Differentiation and Functions in Mathematics  Revised
Gain a good understanding of differentiation and functions in mathematics.
Description
In mathematics functions are the idealization of how a varying quantity depends on another quantity, and Differentiation allows you to find and show rates of change, the two work handinhand. This course will give you a detailed insight to both functions and differentiation, and how to apply them for solving mathematical problems, and questions.
The course starts off with teaching you how to plot equations from a table of values on a graph, form quadratics to exponentials. You will learn about the algebra technique “completing the square” the process of translating functions on the X and Y axis and how to stretch them on both axis. Along with what the discriminant is and how to calculate it, and what inverse and Bijective functions are.
In the second module you will be introduced to basic differentiation and how to differentiate polynomials. You will learn about the equation of a tangent and a normal of a curve, what the second derivative is and how to derive it, differentiation of tangents, products and quotients. The module finishes by teaching you the Chain Rule, the Product Rule, and the Quotient Rule.
Next the course teaches you about the differentiation of logarithms, and how to differentiate trigonometry equations. After which the module discusses the relationship between differentiation and the rates of change, giving you two working examples. You will learn about using differentiation to calculate the turning points on a curve, the applications of differentiation in regards to velocity, acceleration, and electricity. Then the module moves on to showing you how to work out an algebraic formula from just two measurements, and exploring the relationship between different types of functions, their differential, and second derivative.
In the last topic you are introduced to Integration, in mathematics integration is the reverse of differentiation. You will learn about what it is at a basic level, integrating different types of formulas, and how to deal with the powers, indices and fractions for integration. You will be though about what definite integration is and integration with trigonometry and exponential equations.
Start Course NowModules
Functions

Functions  Learning Outcomes

Plotting Quadratic Graphs From Table of Values

Plotting Cubic Graphs From Table of Values

Plotting Reciprocal Graphs From Table of Values

Plotting Exponential Graphs From Table of Values

Matching Equations and Sketches

Sketching Parabola Using Completing The Square

Completing The Square and Sketching The Full Method

Matching Functions and Graphs – Quadratic / Exponential

Translation of Functions Using f(xa)

Translating Functions Using f(x)+a

Stretching Functions in x Direction

Stretching Functions in The y Direction

The Discriminant

Inverse and Bijective Functions

Functions  Lesson Summary
Differentiation  Part 1

Differentiation  Part 1  Learning Outcomes

Basic Differentiation of y = x^n

Differentiation of Polynomials

Equation of a Tangent

Equation of a Normal

Harder Questions on Normals

General Differentiation of x^n

Second Derivative

Differentiation of Tangents

Using Different Variables

Differentiating Products and Quotients

The Chain Rule

The Product Rule

The Quotient Rule

Differentiation  Part 1  Lesson Summary
Differentiation  Part 2

Differentiation  Part 2  Learning Outcomes

Differentiation of Logarithms

Differentiation of y = sinx

Differentiation of y = cosx

Differentiation and Rates of Change

Rate of Change Example 1

Rate of Change Example 2

Differentiation and Turning Points

Differentiation and Matching Graphs

Applications of Differentiation 1 (Displacement / Velocity / Acceleration)

Applications of Differentiation 2 (Voltage / Current)

Maximum Volume of Box

Exploring Relationships Between Graphs of Cubic Functions and Their Differentials

Exploring Relationships Between Graphs of Trigonometric Functions and Their Differentials

Exploring Relationships Between Graphs of Exponential Functions and Their Differentials

Inverse Functions Differentiated

Calculus  Differentiation  Part 2  Lesson Summary
Integration

Integration  Learning Outcomes

Basic Integration

The Integral Sign

Harder Integration

Definite Integration

Area Between Lines

Basic Differential Equations

Integration of Trig Functions (y=cos4x)

Integration of Exponentials

Introducing the Trapezoidal Rule

Trapezoidal Rule Into Integration

Finding the Area Between a Quadratic Function and a Straight Line

Integration  Lesson Summary
Course assessment
Learning Outcomes
Having completed this course students will be able to:
 Identify how to plot Quadratic, cubic, reciprocal and exponential graphs from a table of values
 Identify how to translate or stretch a function along either the x or y axis
 Identify an inverse function and a bijective function
 Recognize how to calculate the gradient of a curve
 Calculate the differentiation of several different types of formulas and equations
 Identify the chain rule, the product rule and the quotient rule
 Calculate the turning points of a curve
 Use differentiation to calculate the displacement, velocity and acceleration, of an object
 Discuss the relationships between different equations/functions and their differentials
 Discuss what basic integration is and calculate it
 Define and calculate definite integration
 Calculate the area under a curve with integration
Certification
All Alison courses are free to enrol, study and complete. To successfully complete this Certificate course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Certificate course, you have the option to acquire an official Certificate, which is a great way to share your achievement with the world. Your Alison Certificate is:
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