MATH1023 Equation Sheet PDF

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MATH1023 EQUATION SHEETModule 2: Models and Differential EquationsFirst-Order Differential Equations Separable Differential EquationsNewton’s Law of Motion Acceleration/VelocityModule 3: Applications of Separable EquationsRadioactive Decay Constant GrowthExponential Growth Logistic GrowthFlow Proble...

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MATH1023 EQUATION SHEET Module 2: Models and Differential Equations First-Order Differential Equations

Separable Differential Equations

Newton’s Law of Motion

Acceleration/Velocity

Module 3: Applications of Separable Equations Radioactive Decay

Constant Growth

Exponential Growth

Logistic Growth

Flow Problems

Flow from a Container

Pollution Problems

Module 4: Linear Differential Equations First-Order Linear Differential Equation

Second-Order Linear Differential Equation

Solving a Linear Differential Equation

Solving Second-Order Equations

General Form of Linear Equations

Properties of Linear Equations

Module 5: Second Order Linear Equations and Oscillations Second Order Linear Equations

Nature of Solutions: Real, Distinct Roots

Nature of Solutions: Real, Repeated Root

Nature of Solutions: Imaginary Roots

The Harmonic Oscillator

Simple Harmonic Motion

Damped Harmonic Oscillator – Supercritical

Damped Harmonic Oscillator – Critical

Damped Harmonic Oscillator – Subcritical

Module 6: More General Differential Equations Inhomogeneous Linear Equations

General Solution

Harmonic Oscillator with Periodic Forcing

Harmonic Oscillator with Periodic Forcing – General Solution

Harmonic Oscillator with Periodic Forcing – Particular Solution

Solving Systems of Equations – Uncoupled/Independent

Solving Systems of Equations – Uncoupled/Solved Successively

Solving Systems of Equations – Coupled/One Variable Eliminated

Module 7: Curves and Surfaces in 3D Space Cartesian Equation of a Plane

Level Curves

Equation of a Plane

Equation of a Sphere

Equation of a Circular Cylinder

Equation of a Paraboloid

Equation of an Ellipse

Module 8: Partial Derivatives and Tangent Planes Partial Derivatives

Derivative Rules

Tangent Plane

Module 9: Further Applications of the Partial Derivative Linearisation

Differentiable Function

Differential – Two Variable Functions

Total Derivative Rule

The Chain Rule

Implicit Differentiation

Module 10: Directional Derivatives and the Gradient Vector Directional Derivative

Gradient Vector

Directional Derivatives and the Gradient Vector

Magnitude of Steepest Increase

Directional Derivative – Angle

Gradient Vector and Level Curves

Normal

Module 11: Second-Order Partial Derivatives and Continuity Second Order Partial Derivatives

Continuity of

f (x , y )

Differentiability of

f (x , y )

Limit of

f (x , y )

Testing Continuity

Mixed Derivatives Theorem

Module 12: Optimising Functions of Two Variables Global Extrema

Critical Point

Local Extrema

Discriminant of

f (x , y )...