Calculus

=**Introductory Calculus Semester I: Course Outline**=

I__. **Unit 1: Functions and Graphs**__ //A. Lesson 1: Functions and Function Notation// a. Topic 1: [|Definition of a function] b. Topic 2: [|Vertical line test] c. Topic 3: [|Function notation] d. Topic 4: [|Finding input & output values] e. Topic 5: [|Domain & range]

B//. Lesson 2: Absolute Value and Piecewise Defined Functions// a. Topic 1: [|Piecewise defined functions] b. Topic 2: [|The absolute value function] c. Topic 3: [|Solving equations involving absolute values]

//C. Lesson 3: Inequalities// a. Topic 1: [|Solving inequalities] b. Topic 2: [|Solving inequalities involving absolute values]

//D. Lesson 4: Composition and Combination of Functions// a. Topic 1: [|Composition of functions] b. Topic 2: [|Inverse functions] c. Topic 3: [|Non-invertible functions]

//E. Lesson 5: Exponential and Logarithmic Functions// a. Topic 1: [|The family of exponential functions] b. Topic 2: [|The number e] c. Topic 3: [|Logarithmic functions] d. Topic 4: [|Solving exponential and logarithmic functions] e. Topic 5: [|Changing the base of logarithmic functions]

//F. Lesson 6: Transformation of Functions// a. Topic 1: [|Horizontal & vertical shifts] b. Topic 2: [|Reflections & symmetry] c. Topic 3: [|Vertical stretches & compressions] d. Topic 4: [|Horizontal stretches & compressions]

//G. Lesson 7: Trigonometric Functions// a. Topic 1: [|Radians and arc length] b. Topic 2: [|The sin and cosine functions] c. Topic 3: [|Other trigonometric functions] d. Topic 4: [|Inverse trigonometric functions] e. Topic 5: [|Trigonometric identities]

//H. Lesson 8: Power, Polynomial and Rational Functions// a. Topic 1: [|Variations] b. Topic 2: [|Power functions] c. Topic 3: [|Polynomial functions] d. Topic 4: [|Rational functions]

__II. **Unit 2: Limits and Continuity**__ //A. Lesson 9: Intuitive Definition of a Limit// a. Topic 1: [|What is a limit?] b. Topic 2: [|Using tables & graphs to find limits] c. Topic 3: [|Application: Using limits to find velocity]

//B. Lesson 10: Algebraic Techniques for Finding Limits// a. Topic 1: [|Calculating limits using limit laws] b. Topic 2: [|Direct substitution property] c. Topic 3: [|Indeterminate forms]

//C. Lesson 11: One-Sided Limits// a. Topic 1: [|Definition of one-sided limits] b. Topic 2: [|Finding one-sided limits] c. Topic 3: [|Existence of limits]

//D. Lesson 12: Infinite Limits// a. Topic 1: [|Definition of infinite limits] b. Topic 2: [|Vertical asymptotes]

//E. Lesson 13: Limits at Infinity// a. Topic 1: [|End-behavior of functions & horizontal asymptotes] b. Topic 2: [|Limit laws of infinite limits] c. Topic 3: [|Oblique asymptotes]

//F. Lesson 14: Limits of Special Trigonometric Functions// a. Topic 1: [|Special limits involving the sine function] b. Topic 2: [|Special limits involving the cosine function] c. Topic 3: [|Special limits involving the tangent function]

//G. Lesson 15: Continuity// a. Topic 1: [|Continuity at a point] b. Topic 2: [|Continuity on a closed interval] c. Topic 3: [|Continuity on an open interval] d. Topic 4: [|Intermediate Value Theorem]

__III. **Unit 3: Derivatives**__ //A. Lesson 16: Definition of the Derivative// a. Topic 1: [|The derivative as the slope of a tangent] b. Topic 2: [|The derivative as the rate of change] c. Topic 3: [|The derivative as a function]

