Contents of Unit – 5

• SL 5.1 – Introduction of differential calculus
• SL 5.2 – Increasing and decreasing functions
• SL 5.3 – Differentiating polynomials
• SL 5.4 – Tangents and normal
• SL 5.5 – Integration introduction, areas between curve and x-axis
• SL 5.6 – Differentiating polynomials, chain, product and quotient rules
• SL 5.7 – The second derivative
• SL 5.8 – Testing for maximum and minimum, optimisation, points of inflexion
• SL 5.9 – Kinematics problems
• SL 5.10 – Indefinite integration, reverse chain, by substitution
• SL 5.11 – Definite integrals, areas under curve onto x-axis and areas between curves
• HL 5.12 – First principles, higher derivatives
• HL 5.13 – Limits and L’Hôpital’s rule
• HL 5.14 – Implicit functions, related rates, optimisation
• HL 5.15 – Further derivatives and indefinite integration of these, partial fractions
• HL 5.16 – Integration by substitution, parts and repeated parts
• HL 5.17 – Areas under curve onto y-axis, volume of revolution (about x- and y-axes)
• HL 5.18 – First-order differential equations (DEs): Euler method, variables separable, integrating factor, homogeneous differential equations using substitution y=vx
• HL 5.19 – Maclaurin series