Mapping Diagrams: From AB to C&DE, Resource

Martin Flashman, 19 maj 2016

Introduction: The more one studies mathematics, the more one encounters the concept of a function. By talking about functions we come to understand how they encode information. To bring a deeper understanding to functions we give them visual expression. Seeing the information of a function presented in a variety of forms helps us recognize more concretely some of its fundamental features. These resource materials have been developed to help students understand functions more sensibly and deeply using four common ways to present the encoded information of a function. Students may have encountered some of these methods previously, but in this resource you will see how each of these methods give us different ways to view the same underlying relation. The four ways that connect an understanding of functions are: Tables of data for "variable" quantities. Algebraic equations that determine a method for determining the value of (controlled or dependent) variable quantities uniquely from the value of other (controlling or independent) variable quantities. The visualization of data for variable quantities using the Cartesian coordinate system. The visualization of data for variable quantities [b]using mapping diagrams.[/b] For more textual connections see: [url]http://users.humboldt.edu/flashman/MD/section-1.1VF.html[/url]

Innehåll

  1. MD from AB to C&DE On-line Resource
    1. Mapping Diagrams Online Resource:Chapters with Drop Down Sections
  2. Visualizing Functions
    1. reading.VFC.0
    2. Mapping Diagram (Real) from Function Table Activity
    3. Mapping Diagram Composition Adjust Arrows
    4. example.TGG.0
    5. example.DTA.0
    6. example.DTS.0
    7. example.DTCOM.0
    8. Mapping diagrams
    9. Mapping diagrams with adjustable output centre
    10. Mapping Diagram, Spreadsheet, Graph, Realign, Focus
    11. Visualizing Numeric Transformations
    12. Guess My Rule with MD
    13. VF.TSS.0.xls Spreadsheet
  3. Linear Functions
    1. example.LF.DA.0.
    2. Example LF.2.1
    3. Example LF.2.2
    4. Example LF 2.3
    5. Example LF.2.4
    6. Example LF 2.5
    7. Example LF.4.1
    8. Example LF.4.2
    9. Example LF.DID.0
    10. example.LF.DFP.0
    11. example.LF.COMP.1.GG
    12. example.LF.DCOMP.0.
    13. example. LF.COMP.3 Composition of Core Linear Functions
    14. example.LF.INV.1.GG
    15. Example LF.INV.2
    16. Example LF.INV.3
    17. example.LF.DINV.0
    18. Example LF.FORM.1 Slope Intercept
    19. Example LF.Form.2. Point-Slope Form
    20. Example LF.FORM.2 Point-Slope Composition
    21. Example LF.FORM.3 Two Point Form
    22. Example LF.FORM.4 Point Slope Composition
    23. example.LF.DFORM.0
    24. Example LF.LEQ.1
    25. Example LF.LEQ.2 Solve Linear Equation (2)
    26. example.LF.LEQ.3.0
    27. example.LF.DLEQ.0
    28. Example.LF.DLEQ2.0 Solve f(x)=g(x) for Linear functions
    29. Example LInEQ.2
  4. Quadratic Functions
    1. Example QF.FORM.1
    2. Example QF.FORM 2
    3. Example QF.FORM 3
    4. Example QF.FORM .4
    5. Example QF.FORM.n
    6. Example QF.2.1
    7. Example QF.2.2
    8. Example QF.2.3
    9. Example QF.2.4
    10. Example QF.3.1
    11. Example QF.3.2
    12. Example QF.COMP.2
    13. Example QF.FORM.DVComp
    14. example.QF.DVFORM.0
    15. example.QF.DSFORM.0
    16. example.QF.DID.0
    17. Example QF.INV.2i
    18. Example QF.INV.2ii
    19. Example QF.INV.3i
    20. Example QF.INV.3ii
    21. example.QF.DSYMM.0
    22. example.QF.INV.1.GG
