Details
Course Overview
This course is the equivalent of an introductory collegelevel calculus course. In this course, students study functions, limits, derivatives, integrals,
and infinite series. Calculus helps scientists, engineers, and financial analysts understand the complex relationships behind realworld phenomena.
Students learn to evaluate the soundness of proposed solutions and apply mathematical reasoning to realworld models. Students also learn to understand
change geometrically and visually (by studying graphs of curves), analytically (by studying and working with mathematical formulas), numerically (by seeing
patterns in sets of numbers), and verbally. Students prepare for the AP Exam and further studies in science, engineering, and mathematics. This is the second semester of MTH520.
Course Outline
SEMESTER ONE
Unit 1: The Basics
Students prepare to study calculus by reviewing some basic precalculus concepts from algebra and trigonometry. They learn what calculus is, why it was
invented, and what it is used for.

PreCalculus Review

Introduction to Calculus

Using a Graphing Calculator

Combining Functions

Composite and Inverse Functions

Graphical Symmetry

Patterns in Graphs
Unit 2: Limits and Continuity
This unit addresses Topic I: Functions, Graphs, and Limits of the College Board's Calculus BC topic outline. Students learn two important concepts that
underlie all of calculus: limits and continuity. Limits help students understand differentiation (the slope of a curve) and integration (the area inside a
curved shape). Continuity is an important property of functions.

Finding Limits Analytically

Asymptotes as Limits

Relative Magnitudes for Limits

When Limits Do and Don't Exist

Continuity

Intermediate and Extreme Value Theorems
Unit 3: The Derivative
This unit addresses Topic II: Derivatives of the College Board's Calculus BC topic outline. Students learn how to calculate a derivative, the slope of a
curve at a specific point. They learn techniques for finding derivatives of algebraic functions (such as y = x2) and trigonometric functions (such as y =
sin x). Students also interpret the derivative as a rate of change and move fluidly between multiple representations including graphs, tables, and
equations.

Slope and Change

Derivative at a Point

The Derivative

The Power Rule

Sums, Differences, Products, and Quotients

Graphs of Functions and Derivatives

Continuity and Differentiability

Rolles and Mean Value Theorems

HigherOrder Derivatives

Concavity

Chain Rule

Implicit Differentiation
Unit 4: Rates of Change
This unit focuses on Second Derivatives and Applications of Derivatives within Topic II: Derivatives of the College Board's Calculus BC topic outline.
Students learn how to use calculus to model and analyze changing aspects of our world. In addition to the AB topics in this unit, BC students analyze polar
and vectorvalued functions.

Extrema

Optimization

Tangent and Normal Lines

Tangents to Polar Curves

Tangent Line Approximation

Rates and Derivatives

Related Rates

Rectilinear Motion

Motion with Vector Functions
Unit 5: The Integral, Part 1
This unit focuses on Topic III: Integrals in the College Board's Calculus BC topic outline. Students learn numerical approximations to definite integrals,
interpretations and properties of definite integrals, the Fundamental Theorem of Calculus, and techniques of antidifferentiation. They learn how to find
areas of curved shapes.

Riemann Sums

Area Approximations

The Definite Integral

Properties of Integrals

Graphing Calculator Integration

Applications of Accumulated Change

Antiderivatives

Composite Functions
SEMESTER TWO
Unit 1: The Integral, Part 2
This unit focuses on Topic III: Integrals in the College Board's Calculus BC topic outline. Students learn the Fundamental Theorem of Calculus, and
techniques of antidifferentiation. They learn how to find areas of curved shapes.

The Fundamental Theorems of Calculus

Definite Integrals of Composite Functions

Analyzing Functions and Integrals
Unit 2: Applications of the Integral
This unit focuses on Topic III: Integrals in the College Board's Calculus BC topic outline. Students learn to use integrals and antiderivatives to solve
problems. In addition to the AB topics, BC students learn to calculate arc length for a smooth curve.

Area Between Curves

More Areas and Averages

Volumes of Revolution

Cross Sections

Arc Length

More Rectilinear Motion

Other Applications of the Definite Integral
Unit 3: Inverse and Transcendental Functions
This unit focuses on Topic II: Derivatives and Topic III: Integrals in the College Board's Calculus BC topic outline. Students learn to calculate and use
derivatives, antiderivatives, and integrals of exponential functions (such as y = 3x where the input variable is an exponent), logarithmic functions (the
inverses of exponential functions), and trigonometric functions (such as y = secant x). In addition to the AB topics, BC students learn how to use
L'Hopital's Rule and the methods of partial fractions and integration by parts. Also, students learn how to find improper integrals, and derivatives and
integrals of parametric functions.

Derivatives of Inverses

Inverse Trigonometric Functions

Logarithmic and Exponential Review

Transcendentals and 1/x

Derivatives of Logarithms and Exponentials

L'Hopital's Rule

Analysis of Transcendental Curves

Integrating Transcendental Functions

Partial Fractions

Integration by Parts

Improper Integrals

Applications of Transcendental Integrals

Derivatives of Parametric Functions

Integrating Parametric and Polar Functions
Unit 4: Separable Differential Equations and Slope Fields
This unit focuses on Topic II: Derivatives of the College Board's Calculus BC topic outline, specifically, on Equations Involving Derivatives. Students
investigate differential equations and solve the equations using a technique called "separating the variables." In addition to the topics covered in AB, BC
students also learn to use Eulers method to estimate the solution of differential equations and use logistic equations to model growth.

Slope Fields

Differential Equations as Models

Euler's Method

Exponential Growth and Decay

Logistic Growth

More Applications of Differential Equations
Unit 5: Sequences and Series
This unit focuses on Topic IV: Polynomial Approximations and Series of the College Board's Calculus BC topic outline, specifically, on Series of Constants
and Taylor Series.

Sequences

Series

Convergence Tests

Radius of Convergence

Functions Defined by Power Series

Taylor and Maclaurin Series

Taylor's Theorem and Lagrange Error
Unit 6: AP Exam Review and Final Exam
Students review what they have learned and become more familiar with APtype questions in preparation for the AP Exam. Students are also provided with
access to previously released AP Exams for practice.

Exam Strategies

Review of Topics

Practice Exams
Unit 7: Calculus Project
Teachers may choose to assign a final project.
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.