This textbook will help you learn to use calculus for solving mathematical, physical and engineering problems. The author taught calculus at Berkeley, and the 2nd edition incorporates many improvements based on the previous edition. Prerequisite material is only high school algebra and some plane geometry, trigonometry and analytic geometry are covered in the book completely.
Proofs are given only for the most important theorems, the theory of limits is de-emphasized until students have mastered differentiation and integration. The authors teach calculus closely related to the physical world, throughout the text they use numerous examples related to distance and velocity.
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.
1.3 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.
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.
4.2 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.
6.3 Differentiation of the Exponential and Logarithmic Functions.
6.4 Graphing and Word Problems.
Jerrold Marsden / Alan Weinstein
0387909745 | 978-0387909745