Syllabus B

 Semester I (through single variable integration) Day Material to be covered 1 1.1 Fundamentals of Modeling 2 1.2 Functions and Graphs 3 1.3 Constructed Functions 4 1.4 Linear Functions and Models 5 Test 1 6 2.1 Exponential Functions and Models 7 8 2.2 Exponential Models in Finance 9 2.3 Polynomial Functions and Models 10 2.4 Choosing a Model 11 Test 2 12 3.1 Average Rates of Change 13 3.2 and 3.3 Instantaneous Rates of Change and Tangent Lines 14 3.4 Derivatives 15 3.5 Percentage Change and Percentage Rates of Change 16 Test 3 17 4.1 Numerically Finding Slopes 18 4.2 Drawing Slope Graphs 19 4.3 Slope Formulas 20 4.4 The Sum Rule 21 4.5 The Chain Rule 22 23 4.6 The Product Rule 24 25 Test 5 26 5.1 Optimization 27 28 5.2 Inflection Points 29 30 5.3 Approximating Change 31 6.1 Results of Change 32 6.2 Trapezoid and Midpoint-Rectangle Approximations 33 6.3 The Definite Integral as a Limit of Sums 34 6.4 Accumulation Functions 35 6.5 The Fundamental Theorem of Calculus 36 6.6 The Definite Integral 37 38 Test 6 39 7.1 Differences of Accumulated Changes 40 7.2 Perpetual Accumulation 41 7.4 Integrals in Economics 42 Review Final Exam (cumulative)
 Semester II (sine models, multivariable calculus, and differential equations) Day Material to be covered 1 Review of Chapters 1 through 6 2 3 4 5 Test 1 6 Review of Sections 7.1, 7.2, and 7.4 7 8 7.3 Streams in Business and Biology 9 7.5 Average Value and Average Rates of Change 10 7.6 Probability Distributions and Density Functions 11 12 Test 2 13 Appendix: Trigonometry 14 8.1 Sine Functions as Models 15 8.2 Rates of Change and Sine Models 16 17 8.3 Derivatives of the Sine and Cosine 18 8.4 Extrema and Points of Inflection 19 8.5 Accumulation in Cycles 20 21 Test 3 22 9.1 Cross-Sectional Models and Multivariable Functions 23 9.2 Contour Graphs 24 25 9.3 Partial Rates of Change 26 27 9.4 Compensating for Change 28 29 Test 4 30 10.1 Multivariable Critical Points 31 32 10.2 Multivariable Optimization 33 34 10.3 Least Squares Optimization 35 Test 5 36 11.1 Differential Equations and Accumulation Functions 37 11.2 Separable Differential Equations 38 39 11.3 Second-Order Differential Equations 40 41 Review 42 Final Exam (cumulative)

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