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Steps Into Calculus

Interactive mindmap which collects together all the resources on calculus produced by the Learning Enhancement Team in the Dean of Students' Office at the University of East Anglia
by

Learning Enhancement Team

on 27 July 2016

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Transcript of Steps Into Calculus

What is Differentiation? Webcast
Click on the rectangle to open the What is Differentiation? Study Guide
A guide describing the meaning and language of differentiation.
Differentiation using the Power Rule Webcast
Click on the rectangle to open the Differentiation using the Power Rule Study Guide
Click on the rectangle to open the Differentiation using the Power Rule Worksheet
Click on the rectangle to open the Differentiation using the Power Rule Model Answers
Resources describing the first major rule of differentiation which finds the derivatives of power functions such as polynomial, reciprocal and roots.
Differentiating Basic Functions Webcast
Click on the rectangle to open the Differentiating Basic Functions Study Guide
Click on the rectangle to open the Differentiating Basic Functions Worksheet
Click on the rectangle to open the Differentiating Basic Functions Model Answers
Chain Rule
Chain Rule Webcast
Click on the rectangle to open the Chain Rule Study Guide
Click on the rectangle to open the Chain Rule
Worksheet
Click on the rectangle to open the Chain Rule Model Answers
The chain rule is a method for differentiating composite functions.
Product Rule
Product Rule Webcast
Click on the rectangle to open the Product Rule Study Guide
Click on the rectangle to open the Product Rule Worksheet
Click on the rectangle to open the Product Rule Model Answers
The product rule is a method for differentiating product functions.
Quotient Rule
Quotient Rule Webcast
Click on the rectangle to open the Quotient Rule Study Guide
The quotient rule is a method for differentiating quotient functions.
Definite
Integrals

Standard
Integrals
A list of fundamental integrals and rules for integrating.
Click on the rectangle to open the Sketching a Graph
Study Guide
Methods you should try to help you sketch a graph.
Five Basic Functions
Five Basic Functions
Webcast
Click on the rectangle to open the Five Basic Functions Factsheet
A factsheet with the properties of the five basic functions power, sine, cosine, exponential and logarithm.
Differentiating Basic Functions
Resources to help you find the derivative of five basic functions: power, sine, cosine, exponential and natural logarithm.
Standard
Derivatives
Standard
Derivatives Webcast
Click on the rectangle to open the Standard
Derivatives
Factsheet
A list of fundamental derivatives and rules of differentiation.
Indices are superscripts which mathematicians use as shorthand to describe how variables and numbers are multiplied together.
Laws of Indices Webcast
Click on the rectangle to open the Laws of Indices Study Guide
Click on the rectangle to open the Laws of Indices Worksheet
Click on the rectangle to open the Laws of Indices Model Solutions
Differentiation using the Power Rule
These resources describe how to use limits in integrals to find values which often correspond to an area.
Sketching a Graph
Sketching a Graph
Webcast
Definite
Integrals Webcast
Click on the rectangle to open the Definite
Integrals Study Guide
Click on the rectangle to open the Integration using the Power Rule Study Guide
Integration using the Power Rule
Webcast
Click on the rectangle to open the Integration using the Power Rule
Model Answers
Click on the rectangle to open the Integration using the Power Rule
Worksheet
What is Integration?
Click on the rectangle to open the What is Integration? Study Guide
Click on the rectangle to open the What is Integration? Worksheet
What is Integration? Webcast
Click on the rectangle to open the What is Integration? Model Answers
Integrating Basic Functions Webcast
Integrating Basic Functions
Click on the rectangle to open the Integrating Basic Functions
Study Guide
Integration and Natural Logarithms Webcast
A substitution method in integration which integrates a function which has a numerator which is the derivative of its denominator.
Click on the rectangle to open the Integration and Natural Logarithms Model Answers
Click on the rectangle to open the Integration and Natural Logarithms Worksheet
Integration and Natural Logarithms
Click on the rectangle to open the Integration and Natural Logarithms Study Guide
A method in integration which can be used to integrate some product functions.
Click on the rectangle to open the Integration by Parts Study Guide
Integration by
Parts Webcast
Integration by Parts
Click on the rectangle to open the Standard
Integrals Factsheet
Standard
Integrals Webcast
Resources to help you integrate five basic functions: power, sine, cosine, exponential and reciprocal.
The first major rule of integration helps you find the integral of a power function such as polynomials, reciprocals and roots.
Resources describing the meaning, symbols and language of integration.
Steps Into Calculus
Mind Map

