This is a college level course covering derivatives, integrals, limits, approximation, and applications and modeling.

Knowledge of algebra, geometry, trigonometry, analytic geometry, and elementary functions.

Two Semesters or Block

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A. Function & Graphs Functions & function notation Absolute value & Piecewise Defined Functions Inequalities Composition & Combination of Functions Exponential & logarithmic functions Transformation of Functions Trigonometric Functions Polynomial & Rational Functions	C. Derivatives Definition of the Derivative Differentiation Rules The Chain Rule Derivatives of Exponential Functions Derivative of Logarithmic Functions Derivatives of Inverse Functions Differentiability & Continuity Implicit Differentiation Logarithmic Differentiation Limits & Continuity of Vector-Valued Functions
B. Limits & Continuity Intuitive Definition of a Limit Algebraic Techniques for Finding Limits One-Sided Limits Infinite Limits Limits at Infinity Limits of Special Trigonometric Functions Continuity	D. Application of the Derivative Tangent & Normal Lines Position, Velocity, & Acceleration (PVA) Related rates Relative Extrema & the First Derivative Test Concavity & the Second Derivative Test Absolute Extrema & Optimization Rolle's Rule & the Mean Value Theorem Differentials

E. Anti-Derivatives Differential Equations and Slope Fields Antiderivatives The Chain Rule for Antiderivatives Antiderivatives of Logarithms Antiderivatives of Inverse Trig Functions Trigonometric Substitutions The Definite Integral Fundamental Theorem of Calculus

F. Application Net Change and Displacement Volume Separable Differential Equations Work Other Applications of Definite Integrals

 

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