiation-2
2. MIT video lectures:
https://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/video-lectures/
3. Lecture notes:
https://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/lecture-notes/
4. Khan Academy:
https://www.khanacademy.org/math/calculus-1
5. Online Calculus resources:
http://www.calculus.org/
6. Paul's Online notes:
http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx
7. Calculus Help - Relatable videos:
https://www.calculus-help.com/tutorials/
8. Ron Larson's Calculus:
http://www.larsoncalculus.com/calc11/.
9. Calculus AB resources:
https://www.numerade.com/courses/calculus-1-ab/
10. Video - Calculus - The foundation of modern science:
https://www.youtube.com/watch?v=rjLJIVoQxz4- 19:03 mins
11. Mr. Wood's resources (great worksheets with answers):
http://www.mathwithmrwood.com/ap-calculus/ap-calculus-differentiation
www.mathwithmrwood.com/ap-calculus
12. Mrs. Gerald's math class:
site.google.com/a/clevelandcountyschools.org/srgerald/calculus-resources-1
13. Calculus formulas and worksheets:
www.math.arizona.edu/~calc/m129Worksheets.html
14. 3 paradoxes that gave us Calculus (video) - 13:34 mins:
www.youtube.com/watch?v=EbHqtENNnSY
15. AP Calculus Hub (Henrico County):
sites.google.com/a/henrico.k12.va.us/ap-calculus/
16. Mr. Wood's resources:
www.mathwithmrwood.com/ap-calculus
November 18, 2020
The textbook:
Finney, Demana, Waits, Kennedy
Calculus, AP* Edition; Graphical, Numerical, Algebraic 4th Edition 2012
Online pdf version:
www.pearson.com/us/higher-education/product/Finney-Downloadable-Teacher-s-Resources-for-Calculus-Graphical-Numerical-Algebraic-4th-Edition/9780132801621.html
Online exercises with solutions SLADER:
www.slader.com/textbook/9780133178579-calculus-graphical-numerical-algebraic-4th-edition/9/quick-review/1/
Chapter 1. Prerequisites for Calculus.
1.1 Lines
1. Rate of change Quizizz:
https://quizizz.com/admin/private?tag=5e38437119efe2001bb5fc5d
2. Calculus Fundamentals:
https://brilliant.org/courses/calculus-done-right/?from_topic=calculus
3. Find a slope of a linear function:
https://www.ixl.com/math/precalculus/find-the-slope-of-a-linear-function- Please, score close to 60 points.
4. Graphing by using slope-intercept form:
https://www.quia.com/cz/43443.html?AP_rand=384401134- Please, collect 4 coins.
5.Find a slope from the graph:
http://www.quia.com/rr/79713.html - Please, earn your 1st million!
6.Parallel or perpendicular lines?
http://www.quia.com/rr/79706.html - Please, earn your 2nd million!
7. Writing linear functions:
Please, complete the worksheet.
8. Perpendicular of parallel lines, Quizizz:
https://quizizz.com/admin/quiz/59f8513421266610007ef87a/parallel-and-perpendicular-lines
9. Linear regression models:
https://mathbits.com/MathBits/TINSection/Statistics1/lineBestFit.html- Please, predict number of calories for food with 17 grams of fat.
10. Check your knowledge of linear equations:
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations- Take the Unit Test, 12 questions. Good luck!
November 19, 2020
1.2 Functions and Graphs
1. Determine domain and range from graphs:
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:introduction-to-the-domain-and-range-of-a-function/e/domain_and_range_0.5- Please, complete 7 questions.
2. Interpreting graphs of functions practice:
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/linear-nonlinear-functions-tut/e/interpreting-graphs-of-linear-and-nonlinear-functions- Please, answer 4 questions.
3. Even and odd functions:
https://www.mathsisfun.com/algebra/functions-odd-even.html- Please, complete 10 questions at the end of the page.
4. Piecewise functions:
https://www.shelovesmath.com/algebra/advanced-algebra/piecewise-functions/
https://www.mathsisfun.com/sets/functions-piecewise.html
Piecewise functions and art (Simba):
https://www.desmos.com/calculator/tewjweialh
Desmos Creative Art ->https://www.desmos.com/art
5. Composite functions:
https://www.mathsisfun.com/sets/functions-composition.html- Please, complete 10 questions at the end of the page.
