The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.

Index S...

saddle pointCritical Point Theorem
scalarExample 2: Vector Components
 Example 3: Vector Length
 Definition of the Inner Product
Scalar Associative LawScalar Multiple - Theorem 3
scalar equationTheorem 1: The Line
 Example 3: Finding the Scalar Equation
scalar fieldCurl of a Vector Field
scalar independent variableIncrement and Differential
scalar multipleScalar Multiple - Theorem 3
scalar multiplesCorollaries
 Example 4
scalar productCorollary 1
 Inner Product
Schwartz' InequalityExtra Problems
secantDefining Other Trigonometric Functions
 Theorem 4: Integrals of Trigonometric Functions
Second Derivative TestSecond Derivative Test
 Example 5
 Second Derivative Test
second order differential equationSecond Order Homogeneous Linear Equations
 Second Order Linear Equations
 General Solution of First Order Differential Equation
 Example 5
 Second Order Differential Equation
second order differential equationsSecond Order Linear Differential Equation with Constant Coefficients
 Principle of Second Order Superposition
second order linear differential equationSecond Order Linear Differential Equation with Constant Coefficients
 Principle of Second Order Superposition
sector of a circleTheorem and Proof
segment of a smooth curveSegment of a Curve
semicircleArea of a Semicircle
 Example 7: Area Under A Semicircle
separable variablesMethod For Solving
separating variablesExample 4 - Nonuniqueness
sequenceExample 1: Some Simple Sequences.
 Example 2: n decimals of π
 Application: Compound Interests
 Theorem 1: Sequences approaching ∞
 Example 8: Sequences Approaching ∞
seriesSums of Infinite Series
 Example 2: Partial Sum Sequence
 Example 4: Ratio Test (Diverging Series)
 Theorem 1: Converging Geometric Series
series, divergenceTheorem 1: Convergence of Absolutly Convergent Series
sets of real numbersSome Important Sets of Real Numbers
shortest distanceProblems
side conditionMethod For Finding Maxima and Minima on a Closed Region
simple closed curveSimple Closed Curve
Simpson's approximationSimpson's Rule
Simpson's RuleNumerical Integration
 Example 3: Simpsons Rule Applied
simulationRiemann Sum
 Definition of Differentials
sinIntegral of a Trigonometric Function
sineTheorem 4: Integrals of Trigonometric Functions
 Second Order Differential Equation
sine, cosineSummary
slant heightExample 1: Line Segment
 Example 1: Point-slope Equation
 Definition: Linear Function
 Example 2
 Example 4
 Theorem 2: Linear Equation
 Average Slope
 Actual Slope
 Average Velocity
 Algebraic Manipulation of Hyperreal Numbers
 Slopes Along Curves
 Existance of Slope
 Theorem 1: Limit As the Slope of a Function
 Changing of Curve Direction
 Theorem 1: Direction of a Curve at the Origin
slope of a lineTheorem 1: Slope Of a Line
 Example 5: Slope of a Line
slope-intercept equationDefinition
 Example 1: Point-slope Equation
smoothSmoothness of Functions
smooth curveLength of a Smooth Curve in Polar Coordinates
 Example 1: Length of a Spiral
 Example 2: Length of an Ark of a Circle
 Simple Closed Curve
solid of revolutionSolids of Revolution
 Region Between Two Curves - Solid of Revolution
 Example 2
 Example 4
solid regionBoundary Of a Solid Region
special theory of relativityExample 7
spherical coordinatesExample 2
spiralExample 2: Tangent Line of a Spiral
spring constantGraphs of Solutions of Second Order Homogeneous Linear Equations
square functionExample 1: The Square Function
 Domain of Functons (exmpl. 1-3 cont.)
square root functionII. Transfer Principle
standard numberTheorem 2:
standard partHow to Compute Limits
Standard Part PrincipleSummary
Standard Part RuleLimit Rules
standard partsTheorem 3:
steady part of the solutionExample 6
steepest descentCorollaries
Stokes' TheoremStokes' Theorem
 Example 2
straight lineIntegral of a Straight Line
 Antiderivative of a Line
 Identity Function
straight line segmentChanging of Curve Direction
substitutionExample 1
 Example 2
 Example 8
 Example 3: Finding Values of Terms by Substitution
sumExample 2: Tail of a Geometric Series
 Example 1: Alternating Harmornic Series Converging
 Theorem 1: Derivatives And Integrals Of Power Series
Sum FunctionTheorem 1
sum ruleIntegration Rules
 Theorem 1: Convergent Sum Rules
 Summary of Series Convergence Tests
 Example 4
 Corollaries: Convergent and Divergent Sums
sums of power seriesDefinition of Power Series
surfaceFunction f of Two Variables
surface areaApplications Of Functions
 Area of Surface of Revolution
surface integralArea Of A Smooth Surface
 Example 1
 Example 2
 Oriented Surface
 Surface Integral
 Example 3
surface of revolutionArea of Surface of Revolution
 Example 2: Curve
 Example 3:
Surfaces of RevolutionCylinders and Cones
symbolDrawing Graphs of Functions

Last Update: 2006-11-25