Differential & Integral Calculus
Functions and Models. Exponential Functions. Inverse Functions and Logarithms. Limits and Derivatives. The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using
the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes.
Derivatives and Rates of Change. The Derivative of a Function. Differentiation Rules. Derivatives of Polynomials and Exponential Functions. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Implicit Differentiation. Derivatives of Logarithmic Functions. Rates of Change in the Natural and Social Sciences. Exponential Growth and Decay. Related Rates. Linear Approximations and Differentials. Hyperbolic Functions. Applications of Differentiation. Maximum and Minimum Values. The Mean Value Theorem. How Derivatives Affect the Shape of a Graph. Indeterminate Forms and Hospital’s Rule. Summary of Curve Sketching. Optimization Problems. Areas and Distances. The Definite Integral. The Evaluation Theorem. The Fundamental Theorem of Calculus. The Substitution Rule. Integration by Parts. Trigonometric Integrals and Trigonometric Substitutions. Numerical Integration. Improper Integrals.Applications of Integration. More about Areas and Volumes. Arc Length, Parametric Curves. Average Value of a Function (Mean Value Theorem).Applications to Physics and Engineering (Work, Force)