PowerPoint Presentations

Click on Lesson #	Text Section Number	Text Section Title	Topics
T	Trial Presentation *(Done during the Course Orientation)*
1	1.1	Real Numbers and the Real Line	Real Numbers, Intervals, Solving Inequalities, Absolute Value
2	1.2	Lines, Circles, and Parabolas	Cartesian Coordinates in the Plane, Increments and Straight Lines, Parallel and Perpendicular Lines, Distance and Circles in the Plane, Parabolas
3	1.3	Functions and Their Graphs	Functions; Domain and Range, Graphs of Functions, Representing a Function Numerically, The Vertical Line Test, Piecewise-Defined Functions
4	1.4	Identifying Functions; Mathematical Models	Increasing Versus Decreasing Functions, Even Functions and Odd Functions: Symmetry, Mathematical Models
5	1.5	Combining Functions; Shifting and Scaling Graphs	Sums, Differences, Products, and Quotients, Composite Functions, Shifting a Graph of a Function, Scaling and Reflecting a Graph of a Function, Ellipses
6	1.6	Trigonometric Functions	Radian Measure, The Six Basic Trigonometric Functions, Periodicity and Graphs of the Trigonometric Functions, Identities, The Law of Cosines, Transformations of Trigonometric Graphs
7	2.1	Rates of Change and Limits	Average and Instantaneous Speed, Average Rates of Change and Secant Lines, Limits of Function Values x-Using Calculators and Computers to Estimate Limits
8	2.2	Calculating Limits Using the Limit Laws	The Limit Laws, Eliminating Zero Denominators Algebraically, The Sandwich Theorem
9	2.3	The Precise Definition of a Limit	Definition of Limit, Examples: Testing the Definition, Finding Deltas Algebraically for Given Epsilons x-Using the Definition to Prove Theorems
10	2.4	One-Sided Limits and Limits at Infinity	One-Sided Limits, Precise Definitions of One-Sided Limits, Limits Involving (sin Θ) / Θ, Finite Limits as x --> ± ∞, Limits at Infinity of Rational Functions, Horizontal Asymptotes, The Sandwich Theorem Revisited, Oblique Asymptotes
11	2.5	Infinite Limits and Vertical Asymptotes	Infinite Limits, Precise Definitions of Infinite Limits, Vertical Asymptotes, Dominant Terms
12	2.6	Continuity	Continuity at a Point, Continuous Functions, Composites, Continuous Extension to a Point, Intermediate Value Theorem for Continuous Functions
13	2.7	Tangents and Derivatives	What is a Tangent to a Curve?, Finding a Tangent to the Graph of a Function, Rates of Change: Derivative at a Point
14	3.1	The Derivative as a Function	Calculating Derivatives from the Definition, Notations, Graphing the Derivative, Differentiable on an Interval; One-Sided Derivatives, When Does a Function Not Have a Derivative at a Point?, Differentiable Functions Are Continuous, The Intermediate Value Property of Derivatives
15	3.2	Differentiation Rules	Powers, Multiples, Sums, and Differences, Products and Quotients, Negative Integer Powers of x, Second and Higher-Order Derivatives,
16	3.3	The Derivative as a Rate of Change	Instantaneous Rates of Change, Motion Along a Line: Displacement, Velocity, Speed, Acceleration, and Jerk, Derivatives and Economics, Sensitivity to Change
17	3.4	Derivatives of Trigonometric Functions	Derivative of the Sine Function, Derivative of the Cosine Function, Simple Harmonic Motion, Derivatives of the Other Basic Trigonometric Functions
18	3.5	The Chair Rule and Parametric Equations	Derivative of a Composite Function, "Outside-Inside" Rule, Repeated Use of the Chain Rule, The Chain Rule with Powers of a Function, Parametric Equations, Slopes of Parametrized Curves
19	3.6	Implicit Differentiation	Implicitly Defined Functions, Lenses, Tangents, and Normal Lines, Derivatives of Higher Order, Rational Powers of Differentiable Functions
20	3.7	Related Rates	Related Rates Equations
21	3.8	Linearization and Differentials	Linearization, Differentials, Estimating with Differentials, Error in Differential Approximation, Sensitivity to Change
22	4.1	Extreme Values of Functions	Local (Relative) Extreme Values, Finding Extrema
23	4.2	The Mean Value Theorem	Rolle's Theorem, The Mean Value Theorem, A Physical Interpretation, Mathematical Consequences, Finding Velocity and Position from Acceleration
24	4.3	Monotonic Functions and The First Derivative Test	Increasing Functions and Decreasing Functions, First Derivative Test for Local Extrema
25	4.4	Concavity and Curve Sketching	Concavity, Points of Inflection, Second Derivative Test for Local Extrema, Learning About Functions from Derivatives
26	4.5	Applied Optimization Problems	Examples from Business and Industry, Examples from Mathematics and Physics, Examples from Economics
27	4.6	Indeterminate Forms and L'Hopital's Rule	Indeterminate Form 0/0, Indeterminate Forms ∞ / ∞, ∞ ∙ 0, ∞ − ∞
28	4.7	Newton's Method	Procedure for Newton's Method, Applying Newton's Method, x-Convergence of Newton's Method x-But Things Can Go Wrong x-Fractal Basins and Newton's Method
29	4.8	Antiderivatives	Finding Antiderivatives, Initial Value Problems and Differential Equations, Antiderivatives and Motion, Indefinite Integrals
30	5.1	Estimating with Finite Sums	Area, Distance Traveled, Displacement Versus Distance Traveled, Average Value of a Nonnegative Function
31	5.2	Sigma Notation and Limits of Finite Sums	Finite Sums and Sigma Notation, Limits of Finite Sums, Riemann Sums
32	5.3	The Definite Integral	Limits of Riemann Sums, Notation and Existence of the Definite Integral, Integrable and Nonintegrable Functions, Properties of Definite Integrals, Area Under the Graph of a Nonnegative Function, Average Value of a Continuous Function Revisited
33	5.4	The Fundamental Theorem of Calculus	Mean Value Theorem for Definite Integrals, Fundamental Theorem - Part 1, Fundamental Theorem - Part 2 (The Evaluation Theorem), Total Area
34	5.5	Indefinite Integrals and the Substitution Rule	The Power Rule in Integral Form, Substitution: Running the Chain Rule Backwards, The Integrals of sin² x and cos² x
35	5.6	Substitution and Area Between Curves	Substitution Formula, Definite Integrals of Symmetric Functions, Areas Between Curves, Integration with Respect to y, Combining Integrals with Formulas from Geometry