    23. example.QF.DINV.0.1
    24. Example QEQ.0
    25. Example QEQ.1
    26. example.QF.DQEQ.0
    27. QF.QEQ.2.0
    28. Example QF.QInEQ.0
    29. Example QF.DQInEQ.0
  5. Other Algebraic Functions
    1. example.OAF.RF.0
    2. Example OAF.PFF.1
    3. Example OAF.PFF.2
    4. Example OAF.PFF.3
    5. Example OAF.PFF.4
    6. example.OAF.DPFF.0
    7. example.OAF.DPSF.0
    8. example.OAF.RFF.1
    9. example.OAF.RFF.2
    10. example.OAF.RFF.3
    11. example.OAF.RFF.4
    12. Example OAF.COMP.1
    13. Example OAF.COMP.2
    14. Example OAF.COMP.3
    15. Example OAF.QCOMP.1
    16. Example OAF.QCOMP.2
    17. example.OAF.DRF.0
    18. example.OAF.CPPF.1.0.
    19. example.OAF.DSYMM.0
    20. example.OAF.BRF.1.0
    21. example.OAF.BRF.2.0
    22. example.OAF.BRF.3.0
    23. example.OAF.BRF.4.0
    24. example.OAF.SAE.1.0
    25. example.OAF.SAE.2.0
    26. example.OAF.DSAE.1.0
    27. example.OAF.DSAE.2.0
    28. example.OAF.CPPF.4.0
    29. example.OAF.CPPF.3.0
    30. example.OAF.CPPF.2.0
    31. example.OAF.CNPF.1.0
    32. example.OAF.CNPF.2.0
    33. example.OAF.CNPF.3.0
    34. example.OAF.CNPF.4.0
    35. example.OAF.DCPPF.0
    36. example.OAF.DCNPF.0
    37. example.OAF.DVNPF.0
    38. example.OAF.DVPPF.0
  6. Other Ways to Define Functions
    1. example.OW.0
    2. example.OW.FDPC.1.0
    3. example.OW.FDPC.2.0
    4. example.OW.FDPC.3.0
    5. example.OW.FDPC.4.0
    6. example.OW.DFDPC.0
    7. example.OW.ICPPF.1.0
    8. example.OW.ICPPF.2.0
    9. example.OW.ICPPF.3.0
    10. example.OW.ICPPF.4.0
    11. example.OW.DICPPF.0
    12. example.OW.IMPL.3.0
    13. example.OW.IMPL.2.0
    14. example.OW.IMPL.1.0
    15. example.OW.DIMPL.1.0.A
    16. example.OW.DIMPL.1.0.B
    17. example.OW.RECF.1.0
    18. example.OW.RECF.2.0
    19. example.OW.RECF.3.0.
    20. example.OW.RECF.4.0
    21. Example OW.DRECF.0 a
    22. Example OW.DRECF.0 b
  7. Exponential and Logarithmic Functions
    1. example.ELF.0
    2. example.ELF.CELF.1.0
    3. example.ELF.CELF.2.0
    4. example.ELF.CELF.3.0
    5. example.ELF.CELF.4.0
    6. ELF.LCELF.1.0
    7. example.ELF.DCELF.0.
    8. example.ELF.DOM.L.1.0
    9. example.ELF.DOM.L.2.0
    10. example.ELF.DOM.L.3.0
    11. example.ELF.DDOM.L.0
    12. example.ELF.NEL.1.0
    13. example.ELF.NEL.2.0
    14. example.ELF.NEL.3.0
    15. example.ELF.IDA.2.0
    16. example.ELF.DIDA.0
    17. example.ELF.AP.1.0.A
    18. example.ELF.AP.1.0.B
    19. example.ELF.AP.2.0.A
    20. example.ELF.AP.2.0.B
    21. example.ELF.AP.3.0.A
    22. example.ELF.AP.3.0.B
    23. proof.ELF.AP.P.1.0
    24. proof.ELF.AP.P.2.0
    25. proof.ELF.AP.P.3.0
    26. proof.ELF.AP.P.4.0
    27. example.ELF.LCELF.1.0
    28. example.ELF.LCELF.2.0
    29. example.ELF.LCELF.3.0
    30. example.ELF.DLCELF.0
    31. example.ELF.INV.1
    32. example.ELF.INV.2.A
    33. example.ELF.INV.2.B
    34. example.ELF.INV.3
    35. example.ELF.SEQ.1.0
    36. example.ELF.SEQ.2.0
    37. example.ELF.SEQ.E.3.0
    38. example.ELF.DSEQ.E.0
    39. example.ELF.SEQ.L.1.0
    40. example.ELF.SEQ.L.2.0
    41. example.ELF.SEQ.L.3.0
    42. example.ELF.DSEQ.L.0
  8. Trigonometric Functions
    1. example.TRIG.0
    2. TRIG.MD.Deg.Rad.0.ggb
    3. TRIG.TRIDEF.2.ggb
    4. TRIG.TRIDEF.MD.ggb
    5. TRIG.circle.DEF.SCT.0.ggb
    6. TRIG.other.MD.Recip.0
    7. TRIG.circle.other.1
    8. Theorem.TRIG.SHAPE.1
    9. theorem.TRIG.SHAPE.2
    10. TRIG.Circle.SYM.0.1
    11. example.TRIG.DSYMM.0
    12. definition.InvTrigF.UnitCircle.ASIN
    13. definition.InvTrigF.UnitCircle.ACOS
