G C Ioannou

A Level Mathematics G C Ioannou

Here I offer a complete lesson on Maths A -Level suitable to Edexcel C4-Integration. This set of notes completely covers the subject with 200 worked examples. With over 20 years experience in teaching A level Mathematics I offer these notes covering a wide range of problems with complete solutions. This Lesson covers theory and formula necessary for the chapter and step by step explanation of all solutions. Problems are arranged in an ascending order of difficulty reaching A Level standard. Its suitable also for any student studying at this level. It includes: 1) a) Standard integration of: 1/x, e^x, sinx, cosx, tanx, secxtanx etc b) General cases of trigonometric functions integration such as: sinkx, coskx, sec^2(kx), seckxtankx, coseckxcotkx, sin(ax+b), cos(ax+b), ...etc using standard results 2) Integration of the cases: (ax+b)^n,1/(ax+b), e^(ax+b), ... using standard results 3) Evaluation of definite integrals. 4) Integration of cases such as: sin^n(x).cosx, cos^n(x).sinx, tan^n(x).sec^2(x).., using standard results 5) Integration of the cases such as: sin^2(x), cos^2(x), tan^2(x), cot^2(x), ... as well their general cases such as: sin^2(kx), cos^2(kx), tan^2(kx), cot^2(kx), ... 6) Integration of cases such as: cos5xcos2x, sin3xcosx, ..etc 7) Integration of cases such as: (x^2+5)^7.(x).., using standard results. 8) Integration using substitutions 9) Integrals of the form sqrt(a^2-x^2) 10) Use partial fractions to integrate cases such as: (x-2)/[(x]3).(x-7)], (x^2+5x+6)/[(x]2).(x-3)^2].. etc 11) Integration of the form: a^x, and the general case a^kx, using standard results 12) Integration by parts 13) integration of secx, tanx, cotx, cosecx, ... 14) Trapezium Rule 15) Areas, and Volumes 16) Areas and volumes in parametric form 17) Investigate the special case of ellipse volume 18) Prove using integration that the area of circle is pr^2 19) Solution of first order differential equation by separation of variables. 20) Use of boundary conditions to find a particular solution for the differential equation. 21) Set of a differential equation to investigate real life problems such as exponential growth and decay.. ie population growth, radioactive decay, Newtons law of cooling, chemical reactions etc