Series Solutions - series Solutions, euler Differential Equations. Higher Order Differential Equations - n th order differential equations, Undetermined coefficients, variation of Parameters, 3 x 3 Systems of Differential Equations. Boundary value problems fourier Series - boundary value problems, eigenvalues and Eigenfunctions, Orthogonal Functions, fourier Sine series, fourier Cosine series, fourier Series. Partial Differential Equations - heat Equation, wave equation, laplace's Equation, separation of Variables. These notes assume no prior knowledge of differential equations. A good grasp of Calculus is required however. This includes a working knowledge of differentiation and integration.
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Several topics rely heavily on trig and knowledge of trig functions. Calculus iii (Math 3435) notes practice Problems assignment Problems - topics included in this set of notes/tutorial are : Three dimensional coordinate system - equations of Lines, Equations of Planes, quadratic Surfaces, functions of Multiple variables, vector Functions, limits, derivatives, and Integrals of Vector Functions. Applications of Partial Derivatives - tangent Plane, normal Line, relative extrema, absolute Extrema, optimization, lagrange multipliers. Multiple Integrals - iterated Integrals, double Integrals, double Integrals in Polar coordinates, Triple etisalat Integrals, Triple Integrals in Cylindrical coordinates, Triple Integrals in Spherical coordinates, Change of Variables, surface Area. Line Integrals - vector fields, line Integrals With Respect to Arc Length, line Integrals With Respect to x and y, line Integrals of Vector fields, fundamental Theorem of Line Integrals, conservative vector fields, potential Functions, Green's Theorem, curl, divergence. Surface Integrals - parametric Surfaces, surface Integrals, surface Integrals of Vector fields, Stokes' Theorem, divergence Theorem. The calculus iii notes/tutorial assume that you've got a working knowledge calculus i, including limits, derivatives and integration. It also assumes that the reader has a good knowledge of several Calculus ii topics including some integration techniques, parametric equations, vectors, and knowledge of three dimensional space. Differential Equations (Math 3301) notes - topics included in this set of notes/tutorial are : First Order Differential Equations - linear Equations, separable Equations, Exact Equations, Equilibrium Solutions, modeling Problems. Second Order Differential Equations - homogeneous and Nonhomogeneous Second Order Differential Equations, fundamental Set of Solutions, Undetermined coefficients, variation of Parameters, mechanical Vibrations Laplace Transforms - definition, Inverse Transforms, Step loss Functions, heaviside functions, dirac-Delta function, solving ivp's, nonhomogeneous ivp, nonconstant coefficient ivp, convolution Integral. Systems of Differential Equations - matrix Form, eigenvalues/Eigenvectors, Phase Plane, nonhomogeneous Systems, laplace Transforms.
Applications of Derivatives - related Rates, Critical points, minimum and Maximum Values, Increasing/Decreasing Functions, Inflection points, concavity, optimization Integration - definition, Indefinite Integrals, definite Integrals, substitution Rule, evaluating Definite Integrals, fundamental Theorem of Calculus Applications of Integrals - average function Value, area between Curves, solids. The calculus I notes/tutorial assume that you've got a working knowledge of Algebra and Trig. There is some review of a couple of Algebra and Trig topics, but for the most part it is assumed that you do have a decent background in Algebra and Trig. These notes assume no prior knowledge of Calculus. Calculus ii (Math 2414) notes practice Problems assignment Problems - topics included in this set of notes/tutorial are : Integration Techniques - integration by parts, Integrals Involving Trig Functions, Trig Substitutions, Integration using Partial Fractions, Integrals Involving roots, Integrals Involving quadratics, Integration Strategy, improper Integrals. Applications of Integrals - arc Length, surface Area, business center of Mass/Centroid, hydrostatic Pressure and Force, probability. Parametric Equations and Polar coordinates - parametric Equations curves, calculus with Parametric Equations (Tangents, Areas, Arc Length and Surface Area polar coordinates, calculus with Polar coordinates (Tangents, Areas, Arc Length and Surface Area). Sequences and Series - sequences, series, convergence/divergence of Series, Absolute series, Integral Test, comparison Test, limit Comparison Test, Alternating Series Test, ratio test, root Test, Estimating the value of a series, power Series, taylor Series, binomial Series Vectors - basics, magnitude, unit Vector, Arithmetic, dot. It is also assumed that you have a fairly good knowledge of Trig.
Exponential and Logarithm Functions - exponential Functions, logarithm Functions, solving Exponential Functions, solving Logarithm Functions, Applications. Systems of Equations - substitution Method, Elimination Method, augmented Matrix, nonlinear Systems. The Algebra notes/tutorial assume that you've had some exposure to the basics of Algebra. In particular estate it is assumed that the exponents and factoring sections will be more of a review for you. Also, it is assumed that you've seen the basics of graphing equations. Graphing particular types of equations is covered extensively in the notes, however, it is assumed that you understand the basic coordinate system and how to plot points. Calculus I (Math 2413) notes practice Problems assignment Problems - topics included in this set of notes/tutorial are : Algebra/Trig review - trig Functions and Equations, Exponential Functions and Equations, logarithm Functions and Equations. Limits - concepts, definition, computing, One-sided Limits, continuity, limits Involving Infinity, l'hospitals Rule derivatives - definition, Interpretations, derivative formulas, power Rule, product Rule,"ent Rule, chain Rule, higher Order Derivatives, Implicit Differentiation, logarithmic Differentiation, derivatives of Trig Functions, Exponential Functions, logarithm Functions, Inverse Trig Functions.
