 TUTORIALS
TUTORIALS HOME

GENERAL MATH
NUMBER SETS
ABSOLUTE VALUE & INEQUALITIES
SETS & INTERVALS
FRACTIONS
POLYNOMIALS
LINEAR EQUATIONS
GEOMETRY
FINITE SERIES
TRIGONOMETRY
EXPONENTS
LOGARITHMS
INDUCTION

CALCULUS
LIMITS
DERIVATIVES
RELATED RATES & OPTIMIZATION
CURVE SKETCHING
INTEGRALS
AREA & VOLUME
INVERSE FUNCTIONS

MAIN
HOME
TESTS
TUTORIALS
SAMPLE PROBLEMS
COMMON MISTAKES
STUDY TIPS
GLOSSARY
CALCULUS APPLICATIONS
MATH HUMOUR

### TUTORIALS

The tutorials are divided into 2 separate sections. The first set of tutorials is based on general mathematical concepts. These tutorials will seem familiar to students since most of the content is a review of calculus-related concepts from high schools courses. A short description of each tutorial from the General Mathematics section is listed below. To visit the tutorial, click the link below each description or the link from the menu on the left-hand side of the page.

# Number Sets

The number sets tutorial defines and gives examples of the different types of numbers that students may encounter in the calculus course.

> | NUMBER SETS Tutorial

# Absolute Value & Inequalities

The absolute value and inequalities tutorial illustrates how to solve inequalities and expressions that involve absolute value symbols. The examples also show how to graph inequalities.

> | ABSOLUTE VALUE & INEQUALITIES Tutorial

# Sets & Intervals

The sets and intervals tutorial contains definitions, such as the union or intersection of sets, from Discrete Mathematics. The rules for proper set notation are defined. The tutorial also contains information about the different types of intervals and how these intervals are expressed in set builder notation and as segments of the real number line.

> | SETS & INTERVALS Tutorial

# Fractions

The fractions tutorial shows students how to evaluate algebraic expressions that involve operations of fractions. The tutorial also illustrates how to convert fractions to decimal form and how to convert between improper fractions and mixed numbers. An added feature is a greatest common denominator / least common multiple calculator that will help students to reduce fractions.

> | FRACTIONS Tutorial

# Polynomials

The polynomials tutorial begins with a few definitions of different terms. It also contains a section on evaluating rational expressions. The most important part of this tutorial is the section on factoring polynomial expressions. Students will be required to factor expressions in all sections of the calculus course.

> | POLYNOMIALS Tutorial

# Linear Equations

The linear equations tutorial defines the different types of linear equations and illustrates how to find the equation of a line using several different formulas. This will become useful when students reach the tangent line section of the calculus course. The tutorial wraps up with a few line theorems and section on graphing linear equations.

> | LINEAR EQUATIONS Tutorial

The quadratic equations tutorial begins with a description of the method of completing the square and a few examples of factoring. The most important part of this tutorial, however, is the section on the quadratic formula. This formula will allow students to find the roots of any quadratic equation, if they exist. The section concludes with a section on graphing quadratic equations (i.e. parabolas).

# Geometry

The geometry tutorial features several different formulas for the area and perimeter and surface area and volume of common 2- and 3-dimensional figures, as well as several other well known formulas from geometry, such as the Pythagorean Theorem. The tutorial also contains information on the equations of circles and other conics. This tutorial will be particularly important to students during the related rates and optimization problems section of the course. Many of the formulas from the geometry tutorial will be required to solve the application problems.

> | GEOMETRY Tutorial

# Finite Series

The finite series tutorial contains the rules for series notation and describes some of the different types of sequences and series. It also contains the different properties of finite series, as well as some theorems that make the calculation of series much easier.

> | FINITE SERIES Tutorial

# Trigonometry

The trigonometry tutorial is one of the largest of the general mathematics tutorials because it covers so much information. The different trigonometric functions and their respective graphs are covered, along with the periodicity of these functions. The tutorial also contains sections covering the sine and cosine laws and arc length. The tutorial concludes with a section covering trigonometric identities and formulas.

It's important that students are familiar with all of the content of this tutorial because almost all calculus sections will include concepts from trigonometry in one way or another.

> | TRIGONOMETRY Tutorial

# Exponents

This very short tutorial features information about exponents and how to simplify exponential expressions using the laws of exponents.

