Excellent collection of guides/resources for Calculus  - online and e-book (download)*1*REVIEW*2*Review : Functions - Here is a quick review of functions, function notation and a couple of fairly important ideas about functions.*4*Review : Inverse Functions - A quick review of inverse functions and the notation for inverse functions.*4*Review : Trig Functions - A review of trig functions, evaluation of trig functions and the unit circle.*4*Review : Solving Trig Equations - A reminder on how to solve trig equations.*4**4*Review : Solving Trig Equations with Calculators, Part I - The previous section worked problem whose answers were always the *apos*standard*apos* angles.*4*In this section we work some problems whose answers are not *apos*standard*apos* and so a calculator is needed.*4*This section is always covered in my class as most trig equations in the remainder will need a calculator.*4**4*Review : Solving Trig Equations with Calculators, Part II - Even more trig equations requiring a calculator to solve.*4*Review : Exponential Functions - A review of exponential functions.*4*Review : Logarithm Functions - A review of logarithm functions and logarithm properties.*4*Review : Exponential and Logarithm Equations - How to solve exponential and logarithm equations.*4*Review : Common Graphs - This section isn*apos*t much. It*apos*s mostly a collection of graphs of many of the common functions that are liable to be seen in a Calculus class.*1*LIMITS*2*Tangent Lines and Rates of Change - In this section we will take a look at two problems that we will see time and again in this course.*4*These problems will be used to introduce the topic of limits.*4**4*The Limit - Here we will take a conceptual look at limits and try to get a grasp on just what they are and what they can tell us.*4*One-Sided Limits - A brief introduction to one-sided limits.*4*Limit Properties - Properties of limits that we*apos*ll need to use in computing limits.  We will also compute some basic limits in this section*4**4*Computing Limits - Many of the limits we*apos*ll be asked to compute will not be *apos*simple*apos* limits.  In other words, we won*apos*t be able to just apply the properties and be done.*4*In this section we will look at several types of limits that require some work before we can use the limit properties to compute them.*4**4*Infinite Limits - Here we will take a look at limits that have a value of infinity or negative infinity.  We*apos*ll also take a brief look at vertical asymptotes.*4**4*Limits At Infinity, Part I - In this section we*apos*ll look at limits at infinity.  In other words, limits in which the variable gets very large in either the positive or negative sense.*4*We*apos*ll also take a brief look at horizontal asymptotes in this section.  We*apos*ll be concentrating on polynomials and rational expression involving polynomials in this section.*4**4*Limits At Infinity, Part II - We*apos*ll continue to look at limits at infinity in this section, but this time we*apos*ll be looking at exponential, logarithms and inverse tangents.*4*Continuity - In this section we will introduce the concept of continuity and how it relates to limits.  We will also see the Mean Value Theorem in this section.*4*The Definition of the Limit - We will give the exact definition of several of the limits covered in this section.  We*apos*ll also give the exact definition of continuity.*1*DERIVATIVES*2*The Definition of the Derivative - In this section we will be looking at the definition of the derivative. *4*Interpretation of the Derivative - Here we will take a quick look at some interpretations of the derivative.*4*Differentiation Formulas - Here we will start introducing some of the differentiation formulas used in a calculus course.*4**4*Product and Quotient Rule - In this section we will took at differentiating products and quotients of functions.*4**4*Derivatives of Trig Functions - We*apos*ll give the derivatives of the trig functions in this section.*4*Derivatives of Exponential and Logarithm Functions - In this section we will get the derivatives of the exponential and logarithm functions.*4*Derivatives of Inverse Trig Functions - Here we will look at the derivatives of inverse trig functions.*4*Derivatives of Hyperbolic Functions - Here we will look at the derivatives of hyperbolic functions.*4**4*Chain Rule - The Chain Rule is one of the more important differentiation rules and will allow us to differentiate a wider variety of functions.*4*Implicit Differentiation - In this section we will be looking at implicit differentiation.  Without this we won*apos*t be able to work some of the applications of derivatives.*4**4*Related Rates - In this section we will look at the lone application to derivatives in this chapter.*4*This topic is here rather than the next chapter because it will help to cement in our minds one of the more important*4*concepts about derivatives and because it requires implicit differentiation.*4**4*Higher Order Derivatives - Here we will introduce the idea of higher order derivatives.*4**4*Logarithmic Differentiation - The topic of logarithmic differentiation is not always presented in a standard calculus course.*4*It is presented here for those how are interested in seeing how it is done and the types of functions on which it can be used.*1*APPLICATIONS OF DERIVATIVES*2*Rates of Change - The point of this section is to remind us of the application/interpretation of derivatives that we were dealing with in the previous chapter.  Namely, rates of change.*4**4*Critical Points - In this section we will define critical points.  Critical points will show up in many of the sections in this chapter so it will be important to understand them.