| Stewart | Whitman Calculus | Explicitly in syllabus for Fall 2009 Math 1271 or Spring 2010 Math 1272? |
|---|---|---|
| Stewart Chapter 1 | ||
| 1.1 Functions and models | 1.3 Functions | No |
| 1.2 Mathematical models: a catalog of essential functions | (absent?) | No |
| 1.3 New functions from old functions | 1.4 Shifts and dilations | Yes |
| 1.4 Graphing calculators and computers | (absent?) | No |
| 1.5 Exponential functions | 4.6 Exponential and logarithmic functions | No |
| 1.6 Inverse functions and logarithms | 4.6 Exponential and logarithmic functions | No |
| Stewart Chapter 2 | ||
| 2.1 The tangent and velocity problems | 2.1 The slope of a function | Yes |
| 2.2 The limit of a function | 2.3 Limits | Yes |
| 2.3 Calculating limits using limit laws | 2.3 Limits | Yes |
| 2.4 The precise definition of a limit | 2.3 Limits | No |
| 2.5 Continuity | 2.5 Adjectives for functions | Yes |
| 2.6 Limits at infinity: horizontal asymptotes | Almost absent-- covered later in 4.8 Limits revisited, but see my handout on this topic or see the relevant section from the calc text pages. |
Yes |
| 2.7 Derivatives and rates of change | 2.2 An example 9.2 Distance, velocity, acceleration |
Yes |
| 2.8 The derivative as a function | 2.4 The derivative function | Yes |
| Stewart Chapter 3 | ||
| 3.1 Derivatives of polynomial and exponential functions | 3.1 The power rule 3.2 Linearity of the derivative |
Yes |
| 3.2 The product and quotient rules | 3.3 The product rule 3.4 The quotient rule |
Yes |
| 3.3 Derivatives of trigonometric functions | 4.3 A hard limit 4.4 The derivative of sin(x), continued 4.5 Derivatives of the trigonometric functions |
Yes |
| 3.4 The chain rule | 3.5 The chain rule | Yes |
| 3.5 Implicit differentiation | 4.9 Implicit differentiation | Yes |
| 3.6 Derivatives of logarithmic functions | 4.7 Derivatives of the exponential and logarithmic functions | Yes |
| 3.7 Rates of change in the natural and social sciences | 2.2 An example 9.2 Distance, velocity, acceleration 9.11 Differential equations |
Yes |
| 3.8 Exponential growth and decay | 9.11 Differential equations | Yes |
| 3.9 Related rates | 6.2 Related rates | Yes |
| 3.10 Linear approximation and differentials | 6.4 Linear approximations | Yes |
| 3.11 Hyperbolic functions | (absent?) | No |
| Stewart Chapter 4 | ||
| 4.1 Maximum and minimum values | 5.1 Maxima and minima | Yes |
| 4.2 The mean value theorem | 6.5 The mean value theorem | Yes |
| 4.3 How derivatives affect the shape of a graph | 5.2 The first derivative test 5.3 The second derivative test 5.4 Concavity and inflection points |
Yes |
| 4.4 Indeterminate forms and L'Hopital's rule | 4.8 Limits revisited | Yes |
| 4.5 Summary of curve sketching | 5.5 Asymptotes and other things to look for | Yes |
| 4.6 Graphing with calculus and calculators | (absent?) | No |
| 4.7 Optimization problems | 6.1 Optimization | Yes |
| 4.8 Newton's method | 6.3 Newton's method | Yes |
| 4.9 Antiderivatives | 7.1 Two Examples 7.2 The fundamental theorem of calculus |
Yes |
| Stewart Chapter 5 | ||
| 5.1 Areas and distances | 7.1 Two Examples | Yes |
| 5.2 The definite integral | 7.2 The fundamental theorem of calculus | Yes |
| 5.3 The fundamental theorem of calculus | 7.2 The fundamental theorem of calculus | Yes |
| 5.4 Indefinite integrals and the net change theorem | 7.2 The fundamental theorem of calculus 7.3 Some properties of integrals |
Yes |
| 5.5 The substitution rule | 8.1 Substitution | Yes |
