Calculus Course Outline Precalculus Review a. Lines b. Functions and graphs c. Exponential Functions d. Parametric Equations e. Logarithmic Functions f. Trigonometry Review Limits and Continuity a. Rates of Change and Limits b. Limits Involving Infinity c. Continuity d. Rates of Change and Tangent Lines Derivatives a. b. c. d. e. f. g. h. i. Derivative of a Function Differentiability Rules for Differentiation Velocity and Other Rates of Change Derivatives of Trig Functions Chain Rule Implicit Differentiation Derivatives of Inverse Trig Functions Derivatives of Exponential and Logarithmic Functions
Applications of Derivatives a. Absolute Extreme Values b. Mean Value Theorem c. Curve Sketching with f’ and f’’ d. Modeling and Optimization e. Linearization and Newton’s Method f. Related Rates Definite Integrals a. Rectangular Approximation Method b. Riemann Sums and Definite Integrals as Area Under A Curve c. Antiderivatives d. Fundamental Theorem of Calculus e. Trapezoidal Rule Differential Equations and Mathematical Modeling a. Antiderivatives and Slope Fields b. Integration by Substitution c. Exponential Growth and Decay Applications of Integrals a. Integral as Net Change b. Areas Under/Between Curves c. Volume by Discs and Washers d. Volume by Cylindrical Shells