> | EXPONENTS Tutorial

# Logarithms

The logarithms tutorial introduces the concept of a logarithm and how to simplify logarithmic expressions using the laws of logarithms. It also contains sections on the natural logarithm and the change of base formula. Students will realize how closely related the concepts of natural logarithms and calculus are once they reach the inverse functions section of the calculus course.

> | LOGARITHMS Tutorial

# Mathematical Induction

The induction tutorial contains guidelines for proving statements using mathematical induction. This is a very powerful method of proof. The only drawback is that proof by mathematical induction can only be used for statements that have number sets that increase or decrease by integer values.

> | MATHEMATICAL INDUCTION Tutorial

The second set of tutorials is based on the mathematics covered in the MATH 1036/1037 courses. Students may be familiar with some of this material from their high school calculus course. However, the content of these tutorials and the calculus course are much more in-depth than the high school level course. A short description of each of the Calculus tutorials is listed below. To visit the tutorial, click the link below each description or the link from the menu on the left-hand side of the page.

# Limits

The limits tutorial begins with a definition of limit using tangent and secant lines. It continues with sections on left- and right-handed limits and infinite limits and vertical asymptotes. Examples show how to calculate limits using the properties of limits. Some new material is covered in the squeeze theorem and the intermediate value theorem. An important section deals with continuous and discontinuous functions and illustrates the different type of discontinuity through graphs. The tutorial ends by revisiting the concepts of tangents and limits and providing a new definition of a limit.

> | LIMITS tutorial

# Derivatives

The derivatives tutorial defines a derivative using the definition of a limit from the previous tutorial. It touches on the different notations for derivatives and the concept of the derivative as a function of x. A theorem for differentiable functions is accompanied by graphs illustrating cases where functions are not differentiable. One of the most important parts of the tutorial is the section on differentiation, where the different formulas for differentiation are listed. These formulas will allow students to easily take the derivative of simple functions.

The tutorial also shows students how to take the derivatives of trigonometric functions. Knowledge of trigonometry will be especially helpful in this section. There are a few short, but important sections that describe the method of implicit differentiation and higher derivatives. Students will need to use these concepts in the later parts of the course. The tutorial wraps up with a short section on linear approximation.

> | DERIVATIVES tutorial

# Related Rates and Optimization

This tutorial lets students put their knowledge of the previous calculus concepts to good use with practical application problems. It begins with related rates and a few examples of the different types of problems. Before tackling optimization problems, the tutorial covers maximum and minimum values. This concept is necessary for optimization problems, as well as drawing the graphs of functions in the curve sketching tutorial.

> | RELATED RATES & OPTIMIZATION tutorial

# Curve Sketching

The curve sketching tutorial illustrates all of the steps that students must take in order to sketch a given function. Some of these steps include finding the intervals of increase/decrease and concavity and the applying the first and second derivative tests to find maximum and minimum values. The tutorial also covers vertical and horizontal asymptotes, as well as the more complicated slant asymptotes. It concludes with a couple examples of sketching curves given only the equation of the function.

> | CURVE SKETCHING tutorial

# Integrals

The integration tutorial shows students how to solve definite and indefinite integrals using special properties and formulas for integration. The tutorial also covers the Fundamental Theorem of Calculus, whose name implies its importance to the calculus course. Another important concept is the substitution rule, which allows students to solve integrals of more complicated functions.

> | INTEGRALS tutorial

# Area and Volume

The area and volume tutorial shows some of the applications of integral calculus. Although these problems are not as practical as other applications of calculus, they show how the concepts from the course can be applied to other areas of mathematics. After completing this tutorial, students should be able to find the area between two given curves and determine the volume of a solid of rotation using one of the methods outlined in the tutorial.

> | AREA & VOLUME tutorial

# Inverse Functions

The inverse functions tutorial combines the concepts of inverse functions, trigonometry, logarithms and calculus. It begins with a thorough definition of inverse functions. The next section illustrates the relation between the e and the natural logarithm and calculus. The formulas for differentiation and integration of logarithmic and exponential functions are given with several examples illustrating the correct use of each formula. The tutorial also covers the method of logarithmic differentiation, which will allow students to take the derivative of functions that were previously too complicated to differentiate.

The last section of the tutorial covers inverse trigonometric functions. The graphs and formulas for differentiation and integration of the three main trigonometric functions are provided, along with a few other formulas. Several examples are included so students can fully grasp the concepts of this tutorial.

> | INVERSE FUNCTIONS tutorial

|Top of Page |

COURSE HOMEPAGES
MATH 1036
MATH 1037

FACULTY HOMEPAGES
Alex Karassev
Ted Chase