Chapter 1:

The Real Numbers • Fundamental Concept Review

Chapter 2:

More Concept Review • The Graphing Calculator

Chapter 3:

The Contrapositive • The Converse and Inverse • IFF Statements

Chapter 4:

Radian Measure of Angles • Trigonometric Ratios • Four Quadrant Signs • Simplifying Trigonometric Expressions

Chapter 5:

Word Problem Review

Chapter 6:

Functions: Their Equations and Graphs • Functional Notation • Domain and Range

Chapter 7:

The Unit Circle • Centerline, Amplitude, and Phase Angle of Sinusoids • Period of a Function • Important Numbers • Exponential Functions

Chapter 8:

Pythagorean Identities • Functions of -θ • Trigonometric Identities • Confunctions • Similar Triangles

Chapter 9:

Absolute Values as a Distance • Graphing "Special " Functions • Logarithms • Base 10 and Base e • Simple Logarithm Problems

Chapter 10:

Quadratic Polynomials • Remainder Theorem • Synthetic Division • Rational Roots Theorem

Chapter 11:

Continuity • Left-hand and Right-hand Limits

Chapter 12:

Sum and Difference Identities • Double-angle Identities • Half-Angle Identities • Graphs of Logarithmic Functions

Chapter 13:

Inverse Trigonometric Functions • Trigonometric Equations

Chapter 14:

Limits of a Function

Chapter 15:

Interval Notation • Products of Linear Factors • Tangents • Increasing and Decreasing Functions

Chapter 16:

Logarithms of Products and Quotients • Logarithms of Powers • Exponential Equations

Chapter 17:

Infinity as a Limit • Undefined Limits

Chapter 18:

Sums, Differences, Products and Quotients of Functions • Composition of Functions

Chapter 19:

The Derivative • Slopes of Curves on a Graphing Calculator

Chapter 20:

Change of Base • Graphing Origin-Centered Conics on a Graphing Calculator

Chapter 21:

Translations of Function • Graphs of Rational Functions I

Chapter 22:

Binomial Expansion • Recognizing the Equations of Conic Sections

Chapter 23:

Trigonometric Functions of nθ • Graphing Conics on a Graphing Calculator

Chapter 24:

New Notation for the Definition of the Derivative • The Derivative of xn

Chapter 25:

The Constant-Multiple Rule for Derivatives • The Derivatives of Sums and Differences • Proof of the Derivative of a Sum

Chapter 26:

Derivatives of ex and In x • Derivative of sin x and cos x • Exponential Growth and Decay

Chapter 27:

Equation of the Tangent Line • Higher-Order Derivatives

Chapter 28:

Graphs of Rational Functions II • A Special Limit

Chapter 29:

Newton and Leibniz • Differentials

Chapter 30:

Graph of tanθ • Graphs of Reciprocal Functions

Chapter 31:

Product Rule • Proof of the Product Rule

Chapter 32:

An Antiderivative • The Indefinite Integral

Chapter 33:

Factors of Polynomial Functions • Graphs of Polynomial Functions

Chapter 34:

Implicit Differentiation

Chapter 35:

Integral of a Constant • Integral of kf(x) • Integral of xn

Chapter 36:

Critical Numbers • A Note about Critical Numbers

Chapter 37:

Differentiation by u Substitution

Chapter 38:

Integral of a Sum • Integral of 1/x

Chapter 39:

Area Under a Curve (Upper and Lower Sums) • Left, Right, and Midpoint Sums

Chapter 40:

Units for the Derivative • Normal Lines • Maximums and Minimums on a Graphing Calculator

Chapter 41:

Graphs of Rational Functions III • Repeated Factors

Chapter 42:

The Derivative of a Quotient • Proof of the Quotient Rule

Chapter 43:

Area Under a Curve as an Infinite Summation

Chapter 44:

The Chain Rule • Alternate Definition of the Derivative • The Symmetric Derivative

Chapter 45:

Using f to Characterize f • Using f to Find Maximums and Minimums

Chapter 46:

Related-Rates Problems

Chapter 47:

Fundamental Theorem of Calculus, Part I • Riemann Sums • The Definite Integral

Chapter 48:

Derivatives of Trigonometric Functions • Summary of Rules for Derivatives and Differentials

Chapter 49:

Concavity and Inflection Points • Geometric Meaning of the Second Derivative • First and Second Derivative Tests

Chapter 50:

Derivatives of Composite Functions • Derivatives of Products and Quotients of Composite Functions

Chapter 51:

Integration by Guessing

Chapter 52:

Maximization and Minimization Problems

Chapter 53:

Numerical Integration of Positive-Valued Functions on a Graphing Calculator

Chapter 54:

Velocity and Acceleration • Motion Due to Gravity

Chapter 55:

Maclaurin Polynomials

Chapter 56:

More Integration by Guessing • A Word of Caution

Chapter 57:

Properties of the Definite Integral

Chapter 58:

Explicit and Implicit Equations • Inverse Functions

Chapter 59:

Computing Areas • More Numerical Integration on a Graphing Calculator

Chapter 60:

Area Between Two Curves • Area Between Curves Using a Graphing Calculator

Chapter 61:

Playing Games with f,f I and f II

Chapter 62:

Work, Distance, and Rates

Chapter 63:

Critical Number (Closed Interval) Theorem

Chapter 64:

Derivatives of Inverse Trigonometric Functions • What to Memorize

Chapter 65:

Falling-Body Problems

Chapter 66:

Substitution • Change of Variable • Proof of the Substitution Theorem

Chapter 67:

Areas Involving Functions of y

Chapter 68:

Even and Odd Functions