Instructor's Resource Guide


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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