    14. definition.InvTrigF.UnitCircle.ATAN
    15. definition.ITrigF
    16. theorem.TRIG.PERIOD,SC
    17. theorem.TRIG.PERIOD.TAN
    18. example.TRIG.DPB.0
    19. example.TRIG.SEQ.1.0.
    20. example.TRIG.SEQ.2.0
    21. example.TRIG.SEQ.3.0.
    22. Example SEQ.SC.4
    23. TRIG.MD All Solve Eqn.3
    24. TRIG.MD.ALLSolveGraph.0
    25. example.TRIG.ID.1.0
    26. example.TRIG.ID.2.0
    27. TRIG.DID.0
    28. TRIG.Circle.A*sin(Bx+C),A*cos(Bx+C).MD.0.1
    29. TRIG.Circle.A*tan(Bx+C)
    30. TRIG.MD.Graph.Table.Atrig(Bx+C)
    31. example.TRIG.COMP.1
    32. example.TRIG.COMP.2
    33. example.TRIG.COMP.3.0
    34. example.TRIG.COMP.4
    35. example.TRIG.LCOMP.1
    36. example.TRIG.LCOMP.2
    37. example.TRIG.LCOMP.3
    38. example.TRIG.LCOMP.4
    39. example.TRIG.SYM.1
    40. Example TRIG.SYM.2
    41. Example TRIG.SYM.3
    42. Example TRIG.SYM.4
    43. theorem.TRIG.TID
    44. Example.TRIG.SEQ.T.1
    45. Example.TRIG.SEQ.T.2
    46. Example TRIG.SEQ.T.3.
  9. Algebra and Elementary Functions
    1. AEF. example.1
    2. AEF.Example.2
    3. Example AEF.0
    4. Mapping Diagrams and Graphs for Arithmetic Operations
    5. Mapping Diagrams (I) for Arithmetic operations to create new functions from old.
    6. Mapping Diagrams (II) for Arithmetic Operations
    7. example.AEF.COMP.1.
    8. example.AEF.COMP.2.
    9. example.AEF.DCOMP.0.
    10. Example AEF.MR.1
    11. Example AEF.DR.1
    12. Example AEF.SR.1
    13. Example AEF.ERU.1
    14. AEF.CSS Composition: Socks and Shoes
    15. Example AEF.NEB Numerical Estimation Bisection
    16. AEF.NEFP Numerical Estimation False Position
    17. Example AEF.NENS Newton Secant Method
    18. Example AEF.NEC Numerical Estimation Comparison
    19. Mapping diagrams - composite functions
    20. AMATYC 2017: Using Mapping Diagrams to Make Sense of Functions and Equations
  10. Calculus I: Continuity & Differentiation
    1. Example.CCD.DDF.1
    2. Example CCD.CCF.2
    3. CCD.DDS.R. Example.2. Singularities with a root function.
    4. Example CCD.DLC.4
    5. Example CCD.DLC.1
    6. Example CCD.DCL.3
    7. CCD.UL: Uniqueness of Limits.Theorem and Proof
    8. Calculus of Limits
    9. Theorem: CCD.IVT.0:
    10. CH1F.ii.Figure 6
    11. CDD.DSMD0: The Derivative of the Sine at x=0: sin'(0)=1
    12. CDD.DCMD0 The Derivative of the Cosine at x=0: cos'(0)=0.
    13. CCD.DSMD: The derivative of the sine and cosine functions
    14. CCD.DDN4S: Four Steps to Find The Derivative
    15. CCD.DE exp'(0)estimated with h>0.
    16. CCD.DEMD.0: exp'(0)=1
    17. CCD.DPN Derivatives for Power Functions (n=1,2,3,...)
    18. CCD.DPZ Derivative of Powers for n= -1,-2,-3,...
    19. CCD,MVT The Mean Value Theorem
  11. Calculus II: Diff'l Eq'ns, Integration & Series
    1. CIS.EM.TMD. Diff'l Eq'ns: Euler's Method, Mapping Diagrams, Slope Fields
    2. CIS.EM. Differential Equations: Mapping Diagram,Slope Field, Solution
    3. CIS.VDI. The Riemann Integral: Mapping Diagram and Graph
    4. CIS.PDI. Properties of the Definite Integral
    5. CIS:PSPDI "Proof" of Sum Property for the Definite Integral
    6. CIS.PSMPDI Scalar Multiple Property "Proof"
    7. CIS.PAPDI "Proof" of Additive Property of Definite Integral
    8. CIS.VMVTI Visualizing the Mean Value Theorem for Integral and its Proofs
    9. CIS.FTCD The Fundamental Theorem of Calculus (Derivative)
  12. Calculus III: Multivariable Functions and Calculus
    1. Mapping Diagram and Graph for 3 Variables
  13. Complex Functions and Calculus
    1. Complex Line Integral: Definition and F.T. Examples

