By DORON ZEILBERGER

These are the handouts I gave out when I taught Calculus I,
Calculus II, and Multivariable Calculus.
The section numbers refer
to the excellent textbook, which was `Calculus, fifth edition', by James
Stewart, published by Thompson, Brooks/Cole.

Added Jan. 1, 2009: The textbook at Rutgers was changed to Jon Rogawski's.
For Calclulus I, there is now a
second edition,
that follows his sections titles.
For Calculus II and Multivariable Calculus, a second edition would not be available
until I would happen to teach them again.

- Chapter 2 (Limits and Derivatives)
- HandOut 2.1 (The Tangent and Velocity Problems)
- HandOut 2.2 (The Limit of a Function)
- HandOut 2.3 (Calculating Limits Using the Limit Laws)
- HandOut 2.4 (The Precise Definition of a Limit)
- HandOut 2.5 (Continuity)
- HandOut 2.6 (Limits at Infinity: Horizontal Asymptotes)
- HandOut 2.7 (Tangents, Velocities, and Other Rates of Change)
- HandOut 2.8 (Derivatives)

- Chapter 3 (Differentiation Rules)
- HandOut 3.1 (Derivatives of Polynomials and Exponential Functions)
- HandOut 3.2 (The Product and Quotient Rules)
- HandOut 3.3 (Rates of Change in the Natural and Social Sciences)
- HandOut 3.4 (Derivatives of Trigonometric Functions)
- HandOut 3.5 (The Chain Rule)
- HandOut 3.6 (Implicit Differentiation)
- HandOut 3.7 (Higher Derivatives)
- HandOut 3.8 (Derivatives of Logarithmic Functions)
- HandOut 3.10 (Related Rates)
- HandOut 3.11 (Linear Approximations and Differentials)

- Chapter 4 (Applications of Differentiation)
- HandOut 4.1 (Maximum and Minimum Values)
- HandOut 4.2 (The Mean Value Theorem)
- HandOut 4.3 (How Derivatives Affect the Shape of a Graph)
- HandOut 4.4 (Indeterminates Forms and L'Hospital's Rule)
- HandOut 4.5 (Summary of Curve Sketching)
- HandOut 4.7 (Optimization Problems)
- HandOut 4.9 (Newton's Method)
- HandOut 4.10 (Antiderivatives)

- Chapter 5 (Intgerals)

- Chapter 6 (Applications of Integration)
- Chapter 7 (Techniques of Integration)
- Chapter 8 (Further Applications of Integration)
- Chapter 9 (Differential Equations)
- Chapter 10 (Parametric Equations and Polar Coordinates)
- Chapter 11 (Infinite Sequences and Series)
- HandOut 11.1 (Sequences)
- HandOut 11.2 (Series)
- HandOut 11.3 (The Integral Test abd Estimates of Sums)
- HandOut 11.5 (Alternating Series)
- HandOut 11.6 (Absolute Convergence and the Ratio and Root Tests)
- HandOut 11.8 (Power Series)
- HandOut 11.9 (Representations of Functions as Power Series)
- HandOut 11.10 (Taylor and Maclaurin Series)
- HandOut 11.11 (The Binomial Series)
- HandOut 11.12 (Applications of Taylor Polynomials)

- The Last Calculus II Handout

- Chapter 12 (Vectors and the Geomery of Space)
- Chapter 13 (Vectors Functions)
- Chapter 14 (Partial Derivatives)
- Chapter 15 (Multiple Integrals)
- HandOut 15.2 (Iterated Integrals)
- HandOut 15.3 (Double Integrals over General Regions)
- HandOut 15.4 (Double Integrals in Polar Coordinates)
- HandOut 15.6 (Surface Area)
- HandOut 15.7 (Triple Integrals)
- HandOut 15.8 (Triple Integrals in Cylindrical and Spherical Coordinates)
- HandOut 15.9 (Change of Variables in Multiple Integrals)

- Chapter 16 (Vector Calculus)
- HandOut 16.2 (Line Integrals Integrals)
- HandOut 16.3 (The Fundamental Theorem for Line Integrals)
- HandOut 16.4 (Green's Theorem)
- HandOut 16.5 (Curl and Divergence)
- HandOut 16.6 (Parametric Surfaces and their Areas)
- HandOut 16.7 (Surface Integrals)
- HandOut 16.8 (Stokes' Theorem)
- HandOut 16.9 (The Divergence Theorem)

- The Last Handout (The Meaning of It All)