Details


7 Integrals and Transcendental Functions 
7.1 The Logarithm Defined as an Integral 
7.2 Exponential Change and Separable Differential Equations 
7.3 Hyperbolic Functions 
7.4 Relative Rates of Growth 

8 Techniques of Integration 
8.1 Integration by Parts 
8.2 Trigonometric Integrals 
8.3 Trigonometric Substitutions 
8.4 Integration of Rational Functions by Partial Fractions 
8.5 Integral Tables and Computer Algebra Systems 
8.6 Numerical Integration 
8.7 Improper Integrals 

9 First-Order Differential Equations 
9.1 Solutions, Slope Fields, and Euler’s Method 
9.2 First-Order Linear Equations 
9.3 Applications 
9.4 Graphical Solutions of Autonomous Equations 
9.5 Systems of Equations and Phase Planes 

10 Infinite Sequences and Series 
10.1 Sequences 
10.2 Infinite Series 
10.3 The Integral Test 
10.4 Comparison Tests 
10.5 The Ratio and Root Tests 
10.6 Alternating Series, Absolute and Conditional Convergence 
10.7 Power Series 
10.8 Taylor and Maclaurin Series 
10.9 Convergence of Taylor Series 
10.10 The Binomial Series and Applications of Taylor Series 

11 Parametric Equations and Polar Coordinates 
11.1 Parametrizations of Plane Curves 
11.2 Calculus with Parametric Curves 
11.3 Polar Coordinates 

11.4 Graphing in Polar Coordinates 
11.5 Areas and Lengths in Polar Coordinates 
11.6 Conic Sections 
11.7 Conics in Polar Coordinates