He is currently a professor of mathematics at Palomar College near San Diego, California, where he has taught for more than 20 years. in Mathematics from California State University, Fullerton and his M.A. Answers to Odd-Numbered Exercises.ĭaniel Clegg received his B.A. Numbers, Inequalities, and Absolute Values. The Fundamental Theorem for Line Integrals. Change of Variables in Multiple Integrals. Triple Integrals in Spherical Coordinates. Discovery Project: The Intersection of Three Cylinders. Triple Integrals in Cylindrical Coordinates. Discovery Project: Volumes of Hyperspheres. Problems Plus.ĭouble Integrals over Rectangles.

Applied Project: Hydro-Turbine Optimization. Discovery Project: Quadratic Approximations and Critical Points. Directional Derivatives and the Gradient Vector. Tangent Planes and Linear Approximations. Discovery Project: Deriving the Cobb-Douglas Production Function. Problems Plus.įunctions of Several Variables. Motion in Space: Velocity and Acceleration. Derivatives and Integrals of Vector Functions. Discovery Project: Putting 3D in Perspective. Discovery Project: The Geometry of a Tetrahedron. Discovery Project: The Shape of a Hanging Chain. Applied Project: Radiation from the Stars. Writing Project: How Newton Discovered the Binomial Series. Representations of Functions as Power Series. Alternating Series and Absolute Convergence. Discovery Project: Families of Polar Curves. Discovery Project: Running Circles Around Circles. PARAMETRIC EQUATIONS AND POLAR COORDINATES.Ĭurves Defined by Parametric Equations. Applied Project: Which Is Faster, Going Up or Coming Down? Predator-Prey Systems. Applied Project: How Fast Does a Tank Drain? Models for Population Growth. Discovery Project: Complementary Coffee Cups. Discovery Project: Patterns in Integrals. Integration of Rational Functions by Partial Fractions. Writing Project: The Origins of l’Hospital’s Rule. Indeterminate Forms and l’Hospital’s Rule. Applied Project: Where to Sit at the Movies. Applied Project: Controlling Red Blood Cell Loss During Surgery. General Logarithmic and Exponential Functions. Exponential Functions and Their Derivatives. Instructors may cover either Sections 6.2–6.4 or Sections 6.2*–6.4*. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS. Writing Project: Newton, Leibniz, and the Invention of Calculus. Indefinite Integrals and the Net Change Theorem.

Applied Project: Planes and Birds: Minimizing Energy. Limits at Infinity Horizontal Asymptotes. What Derivatives Tell Us About the Shape of a Graph. Applied Project: The Calculus of Rainbows. Discovery Project: Polynomial Approximations. Rates of Change in the Natural and Social Sciences. Discovery Project: Families of Implicit Curves. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Applied Project: Building a Better Roller Coaster. Writing Project: Early Methods for Finding Tangents.

Principles of Problem Solving.ĭerivatives and Rates of Change. Mathematical Models: A Catalog of Essential Functions.

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