Calculus I – Jerrold Marsden, A. Weinstein – 2nd Edition

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 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.
4.1 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.