- Chapter 1: FUNCTIONS AND MODELS
- Chapter 1.1: FUNCTIONS AND MODELS
- Chapter 1.2: MATHEMATICAL MODELS: A CATALOG OF ESSENTIAL FUNCTIONS
- Chapter 1.3: NEW FUNCTIONS FROM OLD FUNCTIONS
- Chapter 1.4: GRAPHING CALCULATORS AND COMPUTERS
- Chapter 1.5: EXPONENTIAL FUNCTIONS
- Chapter 1.6: INVERSE FUNCTIONS AND LOGARITHMS
- Chapter 1.7: PARAMETRIC CURVES
- Chapter 2: LIMITS AND DERIVATIVES
- Chapter 2.1: THE TANGENT AND VELOCITY PROBLEMS
- Chapter 2.2: THE LIMIT OF A FUNCTION
- Chapter 2.3: CALCULATING LIMITS USING THE LIMIT LAWS
- Chapter 2.4: CONTINUITY
- Chapter 2.5: LIMITS INVOLVING INFINITY
- Chapter 2.6: DERIVATIVES AND RATES OF CHANGE
- Chapter 2.7: THE DERIVATIVE AS A FUNCTION
- Chapter 2.8: WHAT DOES SAY ABOUT ?
- Chapter 3: DIFFERENTIATION RULES
- Chapter 3.1: DERIVATIVES OF POLYNOMIALS AND EXPONENTIAL FUNCTIONS
- Chapter 3.2: THE PRODUCT AND QUOTIENT RULES
- Chapter 3.3: DERIVATIVES OF TRIGONOMETRIC FUNCTIONS
- Chapter 3.4: THE CHAIN RULE
- Chapter 3.5: IMPLICIT DIFFERENTIATION
- Chapter 3.6: INVERSE TRIGONOMETRIC FUNCTIONS AND THEIR DERIVATIVES
- Chapter 3.7: DERIVATIVES OF LOGARITHMIC FUNCTIONS
- Chapter 3.8: RATES OF CHANGE IN THE NATURAL AND SOCIAL SCIENCES
- Chapter 3.9: LINEAR APPROXIMATIONS AND DIFFERENTIALS
- Chapter 4: APPLICATIONS OF DIFFERENTIATION
- Chapter 4.1: RELATED RATES
- Chapter 4.2: MAXIMUM AND MINIMUM VALUES
- Chapter 4.3: DERIVATIVES AND THE SHAPES OF CURVES
- Chapter 4.4: GRAPHING WITH CALCULUS AND CALCULATORS
- Chapter 4.5: INDETERMINATE FORMS AND LHOSPITALS RULE
- Chapter 4.6: OPTIMIZATION PROBLEMS
- Chapter 4.7: NEWTONS METHOD
- Chapter 4.8: ANTIDERIVATIVES
- Chapter 5: INTEGRALS
- Chapter 5.1: AREAS AND DISTANCES
- Chapter 5.10: IMPROPER INTEGRALS
- Chapter 5.2: THE DEFINITE INTEGRAL
- Chapter 5.3: EVALUATING DEFINITE INTEGRALS
- Chapter 5.4: THE FUNDAMENTAL THEOREM OF CALCULUS
- Chapter 5.5: THE SUBSTITUTION RULE
- Chapter 5.6: INTEGRATION BY PARTS
- Chapter 5.7: ADDITIONAL TECHNIQUES OF INTEGRATION
- Chapter 5.8: INTEGRATION USING TABLES AND COMPUTER ALGEBRA SYSTEMS
- Chapter 5.9: APPROXIMATE INTEGRATION
- Chapter 6: APPLICATIONS OF INTEGRATION
- Chapter 6.1: MORE ABOUT AREAS
- Chapter 6.2: VOLUMES
- Chapter 6.3: VOLUMES BY CYLINDRICAL SHELLS
- Chapter 6.4: ARC LENGTH
- Chapter 6.5: AVERAGE VALUE OF A FUNCTION
- Chapter 6.6: APPLICATIONS TO PHYSICS AND ENGINEERING
- Chapter 6.7: APPLICATIONS TO ECONOMICS AND BIOLO
- Chapter 6.8: PROBABILITY
- Chapter 7: DIFFERENTIAL EQUATIONS
- Chapter 7.1: MODELING WITH DIFFERENTIAL EQUATIONS
- Chapter 7.2: DIRECTION FIELDS AND EULERS METHOD
- Chapter 7.3: SEPARABLE EQUATIONS
- Chapter 7.4: EXPONENTIAL GROWTH AND DECAY
- Chapter 7.5: THE LOGISTIC EQUATION
- Chapter 7.6: PREDATOR-PREY SYSTEMS
- Chapter 8: INFINITE SEQUENCES AND SERIES
- Chapter 8.1: SEQUENCES
- Chapter 8.2: SERIES
- Chapter 8.3: THE INTEGRAL AND COMPARISON TESTS; ESTIMATING SUMS
- Chapter 8.4: OTHER CONVERGENCE TESTS
- Chapter 8.5: POWER SERIES
- Chapter 8.6: REPRESENTATIONS OF FUNCTIONS AS POWER SERIES
- Chapter 8.7: TAYLOR AND MACLAURIN SERIES
- Chapter 8.8: APPLICATIONS OF TAYLOR POLYNOMIALS
Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series) 4th Edition - Solutions by Chapter
Full solutions for Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series) | 4th Edition
Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series) | 4th Edition - Solutions by ChapterGet Full Solutions
See Linear programming problem.
Distance (on a number line)
The distance between real numbers a and b, or |a - b|
Graph of a polar equation
The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.
A set of points in a plane, the absolute value of the difference of whose distances from two fixed points (the foci) is a constant.
The domain of a function’s algebraic expression.
a + 1-a2 = 0, a # 1a
Newton’s law of cooling
T1t2 = Tm + 1T0 - Tm2e-kt
The graph of ƒ(x) = e-x2/2
See Principal nth root
Real part of a complex number
See Complex number.
Reflection across the x-axis
x, y and (x,-y) are reflections of each other across the x-axis.
Use a graphical method, including use of a hand sketch or use of a grapher. When appropriate, the approximate solution should be confirmed algebraically
Standard unit vectors
In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>
The initial digit or digits of a number in a stemplot.
Stretch of factor c
A transformation of a graph obtained by multiplying all the x-coordinates (horizontal stretch) by the constant 1/c, or all of the y-coordinates (vertical stretch) of the points by a constant c, c, > 1.
Symmetric about the origin
A graph in which (-x, -y) is on the the graph whenever (x, y) is; or a graph in which (-r, ?) or (r, ? + ?) is on the graph whenever (r, ?) is
Transpose of a matrix
The matrix AT obtained by interchanging the rows and columns of A.
Vector of length 1.
The square of the standard deviation.
The scale of the tick marks on the x-axis in a viewing window.