1.

MD from AB to C&DE On-line Resource

  • 1. Mapping Diagrams Online Resource:Chapters with Drop Down Sections

1.1.

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2.

Visualizing Functions

  • 1. reading.VFC.0
  • 2. Mapping Diagram (Real) from Function Table Activity
  • 3. Mapping Diagram Composition Adjust Arrows
  • 4. example.TGG.0
  • 5. example.DTA.0
  • 6. example.DTS.0
  • 7. example.DTCOM.0
  • 8. Mapping diagrams
  • 9. Mapping diagrams with adjustable output centre
  • 10. Mapping Diagram, Spreadsheet, Graph, Realign, Focus
  • 11. Visualizing Numeric Transformations
  • 12. Guess My Rule with MD
  • 13. VF.TSS.0.xls Spreadsheet

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3.

Linear Functions

  • 1. example.LF.DA.0.
  • 2. Example LF.2.1
  • 3. Example LF.2.2
  • 4. Example LF 2.3
  • 5. Example LF.2.4
  • 6. Example LF 2.5
  • 7. Example LF.4.1
  • 8. Example LF.4.2
  • 9. Example LF.DID.0
  • 10. example.LF.DFP.0
  • 11. example.LF.COMP.1.GG
  • 12. example.LF.DCOMP.0.
  • 13. example. LF.COMP.3 Composition of Core Linear Functions
  • 14. example.LF.INV.1.GG
  • 15. Example LF.INV.2
  • 16. Example LF.INV.3
  • 17. example.LF.DINV.0
  • 18. Example LF.FORM.1 Slope Intercept
  • 19. Example LF.Form.2. Point-Slope Form
  • 20. Example LF.FORM.2 Point-Slope Composition
  • 21. Example LF.FORM.3 Two Point Form
  • 22. Example LF.FORM.4 Point Slope Composition
  • 23. example.LF.DFORM.0
  • 24. Example LF.LEQ.1
  • 25. Example LF.LEQ.2 Solve Linear Equation (2)
  • 26. example.LF.LEQ.3.0
  • 27. example.LF.DLEQ.0
  • 28. Example.LF.DLEQ2.0 Solve f(x)=g(x) for Linear functions
  • 29. Example LInEQ.2

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4.

Quadratic Functions

  • 1. Example QF.FORM.1
  • 2. Example QF.FORM 2
  • 3. Example QF.FORM 3
  • 4. Example QF.FORM .4
  • 5. Example QF.FORM.n
  • 6. Example QF.2.1
  • 7. Example QF.2.2
  • 8. Example QF.2.3
  • 9. Example QF.2.4
  • 10. Example QF.3.1
  • 11. Example QF.3.2
  • 12. Example QF.COMP.2
  • 13. Example QF.FORM.DVComp
  • 14. example.QF.DVFORM.0
  • 15. example.QF.DSFORM.0
  • 16. example.QF.DID.0
  • 17. Example QF.INV.2i
  • 18. Example QF.INV.2ii
  • 19. Example QF.INV.3i
  • 20. Example QF.INV.3ii
  • 21. example.QF.DSYMM.0
  • 22. example.QF.INV.1.GG
  • 23. example.QF.DINV.0.1
  • 24. Example QEQ.0
  • 25. Example QEQ.1
  • 26. example.QF.DQEQ.0
  • 27. QF.QEQ.2.0
  • 28. Example QF.QInEQ.0
  • 29. Example QF.DQInEQ.0

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5.

