This is the second book of a three-volume work called "Calculus" by Jerrold Marsden and Alan Weinstein. This book is the outgrowth of the authors' experience teaching calculus at Berkeley. It covers techniques and applications of integration, infinite series, and differential equations.

Klappentext

The second of a three-volume work, this is the result of the authors'experience teaching calculus at Berkeley. The book covers techniques and applications of integration, infinite series, and differential equations, the whole time motivating the study of calculus using its applications. The authors include numerous solved problems, as well as extensive exercises at the end of each section. In addition, a separate student guide has been prepared.

Inhalt

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, L'Hôpital's Rule, and Numerical Methods.- 11.1 Limits of Functions.- 11.2 L'Hôpital's Rule.- 11.3 Improper Integrals.- 11.4 Limits of Sequences and Newton's 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 Taylor's Formula.- 12.6 Complex Numbers.- 12.7 Second-Order Linear Differential Equations.- 12.8 Series Solutions of Differential Equations.- Answers.