Details
Course Overview
This course provides a comprehensive survey of differential and integral calculus concepts, including limits, derivative and integral computation,
linearization, Riemann sums, the fundamental theorem of calculus, and differential equations. Content is presented in 10 units and covers various
applications, including graph analysis, linear motion, average value, area, volume, and growth and decay models. In this course students use an online
textbook, which supplements the instruction they receive and provides additional opportunities to practice using the content they've learned. Students will
use an embedded graphing calculator applet (GCalc) for their work on this course; the software for the applet can be downloaded at no charge. This is the second semester of MTH433.
Course Outline
SEMESTER ONE
Unit 1: Limits and Continuity
Students learn to use limits to describe the continuity of functions at a point. They evaluate a limit graphically, numerically, and analytically. They
also learn the conditions and conclusions of the Intermediate Value Theorem.

Concept of a Limit

Algebraic Computation of a Limit

Limits Involving Infinity

Continuity

Intermediate Value Theorem
Unit 2: Derivatives
Students learn to find the derivative and define the differentiability of functions. They use tangent lines to approximate function values, describe linear
motion using derivatives, and learn the relationship between a graph of a function and its derivative.

Concept of a Derivative

Differentiability

Graphs of f and f'

Motion Along a Line

Tangent Line Approximation
Unit 3: Differentiation
Students find the derivative of functions, calculate highorder derivatives, and calculate derivatives of inverse functions.

Basic Computation Rules

Higher Order Derivatives

Product, Quotient, and Chain Rules

Implicit Differentiation

Derivatives of Inverse Functions
Unit 4: Graph Behavior
Students use limits to describe the asymptotes, endbehavior, concavity, and absolute extreme values of a function. They also use graph analysis to sketch
a function.

Asymptotes and EndBehavior

Increasing/Decreasing Behavior and Concavity

Relative Extreme Values and Points of Inflection

Absolute Extreme Values and Extreme Value Theorem

Graph Analysis
Unit 5: Derivative Applications
Students use the mean value and Rolle's theorems. They use derivatives to model situations that involve rates of change and solve problems involving
related rates and optimization.

Mean Value and Rolle's Theorems

Rates of Change

Related Rates

Optimization
SEMESTER TWO
Unit 6: Antidifferentiation
Students learn antiderivatives and indefinite integrals. They find the antiderivative of various functions, create and use slope fields for differential
equations, and solve initial value problems.

Antiderivatives and Definite Integrals

Slope Fields

Basic Computation Rules

Substitution Rule

Initial Value Problems
Unit 7: The Definite Integral
Students learn the relationship between area and Riemann sums. They learn to approximate and evaluate definite integrals and use the Fundamental Theorem of
Calculus.

Area and the Riemann Sums

Approximation Methods

Fundamental Theorem of Calculus, Part 1

Computation of Definite Integrals

Fundamental Theorem of Calculus, Part 2
Unit 8: Integral Applications
Students learn to find the total change in quantities using integrals. They also calculate the average value of functions, use integral functions to define
position, and calculate displacement and distance travelled by an object.

Total Change

Average Value of a Function

Motion Along a Line Revisited
Unit 9: Area and Volume
Students learn to find area bounded by two curves, volume of a solid using cross sections, and volume of solid generated by revolving a region about an
axis.

Area Between Two Curves

Volume of Solids Using Cross Sections

Volume of Solids of Revolution
Unit 10: Differential Equations and Their Applications
Students learn to recognize and solve separable differential equations. They also model and solve problems with differential equations, including
exponential growth and decay problems.

Separable Differential Equations

Modeling Using Differential Equations

Growth and Decay Models
To use this course, you'll need a computer with an Internet connection. Some courses require additional free software programs, which you can download from the Internet.
Hardware and Browsers (Minimum Recommendations)
Windows OS

CPU: 1.8 GHz or faster processor (or equivalent)

RAM: 1GB of RAM

Browser: Microsoft Internet Explorer 9.0 or higher, Mozilla Firefox 10.0 versions or higher, Chrome 17.0 or higher
 At this time our users are encouraged not to upgrade to Windows 10 or Edge (the new browser)
Mac OS

CPU: PowerPC G4 1 GHz or faster processor; Intel Core Duo 1.83 GHz or faster processor

RAM: 1GB of RAM

Browser: Firefox 10.0 versions or higher, Chrome 17.0 or higher (Safari is not supported!)
Internet Connections
It is highly recommended that a broadband connection be used instead of dial up.