| Stewart Chapter 6 | ||
| 6.1 Areas between curves | 9.1 Area between curves | Yes |
| 6.2 Volumes | 9.3 Volume | Yes |
| 6.3 Volumes by cylindrical shells | 9.3 Volume | Yes |
| 6.4 Work | 9.5 Work | No |
| 6.5 Average value of a function | 9.4 Average value of a function | Yes |
| Stewart Chapter 7 | ||
| 7.1 Integration by parts | 8.4 Integration by parts | Yes |
| 7.2 Trigonometric integrals | 8.2 Powers of sines and cosines | Yes |
| 7.3 Trigonometric substitution | 8.3 Trigonometric substitutions | Yes |
| 7.4 Integration of rational functions by partial fractions | 8.5 Rational functions | Yes |
| 7.5 Strategy for integration | 8.6 Additional exercises | Yes |
| 7.6 Integration using tables and computer algebra | (absent?) | No |
| 7.7 Approximate integration | Absent-- see the relevant section in the calc text pages. | Yes |
| 7.8 Improper integrals | 9.7 Kinetic energy; improper integrals | Yes |
| Stewart Chapter 8 | ||
| 8.1 Arc length | 9.9 Arc length | Yes |
| 8.2 Area of a surface | 9.10 Surface area | Yes |
| 8.3 Applications to physics and engineering | 9.6 Center of mass | Yes |
| 8.4 Applications to economics and biology | (absent?) | No |
| 8.5 Probability | 9.8 Probability | No |
| Stewart Chapter 9 | ||
| 9.1 Modelling with differential equations | 9.11 Differential equations | Yes |
| 9.2 Direction fields and Euler's method | Absent-- see the relevant sections on direction fields and Euler's method in the calc text pages | Yes |
| 9.3 Separable equations | 9.11 Differential equations | Yes |
| 9.4 Models for population growth | Some in 9.11 Differential equations, but mostly absent | No |
| 9.5 Linear equations | (absent?) | No |
| 9.6 Predator-prey systems | (absent?) | No |
| Stewart Chapter 10 | ||
| This chapter of Stewart covers parametric equations, polar coordinates, and conic sections |
These topics are either omitted or covered very lightly in Whitman Calculus; see instead Chapter 10 of the calc text pages |
Yes |
| Stewart Chapter 11 | ||
| 11.1 Sequences | 10.1 Sequences | Yes |
| 11.2 Series | 10.2 Series | Yes |
| 11.3 The integral test and estimates of sums | 10.3 The integral test | Yes |
| 11.4 The comparison tests | 10.5 Comparison tests | Yes |
| 11.5 Alternating series | 10.4 Alternating series | No |
| 11.6 Absolute convergence and the ratio and root tests | 10.6 Absolute convergence 10.7 The ration and root tests |
Yes |
| 11.7 Strategy for testing series | (absent?) | No |
| 11.8 Power series | 10.8 Power series | Yes |
| 11.9 Representations of functions as power series | 10.9 Calculus with power series | Yes |
| 11.10 Taylor and Maclaurin series | 10.10 Taylor series 10.11 Taylor's theorem |
Yes |
| 11.11 Applications of Taylor polynomials | 10.12 Additional exercises | Yes |
| Stewart Chapter 12 | ||
| 12.1 Three-dimensional coordinate systems | 11.1 The coordinate system | Yes |
| 12.2 Vectors | 11.2 Vectors | Yes |
| 12.3 The dot product | 11.3 The dot product | Yes |
| 12.4 The cross product | 11.4 The cross product | Yes |
| 12.5 Equations of lines and planes | 11.5 Lines and planes | Yes |
| 12.6 Cylinders and quadric surfaces | (absent?) | No |
| Stewart Chapter 13 | ||
| 13.1 Vector functions and space curves | 12.1 Space curves | Yes |
| 13.2 Derivatives and integrals of vector functions | 12.2 Calculus with vector functions | Yes |
| 13.3 Arc length and curvature | 12.3 Arc length | Yes |
| 13.4 Motion in space: velocity and acceleration | 12.4 Motion along a curve | No |