Understanding Calculus: Problems, Solutions and Tips

Succeed at calculus-the most feared of all math subjects-with this thorough and easy-to-follow guide taught by an award-winning math educator.

• By This Professor
• 01: A Preview of Calculus
• 02: Review—Graphs, Models, and Functions
• 03: Review—Functions and Trigonometry
• 04: Finding Limits
• 05: An Introduction to Continuity
• 06: Infinite Limits and Limits at Infinity
• 07: The Derivative and the Tangent Line Problem
• 08: Basic Differentiation Rules
• 09: Product and Quotient Rules
• 10: The Chain Rule
• 11: Implicit Differentiation and Related Rates
• 12: Extrema on an Interval
• 13: Increasing and Decreasing Functions
• 14: Concavity and Points of Inflection
• 15: Curve Sketching and Linear Approximations
• 16: Applications—Optimization Problems, Part 1
• 17: Applications—Optimization Problems, Part 2
• 18: Antiderivatives and Basic Integration Rules
• 19: The Area Problem and the Definite Integral
• 20: The Fundamental Theorem of Calculus, Part 1
• 21: The Fundamental Theorem of Calculus, Part 2
• 22: Integration by Substitution
• 23: Numerical Integration
• 24: Natural Logarithmic Function—Differentiation
• 25: Natural Logarithmic Function—Integration
• 26: Exponential Function
• 27: Bases other than e
• 28: Inverse Trigonometric Functions
• 29: Area of a Region between 2 Curves
• 30: Volume—The Disk Method
• 31: Volume—The Shell Method
• 32: Applications—Arc Length and Surface Area
• 33: Basic Integration Rules
• 34: Other Techniques of Integration
• 35: Differential Equations and Slope Fields
• 36: Applications of Differential Equations