Detailed Syllabus
| Day |
Section/Subject |
Supplementary Problems |
| Dec. 5 |
5.1 Areas between Curves
5.4 Work
|
5.1 Exercises 21 - 32.
5.4 Exercises 7 - 12.
|
| Dec. 2 |
5.1 Areas between Curves
|
5.1 Exercises 1 - 20.
|
| Dec. 30 |
4.4 Indefinite Integrals and the Net Change Theorem
4.5 The Substitution Rule
|
4.4 Exercises 36 - 42, 46 - 56.
4.5 Exercises 61 - 66.
|
| Nov. 28 |
4.3 The Fundamental Theorem of Calculus, part II
4.4 Indefinite Integrals and the Net Change Theorem
4.5 The Substitution Rule
|
4.3 Exercises 19 - 38, 39 - 42, 53, 61, 62.
4.4 Exercises 19-35.
4.5 Exercises 35 - 51.
|
| Nov. 25 |
4.3 The Fundamental Theorem of Calculus
|
4.3 Exercises 7 - 18, 49 - 52, 64, 68, 69.
|
| Nov. 23 |
4.2 The Definite Integral (the midpoint rule, properties of the
definite integral)
|
4.2 Exercises 17-20, 21-25, 26-30, 33, 34, 35, 39, 41, 47, 48, 49,
51, 55, 56, 57, 58, 59, 63, 65, 68, 71, 73.
|
| Nov. 21 |
4.1 Areas and Distances
4.2 The Definite Integral
|
4.1 Exercises 22, 23, 24, 25, 26, 30.
4.2 Exercises 1, 2, 3, 4, 8.
|
| Nov. 18 |
4.1 Areas and Distances
|
4.1 Exercises 3, 4, 5, 7, 19, 20, 21.
|
| Nov. 16 |
4.4 Indefinite Integrals and the net Change Theorem (indefinite
integrals)
4.5 The Substitution Rule (the substitution rule for indefinite
integrals)
|
4.4 Exercises 1-16.
4.5 Exercises 1-34.
|
| Nov. 14 |
2.9 Linear Approximations and Differentials (differentials)
3.9 Antiderivatives
|
2.9 Exercises 11-18.
3.9 Exercises 1-18, 21-40, 51-56.
|
| Nov. 09 |
3.7 Optimization Problems
|
3.7 Exercises 3, 5, 7, 13, 16, 18, 23-30, 37-41, 43, 45, 46, 51-59,
74.
|
| Nov. 07 |
3.4 Limits at Infinity; Horizontal Asymptotes.
3.5 Summary of Curve Sketching
|
3.4 Exercises 1-4, 9-30, 33-38, 44-52, 54-56.
|
| Nov. 04 |
3.3 How Derivatives Affect the Shape of a Graph (the second
derivative test)
3.4 Limits at Infinity; Horizontal Asymptotes.
|
3.3 Exercises 15, 16, 17, 18, 61, 62, 65, 70.
|
| Nov. 02 |
3.3 How Derivatives Affect the Shape of a Graph (concave upward and
concave downward functions, the concavity test, inflection points)
|
3.3 Exercises 13, 14, 19, 20, 21, 23, 25, 26, 29-20, 53, 54, 57.
|
| Oct. 31 |
3.2 The Mean Value Theorem (the mean value theorem and applications)
3.3 How Derivatives Affect the Shape of a Graph (the
increasing/decreasing test, the first derivative test)
| 3.2 Exercises 23, 24, 25, 27, , 31, 33.
3.3 Exercises 1, 3, 5, 9, 10, 11, 26.
|
| Oct. 28 |
3.1 Maximum and Minimum Values (the closed interval method)
3.2 The Mean Value Theorem (Rolle's theorem)
| 3.1 Exercises 54, 57, 59, 51, 53, 55, 57, 63.
