Unit 4
Specialist Mathematics (Queensland)
Topic 1: Integration and Applications
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Integration resulting in ln|ax+b|
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Proofs of derivatives of Inverse Trigonometric Functions
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Calculating derivatives of inverse trigonometric Functions
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Integration Resulting in Inverse trigonometric functions
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Integration by Substitution Introduction
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Integration by substitution worked examples part 1
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Integration by substitution worked examples part 2
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Integration by linear substitution
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Definite Integral & U substitution: One Weird Trick
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Using trig identities for integration
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Partial Fractions: Improper Rational Functions
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Integration by parts
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Integration by parts: choosing u and v’
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Integration by parts e^xsinx
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Integration by parts: Definite Integrals
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Volumes of solids of revolution introduction
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Volume of solids of revolution: between 2 curves
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Volumes of solids of revolution: Around the y axis
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Simpson’s Rule: Worked Example & Casio Calculator use
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Exponential probability density function: Waiting for stuff
Topic 2: Rates of Change & Differential Equations
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Implicit differentiation
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Solving differential equations
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Solving differential equations given in terms of f(y)
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Setting up differential equations
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Isaac Newton & My Cup of Coffee: Differential Equations Applications
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Differential equations: Mixing Problems
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Modelling Population Growth: The Logistic Equation – Differential Equations
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Verifying solutions to differential equations
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Separable differential equations
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Related Rates: Introduction and Worked Examples
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Related Rates Parametric equations
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Differential Equations with Related Rates
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Introduction to Slope Fields for Differential Equations
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Slope Fields Using the TI NSPIRE
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Displacement velocity acceleration etc
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Velocity in terms of displacement Acceleration in terms of velocity
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Other Expressions for acceleration part 1
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Other Expressions for acceleration part 2
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Simple Harmonic Motion
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Resultant forces
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Momentum
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Newton’s laws of motion
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Newtons laws of motion examples
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Calculating the Normal Reaction Force in an Elevator
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Resolution of force and Acceleration
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Resolution of force and acceleration down an inclined plane
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Variable forces
