Calculus & Analytic Geometry


Course Outline: Basic Concepts: Real Numbers and Real Lines, Polar Coordinates, Parametric Equations, Functions, Algebra of Functions, Inverse Functions, Quadratic Functions, Shifting Graphs, Trigonometric Functions, Complex Numbers, Inequalities, Infinite Series and Sequences, Taylor Series, Rate of Change and Limit, Rules of Finding Limits, Formal Definition of Limit, Extension of the Limit Concepts, L’Hospitals Rule, Continuity, Tangent Lines; Differential Calculus: The Derivatives of a Function, Differentiation Rules, Rates of Change, Derivatives of Trigonometric Functions, Chain Rule Differentiation, Implicit Differentiation and Rational Exponents, Related Rates of Change, Extreme Values of Functions, Mean Value Theorem, First Derivative and Second Derivative Tests for Extreme Values, Optimization, Linearization and Differentials and Newton’s Method; Integral Calculus: Indefinite Integrals, Integration by Substitution, Riemann Sums, Definite Integral, Fundamental Theorem of Calculus, Mean Value Theorem, Substitution in Definite Integrals, Areas between Curves, Finding Volumes by Slicing, Volumes of Solids of Revolution, Cylindrical Shells, Lengths of Plane Curves, Areas of Surfaces of Revolution, Moments and Center of Mass, Fluid Pressures and Forces, Integration by Parts, Improper Integrals, Multiple Integrals and Line Integrals; Linear Algebra and Vector Calculus: Matrices, Operation on Matrices, Inverse of a Matrix, Rank of Matrix, Determinant, Vectors, and Solutions of System of Linear Equations, and Eigen value Problems.