Book Description Idiot's Guides: Calculus II , like its counterpart Idiot's Guides: Calculus I, is a curriculum-based companion book that continues the tradition of taking the sting out of calculus by adding more explanatory graphs and illustrations in easy-to-understand language, practice problems, and even a test at the end. Idiot's Guides: Calculus II is geared for all students who need to succeed in calculus. Show and hide more
Table of Contents
Cover Title Page Copyright Page Contents Introduction Part 1: Review of Pre-Calculus and Calculus I 1 Pre-Calculus Topics Used in Calculus II Trigonometry Exponents and Logarithms Parametric Equations Polar Coordinates Geometric Sequences and Series Partial Fractions 2 Limits, Derivatives, and Basic Integration Limits Derivatives Implicit Differentiation Mean Value Theorem Relative Extremes and Concavity Applications of the Derivative Related Rates 3 Definite and Indefinite Integrals Indefinite Integrals u-Substitutions Fundamental Theorem of Calculus Numerical Approximation Part 2: Length, Area, and Volumes 4 Areas and Approximations Riemann Sums From Numerical Approximations to the True Area Average Value of a Function Area Between Two Curves Simpson’s Rule 5 Volumes and Areas of Solids of Revolutions Volumes of Solids with Defined Cross Sections Disks and Washers Cylindrical Shell Method Arc Length Surface Area Part 3: More Definite and Indefinite Integrals 6 More Integration Techniques Integration by Parts Polynomials and Transcendentals Two Transcendentals 7 Integration with Trigonometric Functions Trigonometric Substitutions Case I: a2+x2 Case II: x2-a2 Case III: a2-x2 Integrals of the Form sinn(x) cosm(x) (When Either m or n Is Odd) Case I: Both m and n Are Odd Case II: Both m and n Are Even Case III: Either m or n Is Odd Integrals with Integrands of the Form tann(x) secm(x) (m Is Even) Integrals with Integrands of the Form tann(x) secm(x) (m Is Odd, n Is Even) 8 Integration with Fractions Completing the Square Integration by Partial Fractions Nonrepeating Linear Factors Repeated Linear Factors Irreducible Quadratic Factors Part 4: The Infinite Series and More 9 To Infinity and Beyond Improper Integrals Infinite Limits of Integration Discontinuities in the Integrand Comparison Test for Improper Integrals 10 Parametric Equations First and Second Derivatives of Parametric Curves Arc Length of a Parametric Curve 11 Polar Coordinates Slope of the Tangent Line Length of an Arc of a Polar Curve Area Under a Curve 12 Introduction to Vectors Scalars and Vectors Displacement, Velocity, and Acceleration 13 Differential Equations Separable Differential Equations Linear Approximations Euler’s Method Slope Fields First Order Linear Differential Equations 14 Infinite Sequences Convergence and Divergence of Sequences Squeeze Theorem Increasing, Decreasing, and Monotonic Sequences 15 Infinite Series Infinite Geometric Series Tests of Convergence Alternating Series Estimating the Sum of Alternating Series 16 Power Series Power Series MacLaurin Series Taylor Series Error Estimates for the MacLaurin and Taylor Series 17 Calculus II Final Exam Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Solutions Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Appendixes A Solutions to “You’ve Got Problems” B Integration Practice Problems and Solutions C Glossary About the Author
