## Student's guide to Calculus by J. Marsden and A. Weinstein  vol. 1 ～ vol. 3

Frederick H. Soon

This book is intended as a guide for students using the text, Calculus III by Jerrold Marsden and Alan Weinstein. It may be unique among such guides in that it was written by a student user of the text. For each section of the text, the guide contains a list of prerequisites, a review quiz (with answers), a list of study goals, some hints for study, solutions to the odd-numbered problems, and a quiz on the section (with answers). For each review section the guide includes solutions to the odd exercises and a chapter test with solutions.

「Nielsen BookData」より

This book is intended as a guide for students using the text, Calculus III by Jerrold Marsden and Alan Weinstein. It may be unique among such guides in that it was written by a student user of the text. For each section of the text, the guide contains a list of prerequisites, a review quiz (with answers), a list of study goals, some hints for study, solutions to the odd-numbered problems, and a quiz on the section (with answers). For each review section the guide includes solutions to the odd exercises and a chapter test with solutions.

「Nielsen BookData」より

[目次]

• 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.- 7.R Review Exercises for Chapter 7.- 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.- 8.R Review Exercises for Chapter 8.- 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.- 9.R Review Exercises for Chpater 9.- Comprehensive Test for Chapters 7 - 9.- 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.- 10.R Review Exercises for Chapter 10.- 11 -- Limits, L'Hopital's Rule, and Numerical Methods.- 11.1 Limits of Functions.- 11.2 L'Hopital's Rule.- 11.3 Improper Integrals.- 11.4 Limits of Sequences and Newton's Method.- 11.5 Numerical Integration.- 11.R Review Exercises for Chapter 11.- 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.- 12.R Review Exercises for Chapter 12.- Comprehensive Test for Chapters 7 - 12.

「Nielsen BookData」より

[目次]

• 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.

「Nielsen BookData」より

書名 Student's guide to Calculus by J. Marsden and A. Weinstein Marsden, Jerrold E. Soon, Frederick H. Weinstein, Alan Marsden J. Weinstein A. Soon Frederick H. (Los Angeles CA USA) vol. 1 vol. 2 vol. 3 Springer-Verlag c1985-c1986 Softcover reprint of the original 1st ed. 1985 3 v. (888 p.) 23 cm 0387962344 0387963480 0387962077 BA01344155 ※クリックでCiNii Booksを表示 英語 アメリカ合衆国
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