Author | Soon, Frederick H. author |
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Title | Student's Guide to Calculus by J. Marsden and A. Weinstein [electronic resource] : Volume I / by Frederick H. Soon |
Imprint | New York, NY : Springer New York, 1985 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5146-0 |
Descript | XIV, 312 p. online resource |
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 โ 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 โ 6