Calculus and Analytic Geometry-I

Contents: Limits and Continuity: Rates of Change and Limits, Rules for Finding Limits, Target Values and Formal Definitions of Limits, Extensions of the Limit Concept, Continuity, Tangent Lines. Derivatives: Derivative of a Function, Differentiation Rules, Rates of Change, Derivatives of Trigonometric Functions, Chain Rule, Implicit Differentiation and Rational Exponents, Related Rate of Change. Applications of Derivatives: Extreme Values of Functions, Mean Value Theorem, First Derivative Test for Local Extreme Values, Graphing with y' and y'', Limits at infinity, Asymptotes, and Dominant Terms, Optimization, Linearization and Differentials, Newton's Method. Integration: Indefinite Integrals, Differential Equations, Initial Value Problems, and Mathematical Modeling, Integration by Substitution-Running the Chain Rule Backward, Estimating with Finite Sums, Riemann Sums and Definite Integrals, Properties, Area, and the Mean Value Theorem, Fundamental Theorem, Substitution in Definite Integrals, Numerical Integration. Application of Integrals: Areas between Curves, Finding Volumes by Slicing, Volumes of Solids of Revolution, Disks and Washers, Cylindrical Shells, Lengths of Plane Curves, Areas of Surfaces of Revolution, Moments and Centers of Mass, Work, Fluid Pressures and Forces, Basic Pattern and other Modeling Applications.