Slope and Equations of Lines. Linear Functions and Applications. The Least Squares Line.
2. Nonlinear Functions.
Properties of Functions. Quadratic Functions; Translation and Reflection. Polynomial and Rational Functions. Exponential Functions. Logarithmic Functions. Applications: Growth and Decay; Mathematics of Finance.
3. The Derivative.
Limits. Continuity. Rates of Change. Definition of the Derivative. Graphical Differentiation.
4. Calculating the Derivative.
Techniques for Finding Derivatives. Derivatives of Products and Quotients. The Chain Rule. Derivatives of Exponential Functions. Derivatives of Logarithmic Functions.
5. Graphs and the Derivative.
Increasing and Decreasing Functions. Relative Extrema. Higher Derivatives, Concavity, and the Second Derivative Test. Curve Sketching.
6. Applications of the Derivative.
Absolute Extrema. Applications of Extrema. Further Business Applications: Economic Lot Size, Economic Order Quantity; Elasticity of Demand. Implicit Differentiation. Related Rates. Differentials. Linear Approximation.
Antiderivatives. Substitution. Area and the Definite Integral. The Fundamental Theorem of Calculus. The Area Between Two Curves. Numerical Integration.
8. Further Techniques and Applications of Integration.
Integration by Parts. Volume and Average Value. Continuous Money Flow. Improper Integrals.
9. Multivariable Calculus.
Functions of Several Variables. Partial Derivatives. Maxima and Minima. Lagrange Multipliers. Total Differentials and Approximations. Double Integrals.
Table 1. Formulas from Geometry. Table 2. Integrals.
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