Author | Marsden, Jerrold. author |
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Title | Calculus I [electronic resource] / by Jerrold Marsden, Alan Weinstein |
Imprint | New York, NY : Springer New York, 1985 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5024-1 |
Descript | XVI, 388 p. 50 illus. online resource |
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 MaximumโMinimum 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 MaximumโMinimum 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.ย ย ย