Other Algebraic Functions

  • 1. example.OAF.RF.0
  • 2. Example OAF.PFF.1
  • 3. Example OAF.PFF.2
  • 4. Example OAF.PFF.3
  • 5. Example OAF.PFF.4
  • 6. example.OAF.DPFF.0
  • 7. example.OAF.DPSF.0
  • 8. example.OAF.RFF.1
  • 9. example.OAF.RFF.2
  • 10. example.OAF.RFF.3
  • 11. example.OAF.RFF.4
  • 12. Example OAF.COMP.1
  • 13. Example OAF.COMP.2
  • 14. Example OAF.COMP.3
  • 15. Example OAF.QCOMP.1
  • 16. Example OAF.QCOMP.2
  • 17. example.OAF.DRF.0
  • 18. example.OAF.CPPF.1.0.
  • 19. example.OAF.DSYMM.0
  • 20. example.OAF.BRF.1.0
  • 21. example.OAF.BRF.2.0
  • 22. example.OAF.BRF.3.0
  • 23. example.OAF.BRF.4.0
  • 24. example.OAF.SAE.1.0
  • 25. example.OAF.SAE.2.0
  • 26. example.OAF.DSAE.1.0
  • 27. example.OAF.DSAE.2.0
  • 28. example.OAF.CPPF.4.0
  • 29. example.OAF.CPPF.3.0
  • 30. example.OAF.CPPF.2.0
  • 31. example.OAF.CNPF.1.0
  • 32. example.OAF.CNPF.2.0
  • 33. example.OAF.CNPF.3.0
  • 34. example.OAF.CNPF.4.0
  • 35. example.OAF.DCPPF.0
  • 36. example.OAF.DCNPF.0
  • 37. example.OAF.DVNPF.0
  • 38. example.OAF.DVPPF.0

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6.

Other Ways to Define Functions

  • 1. example.OW.0
  • 2. example.OW.FDPC.1.0
  • 3. example.OW.FDPC.2.0
  • 4. example.OW.FDPC.3.0
  • 5. example.OW.FDPC.4.0
  • 6. example.OW.DFDPC.0
  • 7. example.OW.ICPPF.1.0
  • 8. example.OW.ICPPF.2.0
  • 9. example.OW.ICPPF.3.0
  • 10. example.OW.ICPPF.4.0
  • 11. example.OW.DICPPF.0
  • 12. example.OW.IMPL.3.0
  • 13. example.OW.IMPL.2.0
  • 14. example.OW.IMPL.1.0
  • 15. example.OW.DIMPL.1.0.A
  • 16. example.OW.DIMPL.1.0.B
  • 17. example.OW.RECF.1.0
  • 18. example.OW.RECF.2.0
  • 19. example.OW.RECF.3.0.
  • 20. example.OW.RECF.4.0
  • 21. Example OW.DRECF.0 a
  • 22. Example OW.DRECF.0 b

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7.

Exponential and Logarithmic Functions

  • 1. example.ELF.0
  • 2. example.ELF.CELF.1.0
  • 3. example.ELF.CELF.2.0
  • 4. example.ELF.CELF.3.0
  • 5. example.ELF.CELF.4.0
  • 6. ELF.LCELF.1.0
  • 7. example.ELF.DCELF.0.
  • 8. example.ELF.DOM.L.1.0
  • 9. example.ELF.DOM.L.2.0
  • 10. example.ELF.DOM.L.3.0
  • 11. example.ELF.DDOM.L.0
  • 12. example.ELF.NEL.1.0
  • 13. example.ELF.NEL.2.0
  • 14. example.ELF.NEL.3.0
  • 15. example.ELF.IDA.2.0
  • 16. example.ELF.DIDA.0
  • 17. example.ELF.AP.1.0.A
  • 18. example.ELF.AP.1.0.B
  • 19. example.ELF.AP.2.0.A
  • 20. example.ELF.AP.2.0.B
  • 21. example.ELF.AP.3.0.A
  • 22. example.ELF.AP.3.0.B
  • 23. proof.ELF.AP.P.1.0
  • 24. proof.ELF.AP.P.2.0
  • 25. proof.ELF.AP.P.3.0
  • 26. proof.ELF.AP.P.4.0
  • 27. example.ELF.LCELF.1.0
  • 28. example.ELF.LCELF.2.0
  • 29. example.ELF.LCELF.3.0
  • 30. example.ELF.DLCELF.0
  • 31. example.ELF.INV.1
  • 32. example.ELF.INV.2.A
  • 33. example.ELF.INV.2.B
  • 34. example.ELF.INV.3
  • 35. example.ELF.SEQ.1.0
  • 36. example.ELF.SEQ.2.0
  • 37. example.ELF.SEQ.E.3.0
  • 38. example.ELF.DSEQ.E.0
  • 39. example.ELF.SEQ.L.1.0
  • 40. example.ELF.SEQ.L.2.0
  • 41. example.ELF.SEQ.L.3.0
  • 42. example.ELF.DSEQ.L.0

