Author | Soon, Frederick H. author |
---|---|
Title | Student's Guide to Calculus by J. Marsden and A. Weinstein [electronic resource] : Volume II / by Frederick H. Soon |
Imprint | New York, NY : Springer New York, 1985 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5150-7 |
Descript | XIV, 282 p. online resource |
7 -- Basic Methods of Integration -- 7.1 Calculating Integrals -- 7.2 Integration by Substitution -- 7.3 Changing Variables in the Definite Integral -- 7.4 Integration by Parts -- 7.R Review Exercises for Chapter 7 -- 8 -- Differential Equations -- 8.1 Oscillations -- 8.2 Growth and Decay -- 8.3 The Hyperbolic Functions -- 8.4 The Inverse Hyperbolic Functions -- 8.5 Separable Differential Equations -- 8.6 Linear First-Order Equations -- 8.R Review Exercises for Chapter 8 -- 9 -- Applications of Integration -- 9.1 Volumes by the Slice Method -- 9.2 Volumes by the Shell Method -- 9.3 Average Values and the Mean Value Theorem for Integrals -- 9.4 Center of Mass -- 9.5 Energy, Power, and Work -- 9.R Review Exercises for Chpater 9 -- Comprehensive Test for Chapters 7 โ 9 -- 10 -- Further Techniques and Applications of Integration -- 10.1 Trigonometric Integrals -- 10.2 Partial Fractions -- 10.3 Arc Length and Surface Area -- 10.4 Parametric Curves -- 10.5 Length and Area in Polar Coordinates -- 10.R Review Exercises for Chapter 10 -- 11 -- Limits, L'Hรดpital's Rule, and Numerical Methods -- 11.1 Limits of Functions -- 11.2 L'Hรดpital's Rule -- 11.3 Improper Integrals -- 11.4 Limits of Sequences and Newton's Method -- 11.5 Numerical Integration -- 11.R Review Exercises for Chapter 11 -- 12 -- Infinite Series -- 12.1 The Sum of an Infinite Series -- 12.2 The Comparison Test and Alternating Series -- 12.3 The Integral and Ratio Tests -- 12.4 Power Series -- 12.5 Taylor's Formula -- 12.6 Complex Numbers -- 12.7 Second-Order Linear Differential Equations -- 12.8 Series Solutions of Differential Equations -- 12.R Review Exercises for Chapter 12 -- Comprehensive Test for Chapters 7 โ 12