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Lesson # |
Text
Section
Number |
Text
Section
Title |
Topics |
|
T |
Trial Presentation (Done
during the Online Course Orientation) |
| 1 |
P.1 |
Lines |
Increments, Slope of a Line, Parallel and
Perpendicular Lines, Equations of Lines, Applications |
| 2 |
P.2 |
Functions and Graphs |
Functions, Domains and Ranges, Viewing and
Interpreting Graphs, Increasing versus Decreasing Functions, Even
Functions and Odd Functions: Symmetry, Functions Defined in Pieces, The
Absolute Value Function, How to Shift a Graph, Composite Functions |
| 3 |
P.3 |
Exponential Functions |
Exponential Growth, Population Growth, The
Exponential Function ex |
| 4 |
P.4 |
Inverse Functions and Logarithms |
One-to-One Functions, Inverses, Finding
Inverses, Logarithmic Functions, Properties of Logarithms, Applications |
|
5 |
P.5 |
Trigonometric Functions and Their Inverses |
Radian Measure, Graphs of Trigonometric
Functions, Values of Trigonometric Functions, Periodicity, Even and Odd
Trigonometric Functions, Transformations of Trigonometric Graphs,
Identities, The Law of Cosines, Inverse Trigonometric Functions,
Identities Involving Arc Sine and Arc Cosine |
| 6 |
P.6 |
Parametric Equations |
Parametrizations of Plane Curves, Lines and
Other Curves, Parametrizing Inverse Functions, An Application |
| 7 |
1.1 |
Rates of Change and Limits |
Average and Instantaneous Speed, Average Rates
of Change and Secant Lines, Limits of Functions, Informal Definition of
Limit, Precise Definition of Limit |
| 8 |
1.2 |
Finding Limits and One-Sided Limits |
Properties of Limits, Eliminating Zero
Denominators Algebraically, Sandwich Theorem, One-Sided Limits, Limits
Involving (sin ß) / ß |
| 9 |
1.3 |
Limits Involving Infinity |
Finite Limits as x approaches
infinity, Limits of Rational Functions as x approaches
± infinity, Horizontal and Vertical Asymptotes: Infinite Limits, Sandwich
Theorem Revisited, Precise Definitions of Infinite Limits, End Behavior
Models and Oblique Asymptotes |
| 10 |
1.4 |
Continuity |
Continuity at a Point, Continuous Functions,
Algebraic Combinations, Composites, Intermediate Value Theorem for
Continuous Functions |
| 11 |
1.5 |
Tangent Lines |
What Is a Tangent to a Curve?, Finding a
Tangent to the Graph of a Function, Rates of Change: Derivative at a Point |
| 12 |
2.1 |
The Derivative as a Function |
Definition of Derivative, Notation, Derivatives
of Constants, Powers, and Sums, Differentiable on an Interval; One-Sided
Derivatives, Graphing f' from Estimated Values,
Differentiable Functions are Continuous, Intermediate Value Property of
Derivative, Second- and Higher-Order Derivatives |
| 13 |
2.2 |
The Derivative as a Rate of Change |
Instantaneous Rates of Change, Motion Along a
Line: Displacement, Velocity, Speed, Acceleration, and Jerk, Sensitivity
to Change, Derivatives in Economics |
| 14 |
2.3 |
Derivatives of Products, Quotients, and Negative
Powers |
Products, Quotients, Negative Integer Powers
of x |
| 15 |
2.4 |
Derivatives of Trigonometric Functions |
Derivative of the Sine Function, Derivative of
the Cosine Function, Simple Harmonic Motion, Derivatives of the Other
Basic Trigonometric Functions, Continuity of Trigonometric Functions |
| 16 |
2.5 |
The Chain Rule and Parametric Equations |
Derivative of a Composite Function,
"Outside-Inside" Rule, Repeated Use of the Chain Rule, Slopes of
Parametrized Curves, Power Chain Rule, Melting Ice Cubes |
| 17 |
2.6 |
Implicit Differentiation |
Implicitly Defined Functions, Derivatives of
Higher Order, Rational Powers of Differentiable Functions |
| 18 |
2.7 |
Related Rates |
Related Rate Equations, Solution Strategy |
| 19 |
3.1 |
Extreme Values of Functions |
The Drilling-Rig Problem, Absolute (Global)
Extreme Values, Local (Relative) Extreme Values, Finding Extreme Values |
| 20 |
3.2 |
The Mean Value Theorem and Differential
Equations |
Rolle's Theorem, Mean Value Theorem, A Physical
Interpretation, Mathematical Consequences, Finding Velocity and Position
from Acceleration, Differential Equations and the Height of a Projectile |
| 21 |
3.3 |
The Shape of a Graph |
First Derivative Test for Increasing Functions
and Decreasing Functions, First Derivative Test for Local Extrema,
Concavity, Points of Inflection, Second Derivative Test for Local Extrema,
Learning about Functions from Derivatives |
| 22 |
3.5 |
Modeling and Optimization |
Examples from Business and Industry, Examples
from Mathematics and Physics, Fermat's Principle and Snell's Law, Examples
from Economics, Modeling Discrete Phenomena with Differentiable Functions |
| 23 |
3.6 |
Linearization and Differentials |
Linearization, Differentials, Estimating Change
with Differentials, Absolute, Relative, and Percentage Change, Sensitivity
to Change |
| 24 |
3.7 |
Newton's Method |
Procedure for Newton's Method |
| 25 |
4.1 |
Indefinite Integrals, Differential Equations,
and Modeling |
Finding Antiderivatives: Indefinite Integrals,
Initial Value Problems, Mathematical Modeling |
| 26 |
4.2 |
Integral Rules; Integration by Substitution |
Rules of Algebra for Antiderivatives, The
Integrals of sin2 x and cos2
x, The Power Rule in Integral Form, Substitution: Running the
Chain Rule Backwards |
| 27 |
4.3 |
Estimating with Finite Sums |
Area and Cardiac Output, Distance Traveled,
Displacement versus Distance Traveled, Volume of a Sphere, Average Value
of a Nonnegative Function, Conclusion |
| 28 |
4.4 |
Riemann Sums and Definite Integrals |
Riemann Sums, Terminology and Notation of
Integration, Area Under the Graph of a Nonnegative Function, Average Value
of an Arbitrary Continuous Function, Properties of Definite Integrals |
| 29 |
4.5 |
The Mean Value and Fundamental Theorems |
Mean Value Theorem for Definite Integrals,
Fundamental Theorem-Part 1, A Geometric Interpretation, Fundamental
Theorem-Part 2, Area Connection |
| 30 |
4.6 |
Substitution in Definite Integrals |
Substitution Formula, Areas Between Curves,
Boundaries with Changing Formulas |
| 31 |
4.7 |
Numerical Integration |
Trapezoidal Approximations, Error in the
Trapezoidal Approximation, Approximations Using Parabolas, Error in
Simpson's Rule |