What is Differentiation?
Laws of Indices
Integration using the
Power Rule
More Complicated Functions Webcast
Click on the rectangle to open the More Complicated Functions Study Guide
Click on the rectangle to open the More Complicated Functions Worksheet
Click on the rectangle to open the More Complicated Functions
Model Answers
Resources about construction more complicated function from more simple ones. This helps in choosing a rule for differentiation.
More Complicated Functions

Using This
Mind Map
Click on the rectangle below to open a document to help you get the most out of this Mind Map
https://portal.uea.ac.uk/documents/6207125/8199642/steps+into+calculus+what+is+differentiation.pdf
https://portal.uea.ac.uk/documents/6207125/8199648/steps+into+calculus+differentiating+basic+functions+worksheet.pdf
https://portal.uea.ac.uk/documents/6207125/8199648/steps+into+calculus+differentiating+basic+functions+model+answers.pdf
https://portal.uea.ac.uk/documents/6207125/8199648/steps+into+calculus+differentiating+basic+functions.pdf
https://portal.uea.ac.uk/documents/6207125/8325203/steps+into+calculus+standard+derivatives+factsheet.pdf
https://portal.uea.ac.uk/documents/6207125/8199651/steps+into+calculus+the+chain+rule+worksheet.pdf
https://portal.uea.ac.uk/documents/6207125/8199651/steps+into+calculus+the+chain+rule.pdf
https://portal.uea.ac.uk/documents/6207125/8199657/steps+into+calculus+the+quotient+rule.pdf
https://portal.uea.ac.uk/documents/6207125/8199654/steps+into+calculus+the+product+rule.pdf
https://portal.uea.ac.uk/documents/6207125/8199654/steps+into+calculus+the+product+rule+worksheet.pdf
https://portal.uea.ac.uk/documents/6207125/8199654/steps+into+calculus+the+product+rule+model+answers.pdf
https://portal.uea.ac.uk/documents/6207125/8198422/bridging+algebra+calculus+more+complicated+functions.pdf
https://portal.uea.ac.uk/documents/6207125/8198422/bridging+algebra+calculus+more+complicated+functions+worksheet.pdf
https://portal.uea.ac.uk/documents/6207125/8198422/bridging+algebra+calculus+more+complicated+functions+model+answers.pdf
https://portal.uea.ac.uk/documents/6207125/8199645/steps+into+calculus+differentiating+using+the+power+rule+model+answers.pdf
https://portal.uea.ac.uk/documents/6207125/8199645/steps+into+calculus+differentiating+using+the+power+rule+worksheet.pdf
https://portal.uea.ac.uk/documents/6207125/8199645/steps+into+calculus+differentiating+using+the+power+rule.pdf
https://portal.uea.ac.uk/documents/6207125/8194846/steps+into+algebra+laws+of+indices+model+answers.pdf
https://portal.uea.ac.uk/documents/6207125/8194846/steps+into+algebra+laws+of+indices+worksheet.pdf
https://portal.uea.ac.uk/documents/6207125/8194846/steps+into+algebra+laws+of+indices.pdf
https://portal.uea.ac.uk/documents/6207125/8199669/steps+into+calculus+what+is+integration.pdf
https://portal.uea.ac.uk/documents/6207125/8199669/steps+into+calculus+what+is+integration+worksheet.pdf
https://portal.uea.ac.uk/documents/6207125/8199669/steps+into+calculus+what+is+integration+model+answers.pdf
https://portal.uea.ac.uk/documents/6207125/8198428/bridging+algebra+calculus+sketching+a+graph.pdf
https://portal.uea.ac.uk/documents/6207125/8199685/steps+into+calculus+integrating+basic+functions.pdf
http://www.uea.ac.uk/services/students/let/study_resources/maths_stats/mathematics/calculus/standard_integrals_factsheet
https://portal.uea.ac.uk/documents/6207125/8199724/steps+into+calculus+integration+by+parts.pdf
https://portal.uea.ac.uk/documents/6207125/8199714/steps+into+calculus+integration+and+natural+logarithms.pdf
https://portal.uea.ac.uk/documents/6207125/8199714/steps+into+calculus+integration+and+natural+logarithms+worksheet.pdf
https://portal.uea.ac.uk/documents/6207125/8199714/steps+into+calculus+integration+and+natural+logarithms+model+answers.pdf
https://portal.uea.ac.uk/documents/6207125/8199672/steps+into+calculus+integrating+using+the+power+rule.pdf