*4*Minimum and Maximum Values - In this section we will take a look at some of the basic definitions and facts involving minimum and maximum values of functions.*4*Finding Absolute Extrema - Here is the first application of derivatives that we*apos*ll look at in this chapter.  We will be determining the largest and smallest value of a function on an interval.*4**4*The Shape of a Graph, Part I - We will start looking at the information that the first derivatives can tell us about the graph of a function.*4*We will be looking at increasing/decreasing functions as well as the First Derivative Test.*4**4*The Shape of a Graph, Part II - In this section we will look at the information about the graph of a function that the second derivatives can tell us.*4*We will look at inflection points, concavity, and the Second Derivative Test.*4**4*The Mean Value Theorem - Here we will take a look that the Mean Value Theorem.*4*Optimization Problems - This is the second major application of derivatives in this chapter.  In this section we will look at optimizing a function, possible subject to some constraint.*4*More Optimization Problems - Here are even more optimization problems.*4**4*L*apos*Hospital*apos*s Rule and Indeterminate Forms - This isn*apos*t the first time that we*apos*ve looked at indeterminate forms.*4*In this section we will take a look at L*apos*Hospital*apos*s Rule.  This rule will allow us to compute some limits that we couldn*apos*t do until this section.*4**4*Linear Approximations - Here we will use derivatives to compute a linear approximation to a function. *4*As we will see however, we*apos*ve actually already done this.*4**4*Differentials - We will look at differentials in this section as well as an application for them.*4*Newton*apos*s Method - With this application of derivatives we*apos*ll see how to approximate solutions to an equation.*4*Business Applications - Here we will take a quick look at some applications of derivatives to the business field.*1*INTEGRALS*2*Indefinite Integrals - In this section we will start with the definition of indefinite integral.  *4*This section will be devoted mostly to the definition and properties of indefinite integrals and we won*apos*t be working many examples in this section.*4**4*Computing Indefinite Integrals - In this section we will compute some indefinite integrals and take a look at a quick application of indefinite integrals.*4**4*Substitution Rule for Indefinite Integrals - Here we will look at the Substitution Rule as it applies to indefinite integrals.*4*Many of the integrals that we*apos*ll be doing later on in the course and in later courses will require use of the substitution rule.*4**4*More Substitution Rule - Even more substitution rule problems. *4*Area Problem - In this section we start off with the motivation for definite integrals and give one of the interpretations of definite integrals.*4**4*Definition of the Definite Integral - We will formally define the definite integral in this section and give many of its properties.*4*We will also take a look at the first part of the Fundamental Theorem of Calculus.*4**4*Computing Definite Integrals - We will take a look at the second part of the Fundamental Theorem of Calculus in this section and start to compute definite integrals.*4*Substitution Rule for Definite Integrals - In this section we will revisit the substitution rule as it applies to definite integrals.*1*APPLICATIONS OF INTEGRALS*2*Average Function Value - We can use integrals to determine the average value of a function.*4*Area Between Two Curves - In this section we*apos*ll take a look at determining the area between two curves.*4**4*Volumes of Solids of Revolution / Method of Rings - This is the first of two sections devoted to find the volume of a solid of revolution.*4*In this section we look that the method of rings/disks.*4**4*Volumes of Solids of Revolution / Method of Cylinders - This is the second section devoted to finding the volume of a solid of revolution.*4*Here we will look at the method of cylinders.*4**4*More Volume Problems - In this section we*apos*ll take a look at find the volume of some solids that are either not solids of revolutions or are not easy to do as a solid of revolution.*4*Work - The final application we will look at is determining the amount of work required to move an object.*4**1*EXTRAS*2*Proof of Various Limit Properties - In we prove several of the limit properties and facts that were given in various sections of the Limits chapter.*4**4*Proof of Various Derivative Facts/Formulas/Properties - In this section we give the proof for several of the rules/formulas/properties of derivatives that we saw in Derivatives Chapter.*4*Included are multiple proofs of the Power Rule, Product Rule, Quotient Rule and Chain Rule.*4**4*Proof of Trig Limits - Here we give proofs for the two limits that are needed to find the derivative of the sine and cosine functions.*4*Proofs of Derivative Applications Facts/Formulas - We*apos*ll give proofs of many of the facts that we saw in the Applications of Derivatives chapter.*4**4*Proof of Various Integral Facts/Formulas/Properties - Here we will give the proofs of some of the facts and formulas from the Integral Chapter as well as a couple from the Applications of Integrals chapter.*4**4*Area and Volume Formulas - Here is the derivation of the formulas for finding area between two curves and finding the volume of a solid of revolution.*4*Types of Infinity - This is a discussion on the types of infinity and how these affect certain limits.*4*Summation Notation - Here is a quick review of summation notation.*4*Constant of Integration - This is a discussion on a couple of subtleties involving constants of integration that many students don*apos*t think about.*4**4* Extremely useful for teachers of Maths/Mathematics working through Calculus I (Math 2413).