Basic Calculus

Part II: Calculus and the Sciences

Introduction
The links Solutions, Additional Exercises, Corrections and Typos, and For the Instructor are pdf files that can be accessed with Acrobat Reader

8. Analysis of Functions
1. Putting a Limit to the Test 2. Continuous Functions 3. Differentiability 4. Derivatives as Rates of Change 5. About Derivatives a. Computing Derivatives b. Some Theoretical Concerns 6. Derivatives of Trigonometric Functions 7. Increase and Decrease of Functions 8. Maximum and Minimum Values 9. Postscript Exercises and Solutions Corrections and Typos For the Instructor	Jacob Bernoulli Johann Bernoulli De L'Hospital Agnesi Euler Gauss Cauchy Weierstrass Riemann Calculus Modules

9. Connections with Statics, Dynamics, and Optics
1. The Pulley Problem of De L'Hospital a. The Solution Using Calculus b. The Solution by Balancing Forces 2. The Suspension Bridge 3. An Experiment of Galileo a. Sliding Icecubes and Spinning Wheels b. Moments of Force and Inertia c. The Mathematics for Galileo's Experiment 4. From Fermat's Principle to the Basic Telescope a. Fermat's Principle amd the Path of a Light Ray b. General Study of Lenses c. Quantitative Analysis of Lenses 5. Postscript Exercises and Solutions Corrections and Typos For the Instructor	The Golden Gate Bridge Galileo and his work Galileo's Working Papers Fermat

10. Basic Functions and their Graphs
1. Exponential Functions 2. Inverse Functions 3. Logarithms 4. Returning to a Problem of Leibniz 5. Inverse Trigonometric Functions 6. Concavity 7. Asymptotes 8. Graphing 9. Postscript Exercises and Solutions Corrections and Typos For the Instructor	The Inventors of Logarithms: Napier Bürgi Briggs Famous Curves

11. The Exponential Function and the Measurement of Age and Growth
1. Nuclear Activity a. The Atom and its Nucleus b. The Discoveries of Rutherford 2. The Earth's Geological History a. Reading Radioactive Clocks b. The Potassium Argon Clock 3. Life Evolves: A Timeline 4. Dating the More Recent Past 5. The World's Population a. Statistics and Trends b. The Logistics Model c. Applying the Logistics Model 6. The Growth of Microorganisms a. The Exponential Phase b. Experimenting with E-coli c. Fermentation Processes 7. Postscript Exercises and Solutions Corrections and Typos For the Instructor	The World of the Atom The Earth The Caves at Vallon-Pont-d'Arc Human Fossile Record U.S. Census Bureau Bacteria Bacteria in the Human Digestive System Mathematical Models in Biology

12. Calculus of Economics
1. Basics of Banking a. Interest b. Investment Plans c. Annuities and Bonds 2. Inflation and the Consumer Price Index 3. Supply and Demand in a Market a. Supply and Demand Functions b. OPEC and the Price of Oil 4. A Firm's Cost of Production a. Cost Functions b. The Method of Least Squares c. Cost Analysis for Electric Companies 5. Price, Revenue, and Profit a. Revenue Functions b. Maximizing Profit c. Profit-maximizing for a Refinery 6. Consumer Surplus 7. Postscript Exercises and Solutions Corrections and Typos For the Instructor	Taurus Phase-out Interest, Anuity, and Mortgage Calculators Bureau of Labor Statistics OPEC U.S. Electric Utility Industry

13. Integral Calculus: Meaning and Methods
1. Riemann Sums and the Definite Integral a. A Return to the Approach of Leibniz b. A Return to the Approach of Newton c. The Fundamental Equality 2. Surface Area 3. Methods of Integration a. The Substitution Method b. Trigonometric Substitution c. Integration by Parts 4. Polar Coordinates a. Graphing Polar Equations b. Areas in Polar Coordinates 5. Differential Equations 6. Postscript Exercises and Solutions Corrections and Typos For the Instructor	Riemann Famous Curves Differential Equations

14. Integral Calculus and the Action of Forces
1. Work and Kinetic Energy a. Variable Force and Work b. Kinetic and Potential Energy 2. Interior Ballistics a. Analysis of Springs b. The Force in a Gun Barrel c. The Springfield Rifle 3. Momentum a. Force as a Function of Time b. Conservation of Momentum 4. The Calculus of Rocket Propulsion a. Thrust b. The Rocket Equation 5. Surprises about Gravity? a. Gravity and Shape b. The Case of the Sphere 6. Returning to the Laws of Kepler a. Force and Polar Coordinates b. The Inverse Square Law 7. Hubble's Law and Einstein's Universe 8. Postscript Exercises and Solutions Corrections and Typos For the Instructor	The Springfield Rifle Alexander Friedmann The Story of Apollo 11 Albert Einstein Images from the Hubble Space Telescope Astronomy Resources on the Web NASA's Homepage Dark Matter and Energy