Student’s Guide to Calculus by J. Marsden and A. Weinstein: Volume I

ISBN-13: 9780387962078 / Angielski / Miękka / 1985 / 312 str.

Frederick H. Soon

Opis

This Student Guide is exceptional, maybe even unique, among such guides in that its author, Fred Soon, was actually a student user of the textbook during one of the years we were writing and debugging the book. (He was one of the best students that year, by the way. ) Because of his background, Fred has taken, in the Guide, the point of view of an experienced student tutor helping you to learn calculus. While we do not always think Fred's jokes are as funny as he does, we appreciate his enthusiasm and his desire to enter into communication with his readers; since we nearly always agree with the mathe- matical judgements he has made in explaining the material, we believe that this Guide can serve you as a valuable supplement to our text. To get maximum benefit from this Guide, you should begin by spending a few moments to acquaint yourself with its structure. Once you get started in the course, take advantage of the many opportunities which the text and Student Guide together provide for learning calculus in the only way that any mathe- matical subject can truly be mastered - through attempting to solve problems on your own. As you read the text, try doing each example and exercise your- self before reading the solution; do the same vith the quiz problems provided by Fred.

Spis treści

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.- R.R Review Exercises for Chapter R.- 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.- 1.R Review Exercises for Chapter 1.- 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.- 2.R Review Exercises for Chapter 2.- 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.- 3.R Review Exercises for Chapter 3.- Comprehensive Test for Chapters 1 – 3.- 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.- 4.R Review Exercises for Chapter 4.- 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.- 5.S Supplement to Chapter 5: Length of Days.- 5.R Review Exercises for Chapter 5.- 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.- 6.R Review Exercises for Chapter 6.- Comprehensive Test for Chapters 1 – 6.