Syllabus A

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

[ Back ]