6. Turtle Crossing activity on Desmos:
https://teacher.desmos.com/activitybuilder/custom/5ddbf9ae009cd90bcdeaadd7
November 20, 2020
1. 3 Exponential Functions 1. Exponential growth and decay -
https://www.mathsisfun.com/algebra/exponential-growth.html- Please, complete 10 questions at the end of the page.
2. Rules for exponents game:
http://www.math-play.com/exponents-pirate-game/exponents-pirate-game_html5.html- Find the treasure!
3. Please, join the class:
https://quizizz.com/join?class=J580319
4. Please, join Calculus class on Khan Academy:
https://www.khanacademy.org/join/67ZG5QNA
5. Domain and range of exponential functions:
https://www.ixl.com/math/calculus/domain-and-range-of-exponential-and-logarithmic-functions- Please, score close to 60 points.
Half-life formula:
November 21, 2020
1.5 Logarithmic functions.
1. Introduction to logarithms:
https://www.mathsisfun.com/algebra/logarithms.html- Please, complete 10 questions at the end of the page.
November 30, 2020
INVERSE AND LOGARITHMIC FUNCTIONS
1. Complete the module for logarithmic functions:
https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs- Please, complete all practice exercises and take the Unit Test. Good luck!
2. Inverse functions:
https://www.mathsisfun.com/sets/function-inverse.html- Please, answer 10 questions at the end of the page.
December 1, 2020
1.6 Trigonometric functions.
1. Please, review trigonometric functions:
https://www.khanacademy.org/math/algebra-home/alg-trig-functions- complete all practice exercises and take a Unit Test.
December 2, 2020
Review 1.1-1.6.
1. Composition of functions.
Quizziz:https://quizizz.com/admin/quiz/5bd303840b948f001a142743/composition-of-functions
Please, join a Calculus class:
https://quizizz.com/join?class=J580319
2. Calculus in 35 minutes:
https://www.youtube.com/watch?v=WsQQvHm4lSw
3. Introduction to limits:
https://www.khanacademy.org/math/calculus-1/cs1-limits-and-continuity
December 3, 2020 Chapter 2. Limits and Continuity.
1. Properties of Limits.
https://www.khanacademy.org/math/calculus-1/cs1-limits-and-continuity/cs1-properties-of-limits/v/limit-properties- Please, complete all practice exercises.
2. Evaluating limits:
https://www.khanacademy.org/math/calculus-1/cs1-limits-and-continuity/cs1-limits-by-direct-substitution/v/limit-by-substitution
3. L'Hopital's rule:
https://www.mathsisfun.com/calculus/l-hopitals-rule.html
December 4, 2020
2.4 Rates of change and Tangent lines
Pierre de Fermat (1601-1665) story - Biography of the Great Thinker:
https://www.youtube.com/watch?v=Ij01HGgxnkA
Marjorie Lee Browne (1914-1979) -https://www.youtube.com/watch?v=kt_l_lFAPjs
Instantaneous Rate of Change (example):
https://www.khanacademy.org/math/in-in-grade-11-ncert/in-in-class11-derivatives/copy-of-derivative-as-instantaneous-rate-of-change-ab/v/approximating-equation-of-tangent-line-word-problem-1
Secant Lines and Rates of Change:
https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-1/e/secants-and-average-rate-of-change - Please, complete all practice exercises.
December 7, 2020
2-2 Limits at infinity.
1. Paul's online notes:
http://tutorial.math.lamar.edu/Classes/CalcI/LimitsAtInfinityI.aspx- Please, complete all practice exercises.
2. Please, complete all practice exercises and take a Quiz 5:
https://www.khanacademy.org/math/calculus-1/cs1-limits-and-continuity#cs1-infinite-limits
December 8, 2020
3.1 Derivatives.
1. Derivatives and Basic rules.
https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-1/e/secants-and-average-rate-of-change
2. Visualizing derivatives:
https://www.khanacademy.org/math/in-in-grade-11-ncert/in-in-class11-derivatives/copy-of-derivative-as-a-function-ab/e/visualizing_derivatives- Please, complete the Practice part.
3. Estimating derivatives at a point:
https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-3/v/estimating-derivative-at-a-point- Please, complete 4 questions.
December 9, 2020 3.3 Rules of differentiation.
1. Connecting differentiability and continuity: determining when derivatives do and do not exist.
https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-4/v/differentiability- Please, complete two practice exercises after that.
2. Applying the power rule:
https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-5/v/power-rule- Please, complete practice exercises.
