Understanding Calculus II: Problems, Solutions, and Tips

Course Overview

Continue your journey in mastering calculus with this step-by-step guide to Calculus II, taught by award-winning Professor Bruce Edwards. This course consists of 36 lectures that delve into exciting techniques and applications of calculus, equipping you with essential skills for solving problems in various fields, including physics, biology, engineering, and economics.

Designed for students who have completed Calculus I, this course presents key concepts in an accessible manner, ensuring you build a solid foundation for further study. Prepare to engage with differential equations, areas and volumes, infinite series, and more, all while enjoying Professor Edwards’s approachable and invigorating teaching style.

Video Lectures

1. Basic Functions of Calculus and Limits – 32 min
   Review essential functions and graphs necessary for solving calculus problems.
2. Differentiation Warm-up – 30 min
   Refresh your knowledge of derivatives from precalculus and their applications.
3. Integration Warm-up – 31 min
   Cover fundamental facts about integration, including definite integrals and the fundamental theorem of calculus.
4. Differential Equations-Growth and Decay – 31 min
   Learn techniques for solving differential equations and their applications in growth and decay.
5. Applications of Differential Equations – 31 min
   Explore orthogonal trajectories and the logistic differential equation.
6. Linear Differential Equations – 31 min
   Investigate linear differential equations and the “magic integrating factor.”
7. Areas and Volumes – 31 min
   Use integration to calculate areas and volumes, including the disk method for solids of revolution.
8. Arc Length, Surface Area, and Work – 30 min
   Review computations for arc length and surface area, and understand the concept of work.
9. Moments, Centers of Mass, and Centroids – 31 min
   Study moments and centers of mass, including the theorem of Pappus.
10. Integration by Parts – 31 min
    Learn to develop the method of integration by parts for finding antiderivatives.
11. Trigonometric Integrals – 31 min
    Explore integrals of trigonometric functions and their evaluation techniques.
12. Integration by Trigonometric Substitution – 32 min
    Apply trigonometric substitution to simplify integrals.
13. Integration by Partial Fractions – 32 min
    Split complex rational functions to facilitate integration.
14. Indeterminate Forms and L’Hopital’s Rule – 31 min
    Discover L’Hôpital’s rule for evaluating limits of indeterminate forms.
15. Improper Integrals – 31 min
    Study integrals with infinite limits and how to approach them.
16. Sequences and Limits – 31 min
    Begin exploring infinite sequences and their characteristics.
17. Infinite Series-Geometric Series – 32 min
    Investigate telescoping series and the properties of geometric series.
18. Series, Divergence, and the Cantor Set – 32 min
    Learn about divergence in series and the intriguing properties of the Cantor set.
19. Integral Test-Harmonic Series, p-Series – 31 min
    Analyze the harmonic series and define conditions for p-series convergence.
20. The Comparison Tests – 31 min
    Develop further convergence tests for series comparisons.
21. Alternating Series – 31 min
    Explore the properties of alternating series and their convergence criteria.
22. The Ratio and Root Tests – 32 min
    Complete your study of convergence tests with the ratio and root tests.
23. Taylor Polynomials and Approximations – 31 min
    Learn to express functions as Taylor polynomials and understand their significance.
24. Power Series and Intervals of Convergence – 30 min
    Discover the concept of a power series and how to find its interval of convergence.
25. Representation of Functions by Power Series – 32 min
    Explore the steps for expressing functions as power series.
26. Taylor and Maclaurin Series – 31 min
    Deepen your understanding of Taylor and Maclaurin series.
27. Parabolas, Ellipses, and Hyperbolas – 30 min
    Review the properties of conic sections and their equations.
28. Parametric Equations and the Cycloid – 31 min
    Learn how to model motion using parametric equations.
29. Polar Coordinates and the Cardioid – 31 min
    Become familiar with polar coordinates and their applications in graphs.
30. Area and Arc Length in Polar Coordinates – 32 min
    Study applications of integration in the polar coordinate system.
31. Vectors in the Plane – 30 min
    Introduction to vectors and their properties in two dimensions.
32. The Dot Product of Two Vectors – 31 min
    Delve into the dot product, its applications, and finding projections.
33. Vector-Valued Functions – 31 min
    Explore vector-valued functions and their derivatives.
34. Velocity and Acceleration – 31 min
    Investigate the motion of a particle using velocity and acceleration vectors.
35. Acceleration’s Tangent and Normal Vectors – 31 min
    Learn about tangent and normal vectors in relation to acceleration.
36. Curvature and the Maximum Bend of a Curve – 31 min
    Discover how curvature relates to the shape of curves and motion.