- CHAPTER
- Analytic geometry in two dimensions
- 1.1 Real numbers
- 1.2 Slopes and equations of lines
- 1.3 Lines and linear equations; parallelism and perpendicularity
- 1.4 Distances, circles, and parabolas
- 1.5 Equations, statements, and graphs
- 1.6 Introduction to velocity and acceleration
- CHAPTER
- Vectors and geometry in three dimensions
- 2.1 Vectors in E3
- 2.2 Coordinate systems and vectors in E3
- 2.3 Scalar products, direction cosines, and lines in E3
- 2.4 Planes and lines in E3
- 2.5 Determinants and applications
- 2.6 Vector products and changes of coordinates in E3
- CHAPTER
- Functions, limits, derivatives
- 3.1 Functional notation
- 3.2 Limits
- 3.3 Unilateral limits and asymptotes
- 3.4 Continuity
- 3.5 Difference quotients and derivatives
- 3.6 The chain rule and differentiation of elementary functions
- 3.7 Rates, velocities
- 3.8 Related rates
- 3.9 Increments and differentials
- CHAPTER
- Integrals
- 4.1 Indefinite integrals
- 4.2 Riemann sums and integrals
- 4.3 Properties of integrals
- 4.4 Areas and integrals x Table of contents
- 4.5 Volumes and integrals
- 4.6 Riemann-Cauchy integrals and work
- 4.7 Mass, linear density, and moments
- 4.8 Moments and centroids in B2 and E3
- 4.9 Simpson and other approximations to integrals
- CHAPTER
- Functions, graphs, and numbers
- 5.1 Graphs, slopes, and tangents
- 5.2 Trends, maxima, and minima
- 5.3 Second derivatives, convexity, and flexpoints
- 5.4 Theorems about continuous and differentiable functions
- 5.5 The Rolle theorem and the mean-value theorem
- 5.6 Sequences, series, and decimals
- 5.7 Darboux sums and Riemann integrals
- CHAPTER
- Cones and conics
- 6.1 Parabolas
- 6.2 Geometry of cones and conics
- 6.3 Ellipses
- 6.4 Hyperbolas
- 6.5 Translation and rotation of axes
- 6.6 Quadric surfaces
- CHAPTER
- Curves, lengths, and curvatures
- 7.1 Curves and lengths
- 7.2 Lengths and integrals
- 7.3 Center and radius of curvature
- CHAPTER
- Trigonometric functions
- -8.1 Trigonometric functions and their derivatives
- 8.2 Trigonometric integrands
- 8.3 Inverse trigonometric functions
- 8.4 Integration by trigonometric and other substitutions
- 8.5 Integration by substituting z= tan e/2
- CHAPTER Table of contents xl
- Exponential and logarithmic functions
- 9.1 Exponentials and logarithms
- 9.2 Derivatives and integrals of exponentials and logarithms
- 9.3 Hyperbolic functions
- 9.4 Partial fractions
- 9.5 Integration by parts
- CHAPTER
- Polar, cylindrical, and spherical coordinates
- 10.1 Geometry of coordinate systems
- 10.2 Polar curves, tangents, and lengths
- 10.3 Areas and integrals involving polar coordinates
- CHAPTER
- Partial derivatives
- 11.1 Elementary partial derivatives
- 11.2 Increments, chain rule, and gradients
- 11.3 Formulas involving partial derivatives
- CHAPTER
- Series
- 12.1 Definitions and basic theorems
- 12.2 Ratio test and integral test
- 12.3 Alternating series and Fourier series
- 12.4 Power series
- 12.5 Taylor formulas with remainders
- 12.6 Euler-Maclaurin summation formulas
- CHAPTER
- Iterated and multiple integrals
- 13.1 Iterated integrals
- 13.2 Iterated integrals and volumes
- 13.3 Double integrals
- grals 13.4 Rectangular coordinate applications of double and iterated inte-
- 13.5 Integrals in polar coordinates
- 13.6 Triple integrals; rectangular coordinates
- 13.3 Double integrals
- 13.7 Triple integrals; cylindrical coordinates xii Table of contents
- 13.8 Triple integrals; spherical coordinates
- APPENDIX
- Proofs of basic theorems on limits
- APPENDIX
- Volumes
- INDEX
lu
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