Calculus I

Buch | Softcover
388 Seiten
1985 | 2nd ed. 1985
Springer-Verlag New York Inc.
978-0-387-90974-5 (ISBN)

Lese- und Medienproben

Calculus I - Jerrold Marsden, Alan Weinstein
42,75 inkl. MwSt
The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems. Examples and Exercises The exercise sets have been carefully constructed to be of maximum use to the students.
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.

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.   

Reihe/Serie Undergraduate Texts in Mathematics
Zusatzinfo XVI, 388 p. 50 illus.
Verlagsort New York, NY
Sprache englisch
Maße 178 x 254 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
ISBN-10 0-387-90974-5 / 0387909745
ISBN-13 978-0-387-90974-5 / 9780387909745
Zustand Neuware
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