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# Understanding Calculus II: Problems, Solutions, and Tips

### Overview

Continue down the road to mastering calculus with this step-by-step guide to Calculus II, taught by an award-winning Professor of Mathematics.

### Syllabus

• By This Professor
• 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'Hopital'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

Bruce H. Edwards

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