Mathematics Methods 3 & 4
Please Note - this is my old 3CD Maths page, and needs revising to match the Methods 3 & 4 Curriculum, but still has some useful material on it
Paul's Notes. An excellent set of university level notes, with expanded explanations and examples for calculus.
A brilliant resource made available by Paul Dawkins of Lamar University. Any use must be in accordance with his Terms and Conditions of use found here : http://tutorial.math.lamar.edu/terms.aspx
The layout can be a bit dodgy on Explorer 11, but adding the address to compatibility view helps. Chrome works fine. Try printing out the notes by chapter or section, but be aware that some of the files are quite large. A link to the notes for his calculus 1 course are also given below.
Paul's Notes Site: http://tutorial.math.lamar.edu/
Calculus notes: http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx
A brilliant resource made available by Paul Dawkins of Lamar University. Any use must be in accordance with his Terms and Conditions of use found here : http://tutorial.math.lamar.edu/terms.aspx
The layout can be a bit dodgy on Explorer 11, but adding the address to compatibility view helps. Chrome works fine. Try printing out the notes by chapter or section, but be aware that some of the files are quite large. A link to the notes for his calculus 1 course are also given below.
Paul's Notes Site: http://tutorial.math.lamar.edu/
Calculus notes: http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx
Classpad Help Series Website: http://www.classpad.com.au/
introduction_to_the_central_limit_theorem.pdf |
Differentiation videos:
https://www.khanacademy.org/math/calculus/differential-calculus/product_rule/v/product-rule?v=h78GdGiRmpM
https://www.khanacademy.org/math/calculus/differential-calculus/product_rule/v/quotient-rule
https://www.khanacademy.org/math/calculus/differential-calculus/chain_rule/v/chain-rule-definition-and-example?v=IiBC4ngwH6E
https://www.khanacademy.org/math/calculus/differential-calculus/product_rule/v/product-rule?v=h78GdGiRmpM
https://www.khanacademy.org/math/calculus/differential-calculus/product_rule/v/quotient-rule
https://www.khanacademy.org/math/calculus/differential-calculus/chain_rule/v/chain-rule-definition-and-example?v=IiBC4ngwH6E
Topic 3.1: Further differentiation and applications
Topic 3.2: Integrals
Topic 3.3: Discrete random variables
Topic 4.1: The logarithmic function
Graphing Log Functions
Topic 4.2: Continuous random variables and the normal distribution
Topic 4.3: Interval estimates for proportions
Algebraic Long Division:
https://www.khanacademy.org/math/trigonometry/polynomial_and_rational/dividing_polynomials/v/polynomial-division
https://www.khanacademy.org/math/trigonometry/polynomial_and_rational/dividing_polynomials/v/polynomial-division
Partial Fractions
http://www.khanacademy.org/math/algebra2/rational-expressions/partial-fraction-expan-alg/v/partial-fraction-expansion-1
http://www.khanacademy.org/math/algebra2/rational-expressions/partial-fraction-expan-alg/v/partial-fraction-expansion-2
http://www.khanacademy.org/math/algebra2/rational-expressions/partial-fraction-expan-alg/v/partial-fraction-expansion-3
http://tutorial.math.lamar.edu/Classes/Alg/PartialFractions.aspx
http://www.khanacademy.org/math/algebra2/rational-expressions/partial-fraction-expan-alg/v/partial-fraction-expansion-2
http://www.khanacademy.org/math/algebra2/rational-expressions/partial-fraction-expan-alg/v/partial-fraction-expansion-3
http://tutorial.math.lamar.edu/Classes/Alg/PartialFractions.aspx
Partial fractions Explanations (more complex than you will need, but the explanations can be followed fairly easily):
Chapter 2 Linear Programming (Graphing Inequalities)
Graphing 2 linear inequalities: https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/graphing-inequalities/v/graphical-system-of-inequalities
Checking Solutions (Defined areas): https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/graphing-inequalities/v/graphing-systems-of-inequalities-2
Modelling situations with inequalities: https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/modeling-with-linear-inequalities/v/u06-l3-t1-we3-graphing-systems-of-inequalities
Graphing 2 linear inequalities: https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/graphing-inequalities/v/graphical-system-of-inequalities
Checking Solutions (Defined areas): https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/graphing-inequalities/v/graphing-systems-of-inequalities-2
