Understanding Calculus II: Problems, Solutions, and Tips [repost]

Calculus II is the payoff for mastering Calculus I. This second course in the calculus sequence introduces you to exciting new techniques and applications of one of the most powerful mathematical tools ever invented. Equipped with the skills of Calculus II, you can solve a wide array of problems in the physical, biological, and social sciences, engineering, economics, and other areas. Success at Calculus II also gives you a solid foundation for the further study of mathematics, and it meets the math requirement for many undergraduate majors.

But beyond these advantages, you will find that the methods you learn in Calculus II are practical, interesting, and elegant, involving ideas that are beautifully simple. Because it can model real-life situations, calculus has an amazing range of uses, and these applications come into full flower in Calculus II.

Understanding Calculus II: Problems, Solutions, and Tips takes you on this exhilarating journey in 36 intensively illustrated half-hour lectures that cover all the major topics of the second full-year calculus course in high school at the College Board Advanced Placement BC level or a second-semester course in college. Drawing on decades of teaching experience, Professor Bruce H. Edwards of the University of Florida enriches his lectures with crystal-clear explanations, frequent study tips, pitfalls to avoid, and—best of all—hundreds of examples and practice problems that are specifically designed to explain and reinforce key concepts.

Few calculus teachers are as qualified, accessible, or entertaining as Professor Edwards, who has won multiple teaching awards and coauthored a best-selling series of calculus textbooks. Many calculus students give up trying to understand why a particular procedure works and resort to memorizing the steps to a solution. With Professor Edwards, the underlying concepts are always clear and constantly reinforced, which greatly eases the path to learning the material.


Lectures

01 Basic Functions of Calculus and Limits
02 Differentiation Warm-up
03 Integration Warm-up
04 Differential Equations—Growth and Decay
05 Applications of Differential Equations
06 Linear Differential Equations
07 Areas and Volumes
08 Arc Length, Surface Area, and Work
09 Moments, Centers of Mass, and Centroids
10 Integration by Parts
11 Trigonometric Integrals
12 Integration by Trigonometric Substitution
13 Integration by Partial Fractions
14 Indeterminate Forms and L'Hôpital's Rule
15 Improper Integrals
16 Sequences and Limits
17 Infinite Series—Geometric Series
18 Series, Divergence, and the Cantor Set
19 Integral Test—Harmonic Series, p-Series
20 The Comparison Tests
21 Alternating Series
22 The Ratio and Root Tests
23 Taylor Polynomials and Approximations
24 Power Series and Intervals of Convergence
25 Representation of Functions by Power Series
26 Taylor and Maclaurin Series
27 Parabolas, Ellipses, and Hyperbolas
28 Parametric Equations and the Cycloid
29 Polar Coordinates and the Cardioid
30 Area and Arc Length in Polar Coordinates
31 Vectors in the Plane
32 The Dot Product of Two Vectors
33 Vector-Valued Functions
34 Velocity and Acceleration
35 Acceleration's Tangent and Normal Vectors
36 Curvature and the Maximum Bend of a Curve