Khan Academy Product and Quotient Rules, 6 video lectures with practice exercises.Khan Academy Chain Rule, 9 video lectures with practice exercises.Khan Academy Power Rule, 5 video lectures with practice exercises.Khan Academy Visualizing Graphs of Functions and their Derivatives, 8 video lectures with practice exercises.Khan Academy Introduction to Derivatives, 12 video lectures with practice exercises.Khan Academy Slope of a Line Secant to a Curve, 6 video lectures with practice exercises.Khan Academy Introduction to Differential Calculus video lecture.Interactive Mathematics Differentiation complete the first 7 lessons.Interactive Mathematics Introduction to Calculus.Khan Academy Introduction to Limits series of video lectures with practice exercises. Maths is Fun Equation of a Straight Line.To get a better understanding of Calculus, review these lessons and quiz: See reference sites above if revision is required for prerequisite topics. Integration can be thought of as measuring the area under a curve, defined by f(x), between two points (a and b above).Ĭalculus is used in all fields of engineering: see this TEDx talk ‘What is Calculus Used For’ by Chemical engineer Jeff Heys.Īssumed prerequisite knowledge: Algebra, functions, trigonometry, sequences and series. The volume of wine barrels was one of the early problems solved using integration. We may be given a rate of change, such as acceleration and we need to work backwards to find the original relationship (or equation) between the two quantities. The second branch is integration, which is the reverse of differentiation. This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. The derivative f′(x) of a curve at a point is the slope (rise over run) of the line tangent to that curve at that point. Calculus allows us to understand things that change, such as the motion of an object, or the change in position of an object over time.Ĭalculus is made up of 2 main branches: The first is differentiation (or derivatives), which help us to find the rate of change of one quantity compared to another. Sequences and Series are used in many fields of engineering.Ĭalculus is one of the greatest achievements of the human mind separately invented by Newton and Leibniz. Public domain image from the Wikimedia Commons The Fibonacci series is used in computer search algorithms, and in biology they describe the pattern of pine cones and flowering of artichokes.Īn approximation of the golden spiral created by drawing circular arcs connecting the opposite corners of squares whose side lengths are successive Fibonacci numbers. The Fibonacci series is the series where each subsequent number is the sum of the previous two or F n = F n-1 + F n-2 . Where the Greek letter sigma ∑ is the mathematical symbol for a sum, or the summation operator. How many grains are placed on an 8×8 chessboard? Since this is a geometric series, the answer for n squares is so for n = 8 x 8= 64 squares, the total number of grains of wheat = 2 64 - 1. We are concerned with two main types of series or sequences of numbers: Arithmetic series were the difference between any two consecutive terms is a constant, and geometric series were the ratio of any two consecutive terms is always the same.Ī well-known example of a geometric series is the ‘Wheat and Chessboard Problem’: Let one grain of wheat be placed on the first square of a chessboard, two on the second, four on the third, eight on the fourth, etc.
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