1031 Mathematics for Life Sciences

Anchor_Mathematics, 17.09.2025

Inhaltsverzeichnis

  1. Basic Functions
    1. Transformations of an unknown function f(x)
    2. Reflections of an unknown function
    3. Line in gradient intercept form
    4. Parabola in factored form
    5. Parabola from completed square
    6. Cubic in translation form
    7. Cubic in factored form
    8. Absolute Value
    9. Hyperbola - Inverse Variation
    10. Circle centre (h,k), radius r
    11. Polynomial degree 4 - quartic in factor form
    12. Polynomial degree 5 - quintic in factor form
  2. Trigonometric Functions
    1. Sine Functions - Sinusoids
    2. Auxiliary Angle Formula for Sine
    3. Phase of Sine Functions - Sinusoids
  3. Exponential and Logarithmic Functions
    1. Exponential graph with variable Base
    2. Log graph with variable base
    3. Exponential graph base e
    4. Log Natural graph base e
  4. Calculus
    1. Differentiation from First Principles - Visualisation
    2. Gradient of an Exponential Function
    3. Gradient of Sine Function
    4. Gradient of Cosine Function

1.

Basic Functions

This chapter show the common transformations of functions, as well as the graphs of the basic functions and relationships

  • 1. Transformations of an unknown function f(x)
  • 2. Reflections of an unknown function
  • 3. Line in gradient intercept form
  • 4. Parabola in factored form
  • 5. Parabola from completed square
  • 6. Cubic in translation form
  • 7. Cubic in factored form
  • 8. Absolute Value
  • 9. Hyperbola - Inverse Variation
  • 10. Circle centre (h,k), radius r
  • 11. Polynomial degree 4 - quartic in factor form
  • 12. Polynomial degree 5 - quintic in factor form

1.1.

Transformations of an unknown function f(x)

Translations and scaling/reflections of an unknown function f(x)
– Anchor_Mathematics

1.2.

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1.7.

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1.9.

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1.10.

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1.11.

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1.12.

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2.

Trigonometric Functions

This chapter shows the basic sine and cosine graphs as well as their transformations

  • 1. Sine Functions - Sinusoids
  • 2. Auxiliary Angle Formula for Sine
  • 3. Phase of Sine Functions - Sinusoids

2.1.

Sine Functions - Sinusoids

Translations and scaling/reflections of the sine and cosine functions
– Anchor_Mathematics

2.2.

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3.

Exponential and Logarithmic Functions

This chapter shows graphs of the exponential and logarithmic functions of any base, and their transformations. There are separate graphs for [b]the[/b] exponential function (base [i]e[/i]) and the natural logarithmic function.

  • 1. Exponential graph with variable Base
  • 2. Log graph with variable base
  • 3. Exponential graph base e
  • 4. Log Natural graph base e

3.1.

Exponential graph with variable Base

Graph in the form y = k(a^(x+b))+c
– Anchor_Mathematics

3.2.

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4.

Calculus

  • 1. Differentiation from First Principles - Visualisation
  • 2. Gradient of an Exponential Function
  • 3. Gradient of Sine Function
  • 4. Gradient of Cosine Function

4.1.

Differentiation from First Principles - Visualisation

Visualisation of gradient between two points becoming gradient of curve at a single point
– Anchor_Mathematics, sihalliday1

4.2.

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