//B. Lesson 17: Differentiation Rules// a. Topic 1: [|Constant rule, constant multiple rule] b. Topic 2: [|Power rule] c. Topic 3: [|Sum rule, difference rule] d. Topic 4: [|Product rule] e. Topic 5: [|Quotient rule] f. Topic 6: [|Trigonometric rules]

//C. Lesson 18: The Chain Rule// a. Topic 1: [|Chain rule definition] b. Topic 2: [|The chain rule with other rules] c. Topic 3[|: Higher-order derivatives]

D. //Lesson 19: Derivatives of Exponential Functions// a. Topic 1: [|Exponential rule] b. Topic 2: [|Base-a exponentials rule]

E. //Lesson 20: Derivative of Logarithmic Functions// a. Topic 1: [|Natural logarithmic rule] b. Topic 2: [|General logarithmic rule]

F. //Lesson 21: Derivatives of Inverse Functions// a. Topic 1: [|Inverse trig rule] b. Topic 2: [|Derivatives of Inverses]

G. //Lesson 22: Differentiability and Continuity// a. Topic 1: [|Differentiability implies continuity] b. Topic 2: [|Non-differentiable functions]

H. //Lesson 23: Implicit Differentiation// a. Topic 1: [|Derivatives of implicitly defined functions]

I. Lesson 24: //Logarithmic Differentiation// a. Topic 1: [|derivatives of complicated expressions]

__IV. **Unit 4: Application of the Derivative**__ A. //Lesson 25: Tangent and Normal Lines// a. Topic 1: [|Tangent lines] b. Topic 2: [|Normal lines]

B. //Lesson 26: Position, Velocity, and Acceleration (PVA)// a. Topic 1: [|Position & velocity] b. Topic 2: [|Acceleration]

C. //Lesson 27: Related Rates// a. Topic 1: [|Defining the problem] b. Topic 2: [|Example problems]

D. //Lesson 28: Relative Extrema and the First Derivative Test// a. Topic 1: [|Relative extrema & critical numbers] b. Topic 2: [|Increasing, decreasing functions & the first derivative]

E. //Lesson 29: Concavity and the Second Derivative Test// a. Topic 1: [|Concavity] b. Topic 2: [|The second derivative test]

F. //Lesson 30: Absolute Extrema and Optimization// a. Topic 1: [|Extreme value theorem] b. Topic 2: [|Sample problem]

G. //Lesson 31: Rolle's Rule and the Mean Value Theorem// a. Topic 1: [|Rolle’s rule] b. Topic 2: [|Mean value theorem]

H. //Lesson 32: Differentials// a. Topic 1: [|Linear approximation] b. Topic 2: [|Differentials]


 * Introductory Calculus Semester II: Course Outline**

__I. **Unit 5: Antiderivatives and Definite Integrals**__ //A//. //Lesson 33: Differential Equations and Slope Fields// a. Topic 1: [|Differential Equations] b. Topic 2: [|Slope Fields]

B. //Lesson 34: Antiderivatives// a. Topic 1: [|Introduction to antiderivatives] b. Topic 2: [|Basic antidifferentiation rules] c. Topic 3: [|Trigonometric antidifferentiation rules]

C. //Lesson 35: The Chain Rule for Antiderivatives// a. Topic 1: [|Simple substitutions] b. Topic 2: [|Trigonometric Integrals]

D. //Lesson 36: Antiderivatives of Exponentials// a. Topic 1: [|Natural exponential functions] b. Topic 2: [|General exponential functions]

E. //Lesson 37: Antiderivatives and Logarithms// a. Topic 1: [|Natural logarithmic functions] b. Topic 2: [|General logarithmic functions]

F. //Lesson 38: Antiderivatives and Inverse Trigonometric Functions// a. Topic 1: [|Rules yielding inverse trig functions] b. Topic 2: [|Rules yielding inverse trig cofunctions]

