Math Shorts - Cool Calculus Problems;

Now that you've learned the basics of calculus, what to do with it? This book shows you how to use the amazing power of calculus to solve complex and intellectually stimulating mathematical problems. In it you'll find six challenging exercises along with detailed solutions documenting every step. To be able to follow the solutions, you should be familiar with differentiation rules (product, chain, quotient) as well as integration by substitution. Readers of the "Math Shorts" series should have completed "Math Shorts - Derivatives", "Math Shorts - Derivatives II" and "Math Shorts - Integrals" before attempting to solve the problems given in this book.

1. Galactic Gravitation:
Compute the gravitational field of a disk-shaped galaxy, derive and apply the conservation of energy

2. Push Ups:
Estimate the change in potential energy and power output during a push up

3. Crossing a River:
Find the fastest path across a river given an undetermined depth profile

4. Summation:
Use Differentiation and Integration to prove basic summation formulas

5. Oscillation:
Show that springs oscillate harmonically, estimate motion based on more complex force fields

6. Train Acoustics:
Find the sound intensity of a finite and infinite line source, estimate the influence of sound absorption