7.1.

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7.2.

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7.3.

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7.4.

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7.5.

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7.6.

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7.7.

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7.8.

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7.9.

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7.10.

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7.11.

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7.12.

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7.13.

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7.14.

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7.15.

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7.16.

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7.17.

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7.18.

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7.19.

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7.20.

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7.21.

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7.22.

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7.23.

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7.24.

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7.25.

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7.26.

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7.27.

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7.28.

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7.29.

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7.30.

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7.31.

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7.32.

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7.33.

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7.34.

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7.35.

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7.36.

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7.37.

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7.38.

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7.39.

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7.40.

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7.41.

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7.42.

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8.

Trigonometric Functions

  • 1. example.TRIG.0
  • 2. TRIG.MD.Deg.Rad.0.ggb
  • 3. TRIG.TRIDEF.2.ggb
  • 4. TRIG.TRIDEF.MD.ggb
  • 5. TRIG.circle.DEF.SCT.0.ggb
  • 6. TRIG.other.MD.Recip.0
  • 7. TRIG.circle.other.1
  • 8. Theorem.TRIG.SHAPE.1
  • 9. theorem.TRIG.SHAPE.2
  • 10. TRIG.Circle.SYM.0.1
  • 11. example.TRIG.DSYMM.0
  • 12. definition.InvTrigF.UnitCircle.ASIN
  • 13. definition.InvTrigF.UnitCircle.ACOS
  • 14. definition.InvTrigF.UnitCircle.ATAN
  • 15. definition.ITrigF
  • 16. theorem.TRIG.PERIOD,SC
  • 17. theorem.TRIG.PERIOD.TAN
  • 18. example.TRIG.DPB.0
  • 19. example.TRIG.SEQ.1.0.
  • 20. example.TRIG.SEQ.2.0
  • 21. example.TRIG.SEQ.3.0.
  • 22. Example SEQ.SC.4
  • 23. TRIG.MD All Solve Eqn.3
  • 24. TRIG.MD.ALLSolveGraph.0
  • 25. example.TRIG.ID.1.0
  • 26. example.TRIG.ID.2.0
  • 27. TRIG.DID.0
  • 28. TRIG.Circle.A*sin(Bx+C),A*cos(Bx+C).MD.0.1
  • 29. TRIG.Circle.A*tan(Bx+C)
  • 30. TRIG.MD.Graph.Table.Atrig(Bx+C)
  • 31. example.TRIG.COMP.1
  • 32. example.TRIG.COMP.2
  • 33. example.TRIG.COMP.3.0
  • 34. example.TRIG.COMP.4
  • 35. example.TRIG.LCOMP.1
  • 36. example.TRIG.LCOMP.2
  • 37. example.TRIG.LCOMP.3
  • 38. example.TRIG.LCOMP.4
  • 39. example.TRIG.SYM.1
  • 40. Example TRIG.SYM.2
  • 41. Example TRIG.SYM.3
  • 42. Example TRIG.SYM.4
  • 43. theorem.TRIG.TID
  • 44. Example.TRIG.SEQ.T.1
  • 45. Example.TRIG.SEQ.T.2
  • 46. Example TRIG.SEQ.T.3.

8.1.

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8.2.

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8.3.

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8.4.

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8.5.

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8.6.

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8.7.

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8.8.

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8.9.

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8.10.

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8.11.

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8.12.

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8.13.

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8.14.

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8.15.

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8.16.

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8.17.

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8.18.

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8.19.

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8.20.

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8.21.

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8.22.

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8.23.

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8.24.

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8.25.

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8.26.

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8.27.

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8.28.

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8.29.

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8.30.

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8.31.

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8.32.

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8.33.

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8.34.

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8.35.

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8.36.

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8.37.

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8.38.

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8.39.