Modelling situations with inequalities: https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/modeling-with-linear-inequalities/v/u06-l3-t1-we3-graphing-systems-of-inequalities
integration_by_partial_fractions.pdf |
partial_fraction_decomposition_purple_math.docx |
Integration:
1. Basic concept of antidifferentiation: https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/indefinite_integrals/v/antiderivatives-and-indefinite-integrals
2. https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/indefinite_integrals/v/indefinite-integrals-of-x-raised-to-a-power
3. http://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/riemann-sums/v/simple-riemann-approximation-using-rectangles
4. http://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/riemann-sums/v/generalizing-a-left-riemann-sum-with-equally-spaced-rectangles
5. https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/definite_integrals/v/riemann-sums-and-integrals
6. https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/definite_integrals/v/evaluating-simple-definite-integral
7. https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/definite_integrals/v/area-between-curves
8. Volume of Solids of revolution about y axis: https://www.youtube.com/watch?v=Y4tHgy0XiUM
and https://www.khanacademy.org/math/integral-calculus/solid_revolution_topic/solid_of_revolution/v/solid-of-revolution-part-6
1. Basic concept of antidifferentiation: https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/indefinite_integrals/v/antiderivatives-and-indefinite-integrals
2. https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/indefinite_integrals/v/indefinite-integrals-of-x-raised-to-a-power
3. http://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/riemann-sums/v/simple-riemann-approximation-using-rectangles
4. http://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/riemann-sums/v/generalizing-a-left-riemann-sum-with-equally-spaced-rectangles
5. https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/definite_integrals/v/riemann-sums-and-integrals
6. https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/definite_integrals/v/evaluating-simple-definite-integral
7. https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/definite_integrals/v/area-between-curves
8. Volume of Solids of revolution about y axis: https://www.youtube.com/watch?v=Y4tHgy0XiUM
and https://www.khanacademy.org/math/integral-calculus/solid_revolution_topic/solid_of_revolution/v/solid-of-revolution-part-6
Fundamental Theorem of Calculus:
Fundamental Theorem of Calculus explanation (not proof):
http://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/fundamental-theorem-of-calculus/v/fundamental-theorem-of-calculus
Fundamental Theorem of Calculus application (including and x^2 example):
http://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/fundamental-theorem-of-calculus/v/applying-the-fundamental-theorem-of-calculus
Fundamental Theorem of Calculus: What happens when x is at the lower boundary?
https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/fundamental-theorem-of-calculus/v/swapping-the-bounds-for-definite-integral
Fundamental Theorem of Calculus and chain rule combination:
https://www.youtube.com/watch?v=lEOjMAmkI-U
Fundamental Theorem of Calculus explanation (not proof):
http://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/fundamental-theorem-of-calculus/v/fundamental-theorem-of-calculus
Fundamental Theorem of Calculus application (including and x^2 example):
http://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/fundamental-theorem-of-calculus/v/applying-the-fundamental-theorem-of-calculus
Fundamental Theorem of Calculus: What happens when x is at the lower boundary?
https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/fundamental-theorem-of-calculus/v/swapping-the-bounds-for-definite-integral
Fundamental Theorem of Calculus and chain rule combination:
https://www.youtube.com/watch?v=lEOjMAmkI-U
Geometric Congruency:
https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/other-triangle-congruence-postulates
https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/v/other-triangle-congruence-postulates
e and compound interest: https://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial/cont-comp-int-and-e/v/e-through-compound-interest
e as a limit: https://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial/cont-comp-int-and-e/v/e-as-limit
Continuous compounding interest: https://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial/cont-comp-int-and-e/v/continuously-compounding-interest-formula-e
The Exponential Function 3C (Chapter 5)