Rejuvenation of Science Engineering and Technology related TLTP and other legacy material

HELM Resources from ReSET Project
A collection of 45 Learning objects derived from Helping Engineers Learn Mathematics in the areas of Differentiation and Integration. These learning objects were created by the ReSET Project.

• Introducing Differentiation : 1 Drawing Tangents
  Explains what is meant by the gradient of a curve and introduces differentiation, by drawing tangents to the curve. Includes a small quiz to test knowledge of positive, negative or zero gradients (Learning Object 1/4).
• Introducing Differentiation : 2 Finding the Gradient at a Specific Point
  Introduces differentiation as a method for finding the gradient at any point. Illustrated by showing example of y(x) = x squared (Learning Object 2/4).
• Introducing Differentiation : 3 Finding the Gradient at a General Point
  Introduces differentiation as a method for finding the gradient of the curve at a general point. Illustrated with example y(x) = x squared. Includes notation for the derivative of x. i.e. dy/dx and y' (Learning Object 3/4).
• Introducing Differentiation : 4 Differentiating Function from First Principles
  Definition of differentiation from first principles (Learning Object 4/4).
• Introducing Differentiation
  A collection of 4 learning objects introducing differentiation from first principles.
• Table of Derivatives : 1 Common Functions
  Using a table of derivatives to perform differentiation of Common Functions. Also contains an interactive quiz to test knowledge of common derivatives. The functions include polynomials, exponentials, logarithms and trigonometric functions (Learning Object 1/3).
• Table of Derivatives : 2 Extending the Table of Derivatives
  Using a table of derivatives to perform differentiation. Rules for differentiating sums, differences and multiplication by a constant. Includes a multiple choice quiz to test knowledge on differentiating common functions (Learning Object 2/3).
• Table of Derivatives : 3 Evaluating a Derivative
  Finding the exact value of a derivative at a particular point. Requires use of a scientific calculator and notepad for evaluating answers for interactive quiz (Learning Object 3/3).
• Table of Derivatives
  A collection of three learning objects dealing with using a table of derivatives. Includes interactive quizzes to test knowledge.
• Higher Derivatives : 1 The Derivative of a Derivative
  Focusing on calculating second and other higher derivatives. Gives examples of calculating higher derivatives of polynomial functions (Learning Object 1/2).
• Higher Derivatives : 2 Notation
  Introducing notation for second and higher derivatives. Includes a short quiz on evaluating higher derivatives for specific values (Learning Object 2/2).
• Higher Derivatives
  A sequence of two learning objects dealing with second and higher derivatives and notation.
• Differentiating a Product
  Introduces the rule for differentiating products of standard functions. Shows how to use the product rule through examples.
• Differentiating a Quotient
  Introduces a rule for differentiating quotients. Shows how to apply this rule through examples and a quiz.
• Differentiating Products and Quotients
  A sequence of two learning objects which deals with the differentiation of products and quotients.
• The Chain Rule : 1 Function of a Function
  This resource describes what is meant by a function of a function, gives examples of such functions and includes a quiz on identifying component parts of composite functions (Learning Object 1/3).
• The Chain Rule : 2 Derivative of a Function of a Function
  This resources describes how to calculate the derivative of a function of a function by using the chain rule. Gives examples of using the chain rule and a multiple choice quiz (Learning Object 2/3).
• The Chain Rule : 3 Power Function
  Uses the chain rule to show a specific example of differentiating power functions, including a quiz (Learning Object 3/3).
• The Chain Rule
  A collection of three learning objects for use in teaching differentiation using the chain rule. Describes what is meant by a function of a function, shows how to differentiate these functions using the chain rule and provides a specific case of the chain rule for power functions.
• Parametric Differentiation : 1 Parametric Differentiation
  Finding derivatives when the equation of a curve is given in parametric form (Learning Object 1/2).
• Parametric Differentiation : 2 Higher Derivatives
  Finding higher derivatives when the equation of a curve is given in parametric form (Learning Object 2/2).
• Parametric Differentiation
  This resource contains a sequence of two Learning Objects dealing with Parametric Differentiation. Finding derivatives when the equation of a curve is given in parametric form.
