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

1. A Preview of Calculus – 33 min
   Introduction to the goals of calculus and the tangent line problem illustrating limits.
2. Review—Graphs, Models, and Functions – 30 min
   Explore properties of graphs and the concept of functions.
3. Review—Functions and Trigonometry – 30 min
   Delve into various types of functions and trigonometric concepts.
4. Finding Limits – 31 min
   Examine limits through numerical, graphical, and analytical methods.
5. An Introduction to Continuity – 31 min
   Understand the conditions for a function to be continuous.
6. Infinite Limits and Limits at Infinity – 31 min
   Analyze functions with infinite limits and their asymptotic behavior.
7. The Derivative and the Tangent Line Problem – 31 min
   Investigate derivatives and their foundational role in differential calculus.
8. Basic Differentiation Rules – 30 min
   Learn techniques for finding derivatives using the power and product rules.
9. Product and Quotient Rules – 31 min
   Explore formulas for differentiation, including higher-order derivatives.
10. The Chain Rule – 31 min
    Discover the chain rule for finding derivatives of composite functions.
11. Implicit Differentiation and Related Rates – 31 min
    Tackle implicit differentiation and problems involving related rates.
12. Extrema on an Interval – 30 min
    Use derivatives to find absolute maximum and minimum values of functions.
13. Increasing and Decreasing Functions – 31 min
    Analyze functions’ behavior using the first derivative test.
14. Concavity and Points of Inflection – 31 min
    Understand concavity through the second derivative and identify points of inflection.
15. Curve Sketching and Linear Approximations – 32 min
    Learn to sketch curves and find tangent lines for approximation.
16. Applications—Optimization Problems, Part 1 – 31 min
    Solve optimization problems by finding relative extrema.
17. Applications—Optimization Problems, Part 2 – 31 min
    Continue optimization challenges with word problems and calculus techniques.
18. Antiderivatives and Basic Integration Rules – 31 min
    Explore the concept of antiderivatives and integration.
19. The Area Problem and the Definite Integral – 31 min
    Learn how to solve area problems using definite integrals.
20. The Fundamental Theorem of Calculus, Part 1 – 30 min
    Understand the connection between derivatives and integrals.
21. The Fundamental Theorem of Calculus, Part 2 – 31 min
    Apply the second fundamental theorem of calculus for variable limits.
22. Integration by Substitution – 31 min
    Master the technique of integration by substitution for simpler integrations.
23. Numerical Integration – 31 min
    Learn approximation techniques such as the trapezoid rule for definite integrals.
24. Natural Logarithmic Function—Differentiation – 31 min
    Explore the natural logarithm and its significance in calculus.
25. Natural Logarithmic Function—Integration – 31 min
    Delve into the integration techniques involving natural logarithms.
26. Exponential Function – 31 min
    Examine the properties and applications of the exponential function.
27. Bases other than e – 31 min
    Study logarithmic functions with bases other than “e” and their applications.
28. Inverse Trigonometric Functions – 31 min
    Understand the properties and applications of inverse trigonometric functions.
29. Area of a Region between 2 Curves – 30 min
    Learn to compute areas between two curves using integration.
30. Volume—The Disk Method – 30 min
    Discover how to calculate the volume of solids of revolution.
31. Volume—The Shell Method – 31 min
    Use the shell method to find volumes and explore toroidal shapes.
32. Applications—Arc Length and Surface Area – 32 min
    Investigate how to calculate arc lengths and surface areas using integrals.
33. Basic Integration Rules – 30 min
    Review integration formulas and their applications.
34. Other Techniques of Integration – 31 min
    Explore integration techniques such as integration by parts.
35. Differential Equations and Slope Fields – 30 min
    Use slope fields to visualize solutions to differential equations.
36. Applications of Differential Equations – 31 min
    Apply differential equations to problems in real-world contexts.