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Revision notes
A Level
Maths
Edexcel
Modelling with Differential Equations

Modelling with Differential Equations

Maths: Edexcel A Level Pure Maths, topic 8.2.7

Test yourself on Modelling with Differential Equations

Practise this topic for free

Previous topic8.2.6 Integration by Partial Fraction Next topic9.1.1 Number Iterations

Maths: Edexcel A Level Pure Maths contents

1 Proof
2 Algebra & Functions
3 Coordinate Geometry
4 Sequences & Series
- 4.1 Binomial Expansion
  4.1.1 Pascal's Triangle
  4.1.2 Factorials
  4.1.3 Binomial Expansion
  4.1.4 Binomial Expansion & Rational Powers (A2 only)
  4.1.5 Binomial Expansion & Rational Powers 2 (A2 only)
- 4.2 Sequences (A2 only)
  4.2.1 Nth term Rules
  4.2.2 Recurring Rules
  4.2.3 Types of Sequences
  4.2.4 Arithmetic Sequences
  4.2.5 Geometric Sequences
  4.2.6 Sigma Notation
  4.2.7 Arithmetic Series
  4.2.8 Geometric Series
  4.2.9 Sum to Infinity of a Geometric Series
  4.2.10 Modelling with Sequences & Series
5 Trigonometry
- 5.1 Using Angles
  5.1.1 Radians
  5.1.2 Arc length
  5.1.3 Area of Sectors
  5.1.4 Area of Segments
- 5.2 Trigonometric Functions
  5.2.1 Unit Circle
  5.2.2 Properties of Trig Functions
  5.2.3 Trigonometry
  5.2.4 Exact values
  5.2.5 Graphs of Trigonometric Functions
  5.2.6 Small Angle Approximation
- 5.3 Triangle Rules
  5.3.1 Sine Rules
  5.3.2 Cosine Rules
  5.3.3 Area of a Triangle
- 5.4 Trigonometric Identities
  5.4.1 Secant, Cosecant & Cotangent
  5.4.2 Pythagorean Identities
  5.4.3 Angle Addition Formulae
  5.4.4 Manipulating the Angle Addition Formulae
  5.4.5 Double Angle Formula
6 Exponentials & Logarithms
- 6.1 Exponentials & Logarithms
  6.1.1 Exponential Function
  6.1.2 Logarithms
  6.1.3 Properties of Logarithms
  6.1.4 Natural Logarithm
  6.1.5 Graphs of Exponents & Logarithms
- 6.2 Exponential Growth Decay
  6.2.1 Population Growth
  6.2.2 Depreciation
  6.2.3 Graphing Linear and Exponential Growth
  6.2.4 Interpreting Exponential Growth and Decay Graphs
  6.2.5 Compound Growth & Decay
  6.2.6 Compund Interest
7 Differentiation
- 7.1 Derivatives
  7.1.1 Gradient of a Curve
  7.1.2 Differentiation from First Principles
  7.1.3 Differentiation from First Principles - Practice
  7.1.4 Differentiation
  7.1.5 Finding derivatives
  7.1.6 Second Order Derivatives
- 7.2 Graphs & Differentiation
  7.2.1 Stationary Points
  7.2.2 Maxima & Minima
  7.2.3 Modelling with Differentiation
  7.2.4 Using Second Derivatives (A2 only)
  7.2.5 Rate of Change (A2 only)
- 7.3 Differentiation With Trigonometry and Exponentials
  7.3.1 Differentiation with Sin & Cos
  7.3.2 Diff. of Exponential Functions
  7.3.3 Differentiation of Trig. Functions 1 (A2 only)
  7.3.4 Differentiation of Trig. Functions 2 (A2 only)
- 7.4 Rules of Differetiation (A2 only)
  7.4.1 Chain Rule
  7.4.2 Product Rule
  7.4.3 Quotient Rule
- 7.5 Parametric & Implicit Differentiation
  7.5.1 Parametric Differentiation
  7.5.2 Implicit Differentiation
8 Integration
- 8.1 Integration
  8.1.1 Integration - Basics
  8.1.2 Integration - Definite Integrals
  8.1.3 Finding Functions
  8.1.4 Area under curves
  8.1.5 Area under x-axis
  8.1.6 Area between curves and lines
- 8.2 Integration (A2 Only)
  8.2.1 Integration - Standard Functions
  8.2.2 Integration - Reverse Chain Rule
  8.2.3 Integration by Substitution
  8.2.4 Integration by Parts
  8.2.5 Integration by Parts - Practice
  8.2.6 Integration by Partial Fraction
  8.2.7 Modelling with Differential Equations
9 Numerical Methods
- 9.1 Finding Solutions
  9.1.1 Number Iterations
  9.1.2 Iterations to 1 Decimal Places
  9.1.3 Iteration Formula
  9.1.4 Locating Roots
  9.1.5 Newton Raphson Method
- 9.2 Finding the Area
  9.2.1 Trapezium Rule
10 Vectors
- 10.1 2D Vectors
  10.1.1 Vectors - Magnitude & Direction
  10.1.2 Unit Vectors
  10.1.3 Vectors - Algebraic Operations
  10.1.4 Position Vectors
  10.1.5 Vector Proofs
  10.1.6 Vectors Word Questions
- 10.2 3D Vectors
  10.2.1 3D Vector Magnitude
  10.2.2 3D Vectors - Algebraic Operations
  10.2.3 Position Vectors 3D
  10.2.4 3D Vectors Word Questions
- 10.3 Vector Proofs
  10.3.1 Coming Soon

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