Ashlock D. Fast Start Advanced Calculus

New York: Morgan & Claypool Publishers, 2019. — 195 p.This book continues the material in two early Fast Start calculus volumes to include multivariate calculus, sequences and series, and a variety of additional applications.
These include partial derivatives and the optimization techniques that arise from them, including Lagrange multipliers. Volumes of rotation, arc length, and surface area are included in the additional applications of integration. Using multiple integrals, including computing volume and center of mass, is covered. The book concludes with an initial treatment of sequences, series, power series, and Taylor's series, including techniques of function approximation.Advanced Derivatives
Partial Derivatives
Implicit Partial Derivatives
Higher-order Partial Derivatives
The Gradient and Directional Derivatives
Tangent Planes
Multivariate and Constrained Optimization
Optimization with Partial Derivatives
The Extreme Value Theorem Redux
Lagrange Multipliers
Advanced Integration
Volumes of Rotation
Arc Length and Surface Area
Multiple Integrals
Mass and Center of Mass
Sequences, Series, and Function Approximation
Sequences and the Geometric Series
Series Convergence Tests
Tails of Sequences
Power Series
Using Calculus to Find Series
Taylor Series
Taylor Polynomials
Useful Formulas
Powers, Logs, and Exponentials
Trigonometric Identities
Speed of Function Growth
Derivative Rules
Sums and Factorization Rules
Geometric Series
Vector Arithmetic
Polar and Rectangular Conversion
Integral Rules
Series Convergence Tests
Taylor Series
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