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8.40.

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8.41.

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8.42.

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8.43.

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8.44.

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8.45.

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8.46.

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9.

Algebra and Elementary Functions

  • 1. AEF. example.1
  • 2. AEF.Example.2
  • 3. Example AEF.0
  • 4. Mapping Diagrams and Graphs for Arithmetic Operations
  • 5. Mapping Diagrams (I) for Arithmetic operations to create new functions from old.
  • 6. Mapping Diagrams (II) for Arithmetic Operations
  • 7. example.AEF.COMP.1.
  • 8. example.AEF.COMP.2.
  • 9. example.AEF.DCOMP.0.
  • 10. Example AEF.MR.1
  • 11. Example AEF.DR.1
  • 12. Example AEF.SR.1
  • 13. Example AEF.ERU.1
  • 14. AEF.CSS Composition: Socks and Shoes
  • 15. Example AEF.NEB Numerical Estimation Bisection
  • 16. AEF.NEFP Numerical Estimation False Position
  • 17. Example AEF.NENS Newton Secant Method
  • 18. Example AEF.NEC Numerical Estimation Comparison
  • 19. Mapping diagrams - composite functions
  • 20. AMATYC 2017: Using Mapping Diagrams to Make Sense of Functions and Equations

9.1.

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9.2.

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9.3.

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9.4.

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9.5.

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9.6.

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9.7.

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9.8.

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9.9.

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9.10.

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9.11.

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9.12.

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9.13.

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9.14.

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9.15.

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9.16.

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9.17.

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9.18.

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9.19.

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9.20.

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10.

Calculus I: Continuity & Differentiation

  • 1. Example.CCD.DDF.1
  • 2. Example CCD.CCF.2
  • 3. CCD.DDS.R. Example.2. Singularities with a root function.
  • 4. Example CCD.DLC.4
  • 5. Example CCD.DLC.1
  • 6. Example CCD.DCL.3
  • 7. CCD.UL: Uniqueness of Limits.Theorem and Proof
  • 8. Calculus of Limits
  • 9. Theorem: CCD.IVT.0:
  • 10. CH1F.ii.Figure 6
  • 11. CDD.DSMD0: The Derivative of the Sine at x=0: sin'(0)=1
  • 12. CDD.DCMD0 The Derivative of the Cosine at x=0: cos'(0)=0.
  • 13. CCD.DSMD: The derivative of the sine and cosine functions
  • 14. CCD.DDN4S: Four Steps to Find The Derivative
  • 15. CCD.DE exp'(0)estimated with h>0.
  • 16. CCD.DEMD.0: exp'(0)=1
  • 17. CCD.DPN Derivatives for Power Functions (n=1,2,3,...)
  • 18. CCD.DPZ Derivative of Powers for n= -1,-2,-3,...
  • 19. CCD,MVT The Mean Value Theorem

10.1.

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10.2.

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10.3.

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10.4.

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10.5.

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10.6.

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10.7.

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10.8.

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10.9.

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10.10.

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10.11.

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10.12.

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10.13.

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10.14.

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10.15.

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10.16.

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10.17.

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10.18.

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10.19.

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11.

Calculus II: Diff'l Eq'ns, Integration & Series

  • 1. CIS.EM.TMD. Diff'l Eq'ns: Euler's Method, Mapping Diagrams, Slope Fields
  • 2. CIS.EM. Differential Equations: Mapping Diagram,Slope Field, Solution
  • 3. CIS.VDI. The Riemann Integral: Mapping Diagram and Graph
  • 4. CIS.PDI. Properties of the Definite Integral
  • 5. CIS:PSPDI "Proof" of Sum Property for the Definite Integral
  • 6. CIS.PSMPDI Scalar Multiple Property "Proof"
  • 7. CIS.PAPDI "Proof" of Additive Property of Definite Integral
  • 8. CIS.VMVTI Visualizing the Mean Value Theorem for Integral and its Proofs
  • 9. CIS.FTCD The Fundamental Theorem of Calculus (Derivative)

11.1.

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11.2.

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11.3.

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11.4.

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11.5.

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11.6.

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11.7.

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11.8.

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11.9.

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12.

Calculus III: Multivariable Functions and Calculus

  • 1. Mapping Diagram and Graph for 3 Variables

12.1.

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13.

Complex Functions and Calculus

  • 1. Complex Line Integral: Definition and F.T. Examples

13.1.

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Information