Dr. Z's Calculus Handouts (First Edition)

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.

Calculus I

• 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)
  • HandOut 5.2 (The Definite Integral)
  • HandOut 5.3 (The Fundamental Theorem of Calculus)
  • HandOut 5.4 (Indefinite Ingerals and the Net Change Theorem)
  • HandOut 5.5 (The Substitution Rule)

Calculus II

• Chapter 6 (Applications of Integration)
  • HandOut 6.1 (Areas between Curves)
  • HandOut 6.2 (Volumes)
  • HandOut 6.3 (Volumes by Cylindrical Shells)
  • HandOut 6.4 (Work)
  • HandOut 6.5 (Average Value of a Function)
• Chapter 7 (Techniques of Integration)
  • HandOut 7.1 (Integration by Parts)
  • HandOut 7.2 (Trigonometric Integrals)
  • HandOut 7.3 (Trigonometric Substitution)
  • HandOut 7.4 (Integration of Rational Functions by Partial Fractions)
  • HandOut 7.7 (Approximate Integration)
  • HandOut 7.8 (Improper Integrals)
• Chapter 8 (Further Applications of Integration)
  • HandOut 8.1 (Arc Length)
  • HandOut 8.2 (Area of a Surface of Revolution)
• Chapter 9 (Differential Equations)
  • HandOut 9.1 (Modeling with Differential Equations)
  • HandOut 9.3 (Separable Equations)
  • HandOut 9.4 (Exponential Growth and Decay)
• Chapter 10 (Parametric Equations and Polar Coordinates)
  • HandOut 10.2 (Calculus with Parametric Curves)
  • HandOut 10.4 (Areas and Lengths in 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
  Handout HandoutLast

Multivariable Calculus

• Chapter 12 (Vectors and the Geomery of Space)
  • HandOut 12.1 (Three-Dimensional Coordinate Systems)
  • HandOut 12.2 (Vectors)
  • HandOut 12.3 (The Dot Product)
  • HandOut 12.4 (The Cross Product)
  • HandOut 12.5 (Equations of Lines and Planes)
• Chapter 13 (Vectors Functions)
  • HandOut 13.1 (Vector Functions and Space Curves)
  • HandOut 13.2 (Derivatives and Integrals of Vector Functions)
  • HandOut 13.3 (Arclength and Curvature)
  • HandOut 13.4 (Motin in Space: Velocity and Acceleration)
• Chapter 14 (Partial Derivatives)
  • HandOut 14.2 (Limits and Continuity)
  • HandOut 14.3 (Partial Derivatives)
  • HandOut 14.4 (Tangent Planes and Linear Approximation)
  • HandOut 14.5 (The Chain Rule)
  • HandOut 14.6 (Directional Derivative and the Gradient Vector)
  • HandOut 14.7 (Maximum and Minimum Values)
  • HandOut 14.8 (Lagrange Multipliers)
• 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)

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