Author | Marsden, Jerrold. author |
---|---|
Title | Calculus II [electronic resource] / by Jerrold Marsden, Alan Weinstein |
Imprint | New York, NY : Springer New York, 1985 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5026-5 |
Descript | 345 p. 43 illus. 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 -- 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 -- 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 -- 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 -- 11 Limits, LโHรดpitalโs Rule, and Numerical Methods -- 11.1 Limits of Functions -- 11.2 LโHรดpitalโs Rule -- 11.3 Improper Integrals -- 11.4 Limits of Sequences and Newtonโs Method -- 11.5 Numerical Integration -- 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 Taylorโs Formula -- 12.6 Complex Numbers -- 12.7 Second-Order Linear Differential Equations -- 12.8 Series Solutions of Differential Equations -- Answers