G. //Lesson 39: Trigonometric Substitutions// a. Topic 1: [|Substitution technique] b. Topic 2: [|Types of expressions]

H. //Lesson 40: The Definite Integral// a. Topic 1: [|Riemann sums] b. Topic 2: [|Definition of the definite integral] c. Topic 3: [|Area between curves] d. Topic 4: [|Approximate integration]

I. //Lesson 41: Fundamental Theorem of Calculus// a. Topic 1: [|Properties of the definite integral] b. Topic 2: [|The Fundamental Theorem of Calculus] c. Topic 3: [|Integral defined functions] d. Topic 4: [|The Mean Value Theorem]

II. **Unit 6: Application of Antiderivatives and Definite Integrals** A. //Lesson 42: Net Change and Displacement// a. Topic 1: [|Net Change Theorem] b. Topic 2: [|Displacement vs. total distance]

B. //Lesson 43: Volume// a. Topic 1: [|Volume of a solid of revolution: circular disks & rings] b. Topic 2: [|Volume of a solid of revolution: cylindrical shells] c. Topic 3: [|Volume of a solid of known cross-section]

C. //Lesson 44: Separable Differential Equations// a. Topic 1: [|Separable equations] b. Topic 2: [|Exponential, bounded growth & decay]

D. //Lesson 45: Work// a. Topic 1: [|Work done moving an object] b. Topic 2: [|Work done on a fluid]

E. //Lesson 46: Other Applications of Definite Integrals// a. Topic 1: [|Center of mass & density] b. Topic 2: [|Costs & probability]

= = = = **Introductory Calculus Semester II: Course Outline** ** 1. __Unit 5: Antiderivatives and Definite Integrals__ ** //A. //    //Lesson 33: Differential Equations and Slope Fields//  a. [|Topic 1: Differential Equations]  b.    [|Topic 2: Slope Fields]   <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> <span style="FONT-FAMILY: Arial, Helvetica, sans-serif"><span style="FONT-FAMILY: Arial, Helvetica, sans-serif"><span style="FONT-FAMILY: Arial, Helvetica, sans-serif">__//B<span style="FONT-FAMILY: Arial, Helvetica, sans-serif">. //__     <span style="FONT-FAMILY: Arial, Helvetica, sans-serif"><span style="FONT-FAMILY: Arial, Helvetica, sans-serif"><span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> <span style="FONT-FAMILY: Arial, Helvetica, sans-serif">__//Lesson 34: Antiderivatives//__ <span style="FONT-FAMILY: Arial, Helvetica, sans-serif"><span style="FONT-FAMILY: Arial, Helvetica, sans-serif"><span style="FONT-FAMILY: Arial, Helvetica, sans-serif"><span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> <span style="FONT-FAMILY: Arial, Helvetica, sans-serif">a. <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> <span style="FONT-FAMILY: Arial, Helvetica, sans-serif">Topic 1: [|Introduction to antiderivatives] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> <span style="FONT-FAMILY: Arial, Helvetica, sans-serif">b. <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> <span style="FONT-FAMILY: Arial, Helvetica, sans-serif">Topic 2: [|Basic antidifferentiation rules] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> <span style="FONT-FAMILY: Arial, Helvetica, sans-serif">c. <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> <span style="FONT-FAMILY: Arial, Helvetica, sans-serif">Topic 3: [|Trigonometric antidifferentiation rules] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> <span style="FONT-FAMILY: Arial, Helvetica, sans-serif">//__C. __//   //__<span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> <span style="FONT-FAMILY: Arial, Helvetica, sans-serif">Lesson 35: The Chain Rule for Antiderivatives   __// <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> <span style="FONT-FAMILY: Arial, Helvetica, sans-serif">a. <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> <span style="FONT-FAMILY: Arial, Helvetica, sans-serif">Topic 1: [|Simple substitutions] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> <span style="FONT-FAMILY: Arial, Helvetica, sans-serif">b. <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> <span style="FONT-FAMILY: Arial, Helvetica, sans-serif">Topic 2: [|Trigonometric Integrals] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> D.   <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Lesson 36: Antiderivatives of Exponentials <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> a.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 1: [|Natural exponential functions] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> b.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 2: [|General exponential functions] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> E.   <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Lesson 37: Antiderivatives and Logarithms <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> a.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 1: [|Natural logarithmic functions] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> b.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 2: [|General logarithmic functions] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> F.   <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Lesson 38: Antiderivatives and Inverse Trigonometric Functions <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> a.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 1: [|Rules yielding inverse trig functions] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> b.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 2: [|Rules yielding inverse trig cofunctions] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> G.   <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Lesson 39: Trigonometric Substitutions <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> a.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 1: [|Substitution technique] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> b.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 2: [|Types of expressions] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> H.   <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Lesson 40: The Definite Integral <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> a.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 1: [|Riemann sums] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> b.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 2: [|Definition of the definite integral] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> c.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 3: [|Area between curves] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> d.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 4: [|Approximate integration] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> I.   <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Lesson 41: Fundamental Theorem of Calculus <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> a.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 1: [|Properties of the definite integral] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> b.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 2: [|The Fundamental Theorem of Calculus] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> c.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 3: [|Integral defined functions] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> d.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 4: [|The Mean Value Theorem] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> II. **<span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt">Unit 6: Application of Antiderivatives and Definite Integrals **<span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> A.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Lesson 42: Net Change and Displacement <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> a.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 1: [|Net Change Theorem] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> b.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 2: [|Displacement vs. total distance] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> B.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Lesson 43: Volume <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> a.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 1: [|Volume of a solid of revolution: circular disks & rings] <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> b.    <span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt"> Topic 2: [|Volume of a solid of revolution: cylindrical shells] <span style="FONT-SIZE: 12pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US; mso-fareast-language: JA; mso-bidi-language: AR-SA">Topic 3: [|Volume of a solid of known cross-section]

