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Catalogue Information
Field name	Details
Dewey Class	515.8
Title	Calculus I ([EBook]) / by Jerrold Marsden, Alan Weinstein.
Author	Marsden, Jerrold E.
Added Personal Name	Weinstein, Alan
Other name(s)	SpringerLink (Online service)
Edition statement	Second Edition.
Publication	New York, NY : Springer , 1985.
Physical Details	XVI, 388 pages, 50 illus. : online resource.
Series	Undergraduate texts in mathematics 0172-6056
ISBN	9781461250241
Summary Note	The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems. This book is an outgrowth of our teaching of calculus at Berkeley, and the present edition incorporates many improvements based on our use of the first edition. We list below some of the key features of the book. Examples and Exercises The exercise sets have been carefully constructed to be of maximum use to the students. With few exceptions we adhere to the following policies. • The section exercises are graded into three consecutive groups: (a) The first exercises are routine, modelled almost exactly on the exam ples; these are intended to give students confidence. (b) Next come exercises that are still based directly on the examples and text but which may have variations of wording or which combine different ideas; these are intended to train students to think for themselves. (c) The last exercises in each set are difficult. These are marked with a star (*) and some will challenge even the best students. Difficult does not necessarily mean theoretical; often a starred problem is an interesting application that requires insight into what calculus is really about. • The exercises come in groups of two and often four similar ones.:
Contents note	Orientation Quizzes -- R Review of Fundamentals -- R.1 Basic Algebra: Real Numbers and Inequalities -- R.2 Intervals and Absolute Values -- R.3 Laws of Exponents -- R.4 Straight Lines -- R.5 Circles and Parabolas -- R.6 Functions and Graphs -- 1 Derivatives and Limits -- 1.1 Introduction to the Derivative -- 1.2 Limits -- 1.3 The Derivative as a Limit and the Leibniz Notation -- 1.4 Differentiating Polynomials -- 1.5 Products and Quotients -- 1.6 The Linear Approximation and Tangent Lines -- 2 Rates of Change and the Chain Rule -- 2.1 Rates of Change and the Second Derivative -- 2.2 The Chain Rule -- 2.3 Fractional Powers and Implicit Differentiation -- 2.4 Related Rates and Parametric Curves -- 2.5 Antiderivatives -- 3 Graphing and Maximum—Minimum Problems -- 3.1 Continuity and the Intermediate Value Theorem -- 3.2 Increasing and Decreasing Functions -- 3.3 The Second Derivative and Concavity -- 3.4 Drawing Graphs -- 3.5 Maximum—Minimum Problems -- 3.6 The Mean Value Theorem -- 4 The Integral -- 4.1 Summation -- 4.2 Sums and Areas -- 4.3 The Definition of the Integral -- 4.4 The Fundamental Theorem of Calculus -- 4.5 Definite and Indefinite Integrals -- 4.6 Applications of the Integral -- 5 Trigonometric Functions -- 5.1 Polar Coordinates and Trigonometry -- 5.2 Differentiation of the Trigonometric Functions -- 5.3 Inverse Functions -- 5.4 The Inverse Trigonometric Functions -- 5.5 Graphing and Word Problems -- 5.6 Graphing in Polar Coordinates -- 6 Exponentials and Logarithms -- 6.1 Exponential Functions -- 6.2 Logarithms -- 6.3 Differentiation of the Exponential and Logarithmic Functions -- 6.4 Graphing and Word Problems -- Answers A.1 -- Index I.1. .
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4612-5024-1
Links to Related Works	Subject References: Functions of real variables . Mathematics . Real Functions . Authors: author . Marsden, Jerrold E. . Marsden, Jerrold E. . Weinstein, Alan . Corporate Authors: SpringerLink (Online service) . Series: Undergraduate texts in mathematics . Classification: 515.8 .

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Calculus I

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