BeschreibungThis 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. Throughout the book, the authors motivate the study of calculus using its applications. Many solved problems are included, and extensive exercises are given at the end of each section. In addition, a separate student guide has been prepared.
Inhaltsverzeichnis7 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.
8.2 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.
Untertitel: 'Undergraduate Texts in Mathematics'. 2nd ed. 1985. Corr. 4th printing 1998. Book. Sprache: Englisch.
Erscheinungsdatum: Januar 1998
Seitenanzahl: 372 Seiten