Understanding Calculus: Problems, Solutions, and Tips
Course Overview
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, Professor Bruce Edwards. This course includes 36 half-hour lectures covering all the major topics of a full-year calculus course. With crystal-clear explanations, frequent study tips, and hundreds of examples and practice problems, this course serves as a steady guide to conquering calculus.
Building on a foundation of high school mathematics, you’ll learn essential techniques that enable you to tackle a wide array of problems in physical sciences, engineering, economics, and more while fostering a deeper appreciation for calculus’s extraordinary power.
Video Lectures
- A Preview of Calculus – 33 min
Introduction to the goals of calculus and the tangent line problem illustrating limits. - Review—Graphs, Models, and Functions – 30 min
Explore properties of graphs and the concept of functions. - Review—Functions and Trigonometry – 30 min
Delve into various types of functions and trigonometric concepts. - Finding Limits – 31 min
Examine limits through numerical, graphical, and analytical methods. - An Introduction to Continuity – 31 min
Understand the conditions for a function to be continuous. - Infinite Limits and Limits at Infinity – 31 min
Analyze functions with infinite limits and their asymptotic behavior. - The Derivative and the Tangent Line Problem – 31 min
Investigate derivatives and their foundational role in differential calculus. - Basic Differentiation Rules – 30 min
Learn techniques for finding derivatives using the power and product rules. - Product and Quotient Rules – 31 min
Explore formulas for differentiation, including higher-order derivatives. - The Chain Rule – 31 min
Discover the chain rule for finding derivatives of composite functions. - Implicit Differentiation and Related Rates – 31 min
Tackle implicit differentiation and problems involving related rates. - Extrema on an Interval – 30 min
Use derivatives to find absolute maximum and minimum values of functions. - Increasing and Decreasing Functions – 31 min
Analyze functions’ behavior using the first derivative test. - Concavity and Points of Inflection – 31 min
Understand concavity through the second derivative and identify points of inflection. - Curve Sketching and Linear Approximations – 32 min
Learn to sketch curves and find tangent lines for approximation. - Applications—Optimization Problems, Part 1 – 31 min
Solve optimization problems by finding relative extrema. - Applications—Optimization Problems, Part 2 – 31 min
Continue optimization challenges with word problems and calculus techniques. - Antiderivatives and Basic Integration Rules – 31 min
Explore the concept of antiderivatives and integration. - The Area Problem and the Definite Integral – 31 min
Learn how to solve area problems using definite integrals. - The Fundamental Theorem of Calculus, Part 1 – 30 min
Understand the connection between derivatives and integrals. - The Fundamental Theorem of Calculus, Part 2 – 31 min
Apply the second fundamental theorem of calculus for variable limits. - Integration by Substitution – 31 min
Master the technique of integration by substitution for simpler integrations. - Numerical Integration – 31 min
Learn approximation techniques such as the trapezoid rule for definite integrals. - Natural Logarithmic Function—Differentiation – 31 min
Explore the natural logarithm and its significance in calculus. - Natural Logarithmic Function—Integration – 31 min
Delve into the integration techniques involving natural logarithms. - Exponential Function – 31 min
Examine the properties and applications of the exponential function. - Bases other than e – 31 min
Study logarithmic functions with bases other than “e” and their applications. - Inverse Trigonometric Functions – 31 min
Understand the properties and applications of inverse trigonometric functions. - Area of a Region between 2 Curves – 30 min
Learn to compute areas between two curves using integration. - Volume—The Disk Method – 30 min
Discover how to calculate the volume of solids of revolution. - Volume—The Shell Method – 31 min
Use the shell method to find volumes and explore toroidal shapes. - Applications—Arc Length and Surface Area – 32 min
Investigate how to calculate arc lengths and surface areas using integrals. - Basic Integration Rules – 30 min
Review integration formulas and their applications. - Other Techniques of Integration – 31 min
Explore integration techniques such as integration by parts. - Differential Equations and Slope Fields – 30 min
Use slope fields to visualize solutions to differential equations. - Applications of Differential Equations – 31 min
Apply differential equations to problems in real-world contexts.

