Calculus How Calculus Works Studymates in Focus In Focus 1st Edition by Christine Tootill ISBN 1842850792 9781842850794

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ISBN 10: 1842850792 
ISBN 13: 9781842850794
Author: Christine Tootill

Calculus How Calculus Works Studymates in Focus In Focus 1st Table of contents:

• Advice to Students
  Practical tips and strategies for approaching calculus studies effectively.

• Working with Changing Quantities
  Introduction to the concept of change and its significance in calculus.

• Notation
  Explanation of the symbols and notation commonly used in calculus.

• What Will Calculus Do for Us?
  Discussion on the applications and importance of calculus in various fields.

• The Quadratic Curve
  Analysis of quadratic functions and their properties.

• The Rectangular Hyperbola
  Study of hyperbolic functions and their characteristics.

• Rates of Change on Straight Line Graphs
  Understanding how rates of change are represented on linear graphs.

• Gradient of a Tangent to a Curve
  Exploration of the concept of the gradient and its calculation.

• From the Gradient of a Chord to the Gradient of a Curve
  Transition from average to instantaneous rates of change.

• It’s the Limit!
  Introduction to the fundamental concept of limits in calculus.

• The Gradient Function of the Quadratic Curve
  Deriving and interpreting the gradient function for quadratic curves.

• The Gradient Function of the Cubic Curve
  Extending the concept of gradient functions to cubic curves.

• Deductions from Previous Results
  Building upon earlier concepts to deepen understanding.

• The General Rule for…
  Presentation of general rules and formulas in calculus.

• Algebraic Manipulation
  Techniques for manipulating algebraic expressions in calculus.

• Negative and Fractional Powers
  Handling of negative and fractional exponents in calculus.

• Repeated Differentiation
  Exploration of higher-order derivatives and their applications.

• What Are Maximum and Minimum Values?
  Identification and calculation of extrema in functions.

• What Do Stationary Points Look Like?
  Analysis of stationary points and their significance.

• Using Differentiation to Find Stationary Points
  Applying differentiation techniques to locate stationary points.

• Distinguishing Between Maximum and Minimum Points
  Methods for determining the nature of stationary points.

• Areas, Perimeters, and Volumes
  Calculating areas under curves, perimeters, and volumes of solids.

• Equation of a Tangent
  Deriving the equation of a tangent line to a curve.

• Equation of a Normal
  Determining the equation of a normal line to a curve.

• Two-Step Differentiation
  Techniques for performing successive differentiation.

• Reversing the Differentiation Process
  Introduction to integration as the reverse process of differentiation.

• Finding the Original Functions from the Gradient Function
  Methods for determining original functions from their derivatives.

• Definite Integrals
  Understanding and calculating definite integrals.

• The Approximate Area Under a Curve
  Estimating areas under curves using various methods.

• Using Integration to Find Areas
  Applying integration techniques to compute areas.

• Practice Questions for Revision and Exam Preparation
  A collection of practice problems to reinforce learning and prepare for assessments.

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