Ebook: Understanding Calculus II: Problems, Solutions, and Tips (The Great Courses)

36 Lectures 1Basic Functions of Calculus and Limits 2Differentiation Warm-up 3Integration Warm-up 4Differential Equations-Growth and Decay 5Applications of Differential Equations 6Linear Differential Equations 7Areas and Volumes 8Arc Length, Surface Area, and Work 9Moments, Centers of Mass, and Centroids 10Integration by Parts 11Trigonometric Integrals 12Integration by Trigonometric Substitution 13Integration by Partial Fractions 14Indeterminate Forms and L'Hôpital's Rule 15Improper Integrals 16Sequences and Limits 17Infinite Series-Geometric Series 18Series, Divergence, and the Cantor Set 19Integral Test-Harmonic Series, p-Series 20The Comparison Tests 21Alternating Series 22The Ratio and Root Tests 23Taylor Polynomials and Approximations 24Power Series and Intervals of Convergence 25Representation of Functions by Power Series 26Taylor and Maclaurin Series 27Parabolas, Ellipses, and Hyperbolas 28Parametric Equations and the Cycloid 29Polar Coordinates and the Cardioid 30Area and Arc Length in Polar Coordinates 31Vectors in the Plane 32The Dot Product of Two Vectors 33Vector-Valued Functions 34Velocity and Acceleration 35Acceleration's Tangent and Normal Vectors 36Curvature and the Maximum Bend of a Curve