http://www.themathpage.com/aPreCalc/precalculus.htm When one thing depends on another, as, for example, the area of a circle depends on the radius, or the temperature on the mountain depends on the height, then we say that the first is a function' of the other." Lawrence Spector, a math teacher at Borough of Manhattan Community College, introduces precalculus with twenty-five topics including logarithms, polynomials of the second degree, irrational numbers and mathematical induction. If you return to the homepage, you'll find another twenty-one trigonometry topics, along with lessons for algebra, plane geometry and calculus.

[|A collection of modules that can be used in the studying or teaching of calculus] > **[|Limits and Continuity]** > **[|Derivatives]** > **[|Applications of Differentiation]** > **[|Integration]** > **[|Applications of Integration]** > **[|Sequences and]****[|Series]**
 * **[|Pre-Calculus]**


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 * || [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Calculus] (1) || [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Functional Analysis] (130) || [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Norms] (11) ||
 * [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Calculus of Variations] (23) || [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Functions] (131) || [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Operator Theory] (24) ||
 * [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Catastrophe Theory] (6) || [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|General Analysis] (11) || [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Polynomials@] ||
 * [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Complex Analysis] (7) || [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Generalized Functions] (30) || [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Roots] (42) ||
 * [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Differential Equations] (7) || [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Harmonic Analysis] (1) || [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Series] (6) ||
 * [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Differential Forms] (34) || [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Inequalities] (73) || [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Singularities] (15) ||
 * [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Differential Geometry] (6) || [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Integral Transforms] (5) || [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Special Functions] (31) ||
 * [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Dynamical Systems] (89) || [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Manifolds@] ||
 * [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Fixed Points] (27) || [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Measure Theory] (72) ||  ||
 * [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Fixed Points] (27) || [[image:http://mathworld.wolfram.com/images/entries/folder.gif width="13" height="12"]] [|Measure Theory] (72) ||  ||