https://portal.uea.ac.uk/documents/6207125/8199682/steps+into+calculus+definite+integrals.pdf
https://portal.uea.ac.uk/documents/6207125/8124756/Interactive+mind+map+guide.pdf
https://portal.uea.ac.uk/documents/6207125/8199672/steps+into+calculus+integrating+using+the+power+rule+worksheet.pdf
https://portal.uea.ac.uk/documents/6207125/8199672/steps+into+calculus+integrating+using+the+power+rule+model+answers.pdf
Click on the rectangle to open the Quotient Rule Worksheet
https://portal.uea.ac.uk/documents/6207125/8199657/steps+into+calculus+the+quotient+rule+worksheet.pdf
Click on the rectangle to open the Quotient Rule Model Answers
https://portal.uea.ac.uk/documents/6207125/8199657/steps+into+calculus+the+quotient+rule+model+answers.pdf
Click on the rectangle to open the Integrating Basic Functions
Worksheet
https://portal.uea.ac.uk/documents/6207125/8199685/steps+into+calculus+integrating+basic+functions+worksheet.pdf
https://portal.uea.ac.uk/documents/6207125/8199685/steps+into+calculus+integrating+basic+functions+model+answers.pdf
Click on the rectangle to open the Integrating Basic Functions
Model Answers
Stationary Points Webcast
Click on the rectangle to open the Stationary Points Study Guide
Stationary Points
A great use of differentiation is finding maximums, minimums and points of inflexion. These are described in this guide.
Finding Stationary Points Webcast
Click on the rectangle to open the Finding Stationary Points Study Guide
Click on the rectangle to open the Finding Stationary Points Worksheet
Click on the rectangle to open the Finding Stationary Points Model Answers
Finding Stationary Points
These resources describe how you can use differentiation to find and identify stationary points on graphs.
https://portal.uea.ac.uk/documents/6207125/8199660/steps+into+calculus+stationary+points.pdf
https://portal.uea.ac.uk/documents/6207125/8199663/steps+into+calculus+finding+stationary+points.pdf
https://portal.uea.ac.uk/documents/6207125/8199663/steps+into+calculus+finding+stationary+points+worksheet.pdf
https://portal.uea.ac.uk/documents/6207125/8199663/steps+into+calculus+finding+stationary+points+model+answers.pdf
Using Trigonometric formulas in Integration
Using certain trigonometric formulas, such as double angle formulas, can significantly simplify some integrations.
Click on the rectangle to open the Using Trigonometric Formulas in Integration Study Guide
https://portal.uea.ac.uk/documents/6207125/8199695/steps+into+calculus+using+trigonometric+formulas+in+integration.pdf
The Differential Operator
You can think of differentiation as the application of an operator to function. This guide explains this idea in more depth.
Click on the rectangle to open the Differential Operator Study Guide
https://portal.uea.ac.uk/documents/6207125/8199666/steps+into+calculus+the+differential+operator.pdf
Implicit Differentiation
Often functions are more complicated than those you can differentiate using the basic rules. This guide looks at how to find the derivative of implicit functions.
Click on the rectangle to open the Implicit Differentiation Study Guide
https://portal.uea.ac.uk/documents/6207125/8321840/steps+into+calculus+implicit+differentiation.pdf
Basics of Partial Differentiation
Many functions have more than one variable as inputs. This guide looks at how to find the derivative of these functions. This process is called partial differentiation
Click on the rectangle to open the Basics of Partial Differentiation Study Guide
https://portal.uea.ac.uk/documents/6207125/8322032/steps+into+calculus+basics+partial+differentiation.pdf
Differential Operator Webcast
Implicit Differentiation webcast
Basics of Partial Differentiation Webcast
Using Trigonometric Formulas in Integration Webcast
https://portal.uea.ac.uk/documents/6207125/8199651/steps+into+calculus+the+chain+rule+model+answers.pdf
https://portal.uea.ac.uk/documents/6207125/8221205/bridging+algebra+calculus+five+basic+functions+factsheet.pdf
Full transcript