It contains all the information that the normal sized table does. Table of Laplace Transforms - here is a list of Laplace transforms for a differential equations class. This table gives many of the commonly used Laplace transforms and formulas. Class Notes and Tutorials, all of the classes, with the exception of Differential Equations, have practice problems (with solutions) you can use for practice as well as a set of assignment problems (without solutions/answers) for instructors to use if they wish. Notes, practice Problems, assignment Problems - topics included in this set of notes/tutorial are : Preliminaries - exponent Properties, rational Exponents, negative exponents, radicals, polynomials, factoring, rational Expressions, complex Numbers. Solving Equations and Inequalities - linear Equations, quadratic Equations, completing the Square, quadratic Formula, applications of Linear and quadratic Equations, reducible to quadratic Form, Equations with Radicals, linear Inequalities, polynomial rational Inequalities, Absolute value equations inequalities. Graphing and Functions - graphing Lines, circles, and piecewise functions, function Definition, function Notation, function Composition, Inverse functions. Common Graphs - parabolas, Ellipses, hyperbolas, Absolute value, square root, constant Function, rational Functions, Shifts, reflections, symmetry. Polynomial Functions - dividing Polynomials, zeroes/Roots of Polynomials, finding Zeroes of Polynomials, Graphing Polynomials, partial Fractions.
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Cheat Sheets tables, algebra Cheat Sheet - this is as many common algebra facts, properties, formulas, and functions that I could think. There is also a federalist page of common algebra errors included. Currently the cheat sheet is four pages long. Algebra Cheat Sheet (Reduced) - this is the same cheat sheet as above except it has been reduced so that it will fit onto the front and back of a single piece of paper. It contains all the information that the normal sized cheat sheet does. Trig Cheat Sheet - here is a set of common trig facts, properties and formulas. A unit circle (completely filled out) is also included.
Currently this cheat sheet is four pages long. Trig Cheat Sheet (Reduced) - my standard trig cheat sheet reduced to fit onto the front and back of a single piece of paper. Calculus Cheat Sheets - these are a series of Calculus Cheat Sheets that covers most of a standard Calculus I course and a few topics from a calculus ii course. Common Derivatives and Integrals - here is a set of common derivatives and integrals that are used somewhat regularly in a calculus i or Calculus ii class. Also included are reminders on several integration techniques. Common Derivatives and Integrals (Reduced) - my common derivatives and integrals table reduced to fit onto the front and back of a single piece of paper.
I've tried to proof read these pages and catch as many typos as I could, however it just isn't possible to catch all of them when you are also the person who wrote the material. Fred, mike and david have caught quite a few typos that I'd missed and been nice enough to send them my way. Thanks again Fred, mike and david! If you are one of my current students and are here looking for homework assignments i've got a set of links that will get you to the right pages listed here. At present i've gotten the notes/tutorials for my Algebra (Math 1314 calculus I (Math 2413 calculus ii (Math 2414 calculus iii (Math 3435) and Differential Equations (Math 3301) class online. I've also got a couple of review/Extras available as well.
Among the reviews/extras that i've got are an Algebra/Trig review for my calculus Students, a complex Number primer, a set of Common Math Errors, and some tips on How to Study math. I've made most of the pages on this site available for download as well. These downloadable versions are in pdf format. Each subject on this site is available as a complete download and in the case of very large documents i've also split them up into smaller portions that mostly correspond to each of the individual topics. Near the top of each page you will see one or two download buttons depending on whether the subject is available as only as a complete document or is also available in pieces. You can see a complete listing of all the available downloads by selecting the. Downloads option in the menu. Here is a complete listing of all the subjects that are currently available on this site as well as brief descriptions of each.
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Share your Story featured story, explore teacher Resources by Grade. Welcome to my online math tutorials and notes. The intent of this site is to provide a complete set of free online (and downloadable) notes and/or tutorials for classes that I teach. I've tried to write the notes/tutorials in such a way that they should be accessible to anyone wanting to learn the subject regardless of whether you are in my classes or not. In other words, they do not assume you've summary got any prior apple knowledge other than the standard set of prerequisite material needed for that class. In other words, it is assumed that you know Algebra and Trig prior to reading the calculus I notes, know Calculus I prior to reading the calculus ii notes, etc. The assumptions about your background that i've made are given with each description below. I'd like to thank Fred., mike. For all the typos that they've found and sent my way!
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