3. Basic derivatives rules:
https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-6a/v/derivative-properties-and-polynomial-derivatives- Please, complete all practice exercises.
4. Derivative rules:
https://www.mathsisfun.com/calculus/derivatives-rules.html- Please, complete all 13 questions at the end of the page.
December 10, 2020
Differentiation rules (cont.). Product and Quotient rules.
1. Please, practice product rule:
https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-8/v/applying-the-product-rule-for-derivatives
2. Please, practice Quotient rule:
https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-9/v/quotient-rule- Complete all practice exercises, please.
December 11, 2020
Differentiation of trigonometric functions.
1. Differentiation of sine, cos functions.
https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-7/v/derivatives-of-sinx-and-cosx-
Please, complete all practice exercises.
2.Differentiation of tangent, cotangent and secant functions.
https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-10/v/derivatives-of-tanx-and-cotx- Please, complete all practice exercises.
3. Take the Quiz #3.https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/quiz/ab-2-10-quiz?modal=1
4. Take the Unit Test. Good luck!
https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/test/ab-diff-1-optional-unit-test?modal=1
5. Desmos. Derivatives:https://www.desmos.com/calculator/qtzamwcdrk
December 14, 2020
Field-trip-> National Air and Space Museum, Steven F. Udvar-Hazy, Chantilly, VA
https://airandspace.si.edu/udvar-hazy-center
Museum guide:
https://airandspace.si.edu/sites/default/files/hazy-space-hangar.pdf
What's TOPS at the Udvar-Hazy Center?:
https://airandspace.si.edu/sites/default/files/hazy-whats-tops.pdf
December 15, 2020
Chapter 4.
4.1Chain Rule. Derivative of the composite function. Second derivative.
1. Please, complete practice exercises in the following module:
https://www.khanacademy.org/math/calculus-1/cs1-derivatives-chain-rule-and-other-advanced-topics
2. Second derivatives:
https://www.mathsisfun.com/calculus/second-derivative.html- Please, answer 20 questions.
December 16, 2020
4.2 Implicit differentiation.
1. Please, complete all practice exercises:
https://www.khanacademy.org/math/calculus-1/cs1-derivatives-chain-rule-and-other-advanced-topics/cs1-implicit-differentiation/v/implicit-differentiation-1
2. Please, practice second derivatives:
https://www.khanacademy.org/math/calculus-1/cs1-derivatives-chain-rule-and-other-advanced-topics/cs1-second-derivatives/v/second-derivatives.
3. Differentiation inverse functions:
https://www.khanacademy.org/math/calculus-1/cs1-derivatives-chain-rule-and-other-advanced-topics/cs1-differentiating-inverse-functions/v/derivatives-of-inverse-functions- Please, complete all practice exercises.
Nicknames for derivatives:
1st derivative - "prime"
2nd derivative - "second"
3rd derivative - "jerk"
4th derivative - "snap" or "jounce"
5th derivative - "crackle"
6th derivative - "pop"
They go: distance, speed, acceleration, jerk, snap, crackle and pop
December 17, 2020Chapter 5. Application of derivatives.
5.1 Extreme Values of functions.
https://www.mathsisfun.com/calculus/maxima-minima.html
Please, complete 10 questions at the end of the page.
1. Please, complete practice exercises:
https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/ab-5-4/v/relative-minima-maxima
December 18, 2020
5.2 Mean Value Theorem
1. Finding relative minimum and maximum:
https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/ab-5-4/e/critical-numbers- Please, complete practice exercises.
2. Finding absolute extremas:
https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/ab-5-5/v/using-extreme-value-theorem- Please, complete all practice exercises.
3. Mean value Theorem:
https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/ab-5-1/v/mean-value-theorem-1- Please, complete all practice exercises.
January 11, 2021
Applications for derivatives.
1. Meaning of a derivative in context:
https://www.khanacademy.org/math/calculus-1/cs1-applications-of-derivatives- Please, complete practice exercises.
2. Straight line motion:
https://www.khanacademy.org/math/calculus-1/cs1-applications-of-derivatives/cs1-straight-line-motion/v/one-dimensional-motion-with-calculus- Please, complete practice exercises.
3. Non-motion applications of derivatives:
https://www.khanacademy.org/math/calculus-1/cs1-applications-of-derivatives/cs1-non-motion-applications-of-derivatives/v/modeling-a-forgetting-curve
4. Take the Quiz #1.
January 12, 2020
Related rates.
