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• Semester One (Chapters P-3)
  
  • Preparation for Calculus (Chapter P)
    
    • Graphs and Models -- the graph of an equation; intercepts of a graph; symmetry of a graph; points of intersection; mathematical models.
    • Linear Models and Rates of Change -- the slope of a line; equations of lines; ratios and rates of change; graphing linear models; parallel and perpendicular lines.
    • Functions and Their Graphs -- functions and function notation; the domain and range of a function; the graph of a function; transformations of functions; classifications and combinations of functions.
    • Fitting Models to Data -- fitting a linear model to data; fitting a quadratic model to data; fitting a trigonometric model to data.
    • Review of Trig Functions (Appendix A.3) -- Angles and Degree Measure; Radian Measure; Trigonometric Functions; Evaluating Trigonometric Functions; Solving Trigonometric Functions; Graphing Trigonometric Functions.
  • Limits and Their Properties (Chapter 1)
    • A Preview of Calculus -- What is Calculus? the tangent line problem; the area problem.
    • Finding Limits Graphically and Numerically
    • Evaluting Limits Analytically -- properties of limits; a strategy for finding limits; cancellation and rationalization techniques.
    • Continuity and One-Sided Limits -- continuity at a point and on an open interval; one-sided limits and continuity on a closed interval; properties of continuity; the Intermediate Value Theorem.
    • Infinite Limits -- vertical asymptotes.
  • Differentiation (Chapter 2)
    • The Derivative and Tangent Line Problem -- the tangent line problem; the derivative of a function; differentiability and continuity.
    • Basic Differentian Rules and Rates of Change -- the constant rule; the power rule; derivatives of sine and cosine; rates of change.
    • The Product and Quotient Rules and Higher Order Derivatives -- product rule; quotient rule; derivatives of trigonometric functions; higher-order derivatives.
    • The Chain Rule -- the chain rule; the general power rule; sinmplifying derivatives; trigonometric functions and the chain rule.
    • Implicite Differentiation
    • Related Rates -- finding related rates; problem solving with related rates.
  • Appications of Differentiation (Chapter 3)
    
    • Extrema on an Interval -- extrema of a function; relative extrema and critical numbers; finding absolute extreme on a close interval.
    • Rolle's Theorem and the Mean Value Theorem
    • Increasing and Decreasing Function and the First Derivative Test
    • Concavity and the Second Derivative Test -- concavity; points of inflection; the second derivative test.
    • Limits at Infinity -- limits at infinity; horizontal asymptotes.
    • A Summary of Curve Sketching Information
    • Optimization Problems -- applied minimum and maximum problems.
    • Business and Economics Applications

• Semester Two Chapters (Chapters 4-7)
  • Integration (Chapter 4)
    
  • Logarithmic, Exponential and Other Transcendental Functions (Chapter 5)
  • Application of Integration (Chapter 6)
  • Integration Techniques, L'Hopital's Rule and Improper Integrals(Chapter 7)

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