• Basic Concepts of Integration : 1 Differentiation in Reverse
  Introduces integration as being the reverse process of integration (Learning Object 1/3).
• Basic Concepts of Integration : 2 Table of Integrals
  Shows a table of integrals and works through various examples of integration from the table (Learning Object 2/3).
• Basic Concepts of Integration : 3 Two Rules of Integration
  Introduces rules for integrating sums (differences) and scalar products. Includes many step by step examples of applying these rules (Learning Object 3/3).
• Basic Concepts of Integration
  A collection of three learning objects relating to the basic concepts of integration. Includes integration as differentiation in reverse, a table of integrals of common functions, the sum (difference) rule and the scalar multiple rules for integration.
• Definite Integrals : 1 What is a Definite Integral?
  Explanation of the concept of definite integrals (Learning Object 1/3).
• Definite Integrals : 2 Evaluating Definite Integrals
  Examples of evaluating definite integrals. Interactive quiz to test evaluation of definite integrals. Notepad and scientific calculator may be required to evaluate questions (Learning Object 2/3).
• Definite Integrals : 3 Some Integrals with Infinite Limits
  Example of definite integration where one of the limits is infinite. Describes how to solve an integral of this type (Learning Object 3/3).
• Definite Integrals
  A collection of three learning objects relating to definite integrals. Describes what a definite integral is, gives examples on how to solve definite integrals and gives a further example on how to evaluate some integrals which have infinite limits. May require notepad and scientific calculate to evaluate some questions.
• Area Bound by Curve : 1 Calculating the Area under a Curve
  Using Integration to calculate the area of a graph bound by the curve (Learning Object 1/3).
• Area Bound by Curve : 2 Above the X Axis
  Worked example using integration to calculate the area bound by a curve above the X Axis. Also includes an interactive quiz with further examples. Notepad and scientific calculator may be required to calculate answers (Learning Object 2/3).
• Area Bound by Curve : 3 Area Below the X Axis
  Worked example using integration to find area under graph when function goes below the x-axis. Also indicates method for calculating the area for functions which lie both above and below the x-axis (Learning Object 3/3).
• Area Bound by Curve
  A collection of three Learning Objects using integration as a means of finding the area bound by a curve.
• Integration by Parts : 1 Indefinite Integration
  Integration by parts technique for integrating products of functions. This learning objects deals with indefinite integrals and shows many worked examples (Learning Object 1/2).
• Integration by Parts : 2 Definite Integration
  Integration by parts technique for integrating products of functions. This learning objects deals with definite integrals and shows rule applied more than once to same integral (Learning Object 2/2).
• Integration by parts
  A collection of two learning objects dealing with integration by parts. Shows both indefinite and definite integration.
• Integration by Substitution : 1 Making a Substitution
  Uses simple substitutions to make integrating complicated functions easier. Shows example of substitutions being made (Learning Object 1/3).
• Integration by Substitution : 2 Definite Integrals
  Focuses on rewriting the limits in terms of the new variable whilst using integration by substitution for definite integrals (Learning Object 2/3).
• Integration by Substitution : 3 Integrals Giving Rise to Logarithms
  Special case of using integration by substitution when integrating a quotient when the numerator is the derivative of the denominator. Shows how to solve by inspection giving rise to a logarithmic solution (Learning Object 3/3).
• Integration by Substitution
  A collection of three learning objects demonstrating integration by substitution. Shows how to make a substitution, explains changing the limits for definite integrals and some special cases.
• Integration using Partial Fractions
  Integrating complicated algebraic functions by simplify into partial fractions. Shows a worked example then gives further examples to try. A notepad may be required to calculate solutions to these examples.
• Integration of Trigonometric Functions : 1 Simple
  Use trigonometric identities to write integrands in alternative forms to enable them to be integrated (Learning Object 1/2).
• Integration of Trigonometric Functions : 2 Complicated
  This resource describes how to integrate more complicated functions such as sine squared x by rewriting in simpler terms (Learning Object 2/2).
• Integration of Trigonometric Functions
  A collection of two learning objects dealing with the integration of trigonometric functions. Includes both simple and more complicated functions.