1. Introduction to related rates:
https://www.khanacademy.org/math/calculus-1/cs1-applications-of-derivatives/cs1-introduction-to-related-rates/v/rates-of-change-between-radius-and-area-of-circle- Please, complete practice exercises.
2. Solving related rates problems:
https://www.khanacademy.org/math/calculus-1/cs1-applications-of-derivatives/cs1-introduction-to-related-rates/v/rates-of-change-between-radius-and-area-of-circle- Please, complete practice exercises. Please, take the Quiz #2.
3. Approximation with local linearity:
https://www.khanacademy.org/math/calculus-1/cs1-applications-of-derivatives/cs1-approximation-with-local-linearity/v/local-linearization-intro- Please, complete practice exercises.
4. L'Hopital's rule:
https://www.khanacademy.org/math/calculus-1/cs1-applications-of-derivatives/cs1-lhpitals-rule/v/introduction-to-l-hopital-s-rule- Please, complete practice exercises.
5. L'Hopital's rule: Composite exponential functions->
https://www.khanacademy.org/math/calculus-1/cs1-applications-of-derivatives/cs1-lhpitals-rule-composite-exponential-functions/v/tricky-lhopitals-rule-problem- Please, complete practice exercises.
6. Take the Unit Test. Good luck!
January 13, 2020
1. Derivatives of inverse functions:
https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-2-new/ab-3-3/e/derivatives-of-inverse-functions- Please, complete all practice exercises.
January 14, 2020
1. Differentiation of trigonometric functions:
https://www.khanacademy.org/math/in-in-grade-12-ncert/in-in-continuity-differentiability/copy-of-trigonometric-functions-differentiation-ab/e/differentiate-trigonometric-functions- Please, answer 4 questions.
2. Mathbits. Numerical derivatives:
https://www.mathbits.com/MathBits/TISection/Calculus/Derivative.htm
3. Derivatives of exponential and logarithmic functions:
tutorial.math.lamar.edu/classes/calci/diffexplogfcns.aspx
January 15, 2020
1. Introduction to Integral Calculus.
https://www.khanacademy.org/math/integral-calculus/ic-integration/ic-integral-calc-intro/v/introduction-to-integral-calculus
2. Accumulation of change:
https://www.khanacademy.org/math/integral-calculus/ic-integration/ic-integral-calc-intro/e/area-under-a-rate-function-equals-net-change- Please, answer 4 questions.
3. Approximation with Riemann sums.
https://www.khanacademy.org/math/integral-calculus/ic-integration/ic-riemann-sums/v/simple-riemann-approximation-using-rectangles- Please, complete 3 practice exercises.
4. Summation notation.
https://www.khanacademy.org/math/integral-calculus/ic-integration/ic-summation-notation/v/sigma-notation-sum- Please, complete practice exercise.
January 18, 2020
1. Integrals.
https://www.khanacademy.org/math/integral-calculus/ic-integration
2. Approximation with Riemann sums:
https://www.khanacademy.org/math/integral-calculus/ic-integration/ic-riemann-sums/v/simple-riemann-approximation-using-rectangles-Please, complete practice exercises.
3. Riemann summation.
https://www.khanacademy.org/math/integral-calculus/ic-integration/ic-riemann-sums-summation-notation/v/generalizing-a-left-riemann-sum-with-equally-spaced-rectangles- Please, complete all practice exercises.
4. Take the Quiz #1:
https://www.khanacademy.org/math/integral-calculus/ic-integration/quiz/ic-definite-integral-definition-quiz?modal=1- Good luck!
January 19, 2020
Integration rules.
1. Introduction to integrals:
https://www.mathsisfun.com/calculus/integration-introduction.html- Please, answer 10 questions at the end of the page.
2. Integration rules:
https://www.mathsisfun.com/calculus/integration-rules.html- Please, complete 10 questions at the end of the page.
3 Useful link - Finding Numerical Derivatives on TI-84+:
https://www.mathbits.com/MathBits/TISection/Calculus/Derivative.htm
4. Please, practice reverse power rule:
https://www.khanacademy.org/math/integral-calculus/ic-integration/ic-reverse-power-rule/v/indefinite-integrals-of-x-raised-to-a-power- Please, complete all practice exercises.
5. Fundamental Theorem of Calculus (Average value of functions):
https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-7/v/connecting-the-first-and-second-fundamental-theorems-of-calculus- Please, complete all practice exercises and take the Quiz #2. Good luck!
