Maths in Action - Advanced Higher Mathematics 2

Part 1 Proof and elementary number theory: some definitions; related implications; direct proof; indirect proof (proof by contradiction, proof by contrapositive); the fundamental theorem of arithmetic; proof by induction; the binomial theorem revisited. Part 2 Further differentiation: derivative of inverse functions; inverse trigonometric functions; implicit and explicit functions; first derivatives of implicit functions; second derivatives of implicit functions; logarithmic differentiation; parametric equations; first and second derivatives of parametric equations. Part 3 Applications of differentiation: motion in a plane; related rates of change. Part 4 Further integration: inverse trigonometric functions and standard integrals; integrals of rational functions; integration by parts; differential equations; variables separable; applications of differential equations.