Kendon Black

This is the Powerpoint companion to the Word doc. This is a full lesson/teachers reference for integration using U-substitution. It goes over the basic technique, gives examples, explains separating the differentials (isolating the du, isolating the dx). It shows how to check your answer by differentiating and gives examples. There's discussion on how to choose the correct u and how to manipulate the leading coefficient. There are examples where you have to run a u-sub multiple times. Challenge

This is a full lesson/teachers reference for integration using U-substitution. It goes over the basic technique, gives examples, explains separating the differentials (isolating the du, isolating the dx). It shows how to check your answer by differentiating and gives examples. There's discussion on how to choose the correct u and how to manipulate the leading coefficient. There are examples where you have to run a u-sub multiple times. Challenge problems are given where, for example, after the i

This is a document covering all of the convergence tests for series. For each one, there is an explanation, applicable formula, and worked example. The answer to each example is either converges conditionally, converges absolutely, or diverges. Tests include Divergence/nth Term Test, Geometric Series Test, P-Series Test, Telescoping Series Test (with and without partial fraction decomposition required), Integral Test, Ratio Test, Root Test, Direct Comparison Test, Limit Comparison Test, Alternat

This is a thorough lesson on sequences and series. Although it does not include all of the convergence tests. (Those are in the next document.) The document focuses on definitions of various terms, types of series, and there properties. It includes 18 example problems. Topics tackled include sequence notation, series notation (summation notation), writing the terms of a sequence given the definition and vice versa, recursively-defined sequences, bounds, increasing/decreasing/non-increasing/non-d

This lesson covers the two types of trigonometric integrals. The first type features integrands that contain one or more trig functions. Evaluating these often involves manipulating the integrand using the trig identities in order to get it into an integrable format. I provide ten examples, covering all the techniques that students are likely to run into in these types of problems. The second type features integrals with square roots whose radicands are in the form a^2 - x^2, a^2 + x^2, or x^2-a

This is what I believe to be a complete document on integration by parts. It includes the proof/derivation, the ILATE strategy for choosing u, and nine worked examples. The examples tackle concepts of indefinite integrals, definite integrals, multiple integration by parts/tabular integration, using integration by parts to prove an antiderivative formula, the circular integration trick, and the setting-C-to-a-particular-value trick.

This is a full lesson/teachers reference for integration using U-substitution. It goes over the basic technique, gives examples, explains separating the differentials (isolating the du, isolating the dx). It shows how to check your answer by differentiating and gives examples. There's discussion on how to choose the correct u and how to manipulate the leading coefficient. There are examples where you have to run a u-sub multiple times. Challenge problems are given where, for example, after the i

This is what I consider to be a complete lesson on L'Hôpital's rule. It contains the definition of both the stronger form and weaker form, as well as the proof with visual aids. It covers indeterminate forms 0/0, +/- inf/inf, +/- inf * 0, inf - inf, 1^inf, 0^0, and +/- inf^0. It contains examples w/ solutions of each. There are eleven worked out examples in total.

This is what I consider to be a complete lesson on L'Hôpital's rule. It contains the definition of both the stronger form and weaker form, as well as the proof with visual aids. It covers indeterminate forms 0/0, +/- inf/inf, +/- inf * 0, inf - inf, 1^inf, 0^0, and +/- inf^0. It contains examples w/ solutions of each. There are eleven worked out examples in total.

This lesson covers the two types of trigonometric integrals. The first type features integrands that contain one or more trig functions. Evaluating these often involves manipulating the integrand using the trig identities in order to get it into an integrable format. I provide ten examples, covering all the techniques that students are likely to run into in these types of problems. The second type features integrals with square roots whose radicands are in the form a^2 - x^2, a^2 + x^2, or x^2-a

This is a lesson on integration by partial fraction decomposition. It includes an explanation and three examples. The denominators in the examples break up into distinct linear factors, one quadratic and one linear factor, and a quadratic factor raised to the third power, respectively. The lesson assumes prior knowledge of solving systems of linear equations, integration by table, and integration by u-substitution.

This is a full lesson on polar coordinates and equations. It contains the following: definitions and diagrams of the polar coordinate system, converting between polar and rectangular coordinates, converting between polar and rectangular equations, graphing polar equations, finding points of intersection of polar equations, symmetry of polar graphs, and miscellaneous questions involving polar systems. Examples of each topic are included.

This is a 50-minute assessment covering set notation, subsets/proper subsets, set operations, Venn Diagrams, Cartesian Products, and cardinality. This is high school level; typically students would see this in 10th or 11th grade. Answer key is included.

This is what I consider to be a complete lesson on L'Hôpital's rule. It contains the definition of both the stronger form and weaker form, as well as the proof with visual aids. It covers indeterminate forms 0/0, +/- inf/inf, +/- inf * 0, inf - inf, 1^inf, 0^0, and +/- inf^0. It contains examples w/ solutions of each. There are eleven worked out examples in total. Bundle contains Word doc and corresponding PowerPoint.

This is the only complete and completely correct number classification diagram that I know of. Unsatisfied with what I found on the internet, I created it myself. The diagram has all of the following properties: examples of each type of number, rules for each type (rational must be able to write as p/q where p and q and integers and q not equal to 0), shows the complete hierarchy (all natural numbers are whole numbers, all whole numbers are integers, all integers are rational numbers, all ration

This is a full lesson on polar coordinates and equations. It contains the following: definitions and diagrams of the polar coordinate system, converting between polar and rectangular coordinates, converting between polar and rectangular equations, graphing polar equations, finding points of intersection of polar equations, symmetry of polar graphs, and miscellaneous questions involving polar systems. Examples of each topic are included. The presentation is free of transitions and styling so you

This is a full lesson on polar coordinates and equations. It contains the following: definitions and diagrams of the polar coordinate system, converting between polar and rectangular coordinates, converting between polar and rectangular equations, graphing polar equations, finding points of intersection of polar equations, symmetry of polar graphs, and miscellaneous questions involving polar systems. Examples of each topic are included.

This is a bundle of my trigonometric integrals lesson. It bundles the Word document and Powerpoint versions.

This lesson describes how to calculate the number of distinct permutations when selecting r things from n choices. (The number of distinct permutations is different than the number of (regular) permutations when the set of n has repeats. For example, how many ways can you rearrange the letters in MOM? The answer is 3 even though perm(3,3) = 6.) This is my own formula/algorithm that I developed while teaching precalculus. Our textbook described how to find the number of distinct permutatio