Rough correspondence between
Whitman Calculus and
Stewart's Calculus: early transcendentals, Vol. 1
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
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