Contents of Unit – 5

• SL 5.1 – Introduction of differential calculus
• SL 5.2 – Increasing and decreasing functions
• SL 5.3 – Differentiating polynomials, n∈Zn \in \mathbb{Z}n∈Z
• SL 5.4 – Tangents and normal
• SL 5.5 – Integration introduction, areas between curve and x-axis
• SL 5.6 – Stationary points, local maximum and minimum
• SL 5.7 – Optimisation
• SL 5.8 – Trapezoid rule
• HL 5.9 – Differentiating standard functions and derivative rules
• HL 5.10 – Second derivatives, testing for maximum and minimum
• HL 5.11 – Indefinite integration, reverse chain rule, by substitution
• HL 5.12 – Areas under a curve onto x- or y-axis, volumes of revolution about the x- and y-axis
• HL 5.13 – Kinematic problems
• HL 5.14 – Setting up a differential equation (DE), solve by separating variables
• HL 5.15 – Slope fields
• HL 5.16 – Euler’s method for first-order differential equations (DEs)
• HL 5.17 – Phase portrait
• HL 5.18 – Euler’s method for second-order differential equations (DEs)