Calculus and Analytic Geometry-II

Contents: Transcendental Functions: Inverse Functions and Their Derivatives, Natural Logarithms, Exponential Function, a^x and log_a(x), Growth and Decay, L'Hopital's Rule, Relative Rates of Growth, Inverse Trigonometric Functions, Derivatives of Inverse Trigonometric Functions; Integrals, Hyperbolic Functions, First Order Differential Equations, Euler's Numerical Method; Slope Fields. Techniques of Integration: Basic Integration Formulas, Integration by Parts, Partial Fractions, Trigonometric Substitutions, Integral Tables and CAS, Improper Integrals. Infinite Series: Limits of Sequences of Numbers, Theorems for Calculating Limits of Sequences, Infinite Series, Integral Test for Series of Nonnegative Terms, Comparison Tests for Series of Nonnegative Terms, Alternating Series, Absolute and Conditional Convergence, Power Series, Taylor and Maclaurin Series, Convergence of Taylor Series; Error Estimates, Applications of Power Series. Conic Sections, Parameterized Curves, and Polar Coordinates: Conic Sections and Quadratic Equations, Classifying Conic Sections by Eccentricity, Quadratic Equations and Rotations, Parameterizations of Plane Curves, Calculus with Parameterized Curves, Polar Coordinates, Graphing in Polar Coordinates, Polar Equations for Conic Sections, Integration on Polar Coordinates. Vectors and Analytic Geometry in Space: Vectors in the plane, Cartesian (Rectangular) Coordinates and Vectors in Space, Dot Products, Cross Products, Lines and Planes in Space, Cylinders and Quadric Surfaces, Cylinders and Spherical Coordinates.