3.2 Exercises 1, 3, 5, 6, 19, 21.
|
| Oct. 26 |
3.1 Maximum and Minimum Values (extreme values, local maxium/minimum,
the extreme value theorem, critical numbers, Fermat's theorem)
|
3.1 Exercises 2, 4, 6, 8, 9, 10, 11, 12, 15, 17, 19, 21, 23, 25, 27,
30-42, 68, 69, 72.
|
| Oct. 24 |
2.8 Related Rates
2.9 Linear Approximations and Differentials
|
2.8 Exercises 11, 13, 14, 15, 17-24, 27, 34-39, 45.
2.9 Exercises 2, 4, 8, 10.
|
| Oct. 21 |
2.6 Implicit Differentiation
2.7 Rates of Change in the Natural and Social Sciences
2.8 Related Rates
|
2.6 Exercises 30-32, 45, 46, 47, 49, 51, 56, 57, 61.
2.7 Exercises 7, 9, 13, 15, 18, 21, 28, 31, 35.
2.8 Exercises 1-10.
|
| Oct. 19 |
2.5 The Chain Rule
2.6 Implicit Differentiation
|
2.5 Exercises 26-46, 48, 50, 51, 52, 59, 62, 63-72, 85-89.
6.6 Exercises 1-14, 25-28.
|
| Oct. 17 |
2.4 Derivatives of Trigonometric Functions
2.5 The Chain Rule
|
2.4 Exercises 1-24, 29-35, 39-38
2.5 Exercises 7-25.
|
| Oct. 14 |
2.3 Differentiation Formulas (the product and quotient rules);
|
2.3 Exercises 1, 2, 3, 4, 5, 6, 24, 27, 29, 30, 31, 32, 33, 34, 35,
36, 37, 38, 39, 40, 61, 62, 67, 68, 69, 70, 80, 81, 82, 83, 85, 86, 95,
97, 98, 99, 100, 105.
|
| Oct. 12 |
2.2 The Derivative as a Function (higher derivatives)
2.3 Differentiation Formulas (derivative of a constant function, the
power rule, the constant multiple rule, the sum rule, the difference
rule); |
2.2 Exercises 41, 42, 43, 44, 48, 49, 53.
2.3 Exercises 1, 2, 3, 4, 5, 6, 24, 45, 52, 59, 60, 64, 75, 76,
77, 93, 94, 103.
|
| Oct. 7 |
2.2 The Derivative as a Function (differentiable
functions, the derivative, the graph of a differentiable
function) |
2.2 Exercises 3, 4, 5, , 14, 16, 20, 22, 24, 28, 30, 34, 36, 37. |
| Oct. 5 |
2.1 Derivatives and rates of change (rates of change, velocities)
|
2.1 Exercises 16, 17, 22, 23, 33, 35, 37, , 45, 47, 50. |
| Oct. 3 |
2.1 Derivatives and rates of change (tangents, the equation of the
tangent line to a curve at a point, rates of change) |
2.1 Exercises 1, 3, 6, 8, 9. |
| Sept. 30 |
1.8 Continuity (classes of continuous functions, the intermediate
value theorem) |
1.8 Exercises 40, 42, 46, 48, 49, 50, 52, 54, 56, 63, 64, 66,
67, 69. |
| Sept. 28 |
1.8 Continuity ( continuity at a point, and on open and closed
intervals, removable and non-removable disconinuities, properties of
continuous functions) |
1.8 Exercises 2, 5, 7, 9, 12, 16, 18, 20, 22, 23, 25, 29, 35, 37.
|
| Sept. 26 |
1.5 The Limit of a Function (infinite limits and vertical asymptotes)
1.8 Continuity
| 1.5 Exercises 29-37.
1.8 Exercises 3, 4.
|
| Sept. 23 |
1.5 The Limit of a Function (one-sided limits)
1.6 Calculating Limits using the Limit Laws
| 1.5 Exercises 2, 3, 4, 7, 8, 15, 16, 17.
1.6 Exercises 48, 49, 50, 51, 52.
|
| Sept. 21 |
1.5 The Limit of a Function
1.6 Calculating Limits using the Limit Laws
| 1.5 Exercises 1, 12, 19.
1.6 Exercises 1, 2, 3, 5, 9, 10, 11-32, 38, 40, 42-46, 53, 59, 60, 62,
63.
|
| Sept. 19 |
1.3 New Functions from Old Functions (composition of functions)
1.5 The Limit of a Function
| 1.3 Exercises 32, 34, 38, 40, 42, 44, 53, 55, 59. |
| Sept. 16 |
1.2 Mathematical Models: A Catalog of Essential Functions (the
tangent function)
1.3 New Functions from Old Functions (combination of functions)
| 1.3 Exercises 1, 3, 5, 9, 13, 29, 30. |
| Sept. 14 |
1.2 Mathematical Models: A Catalog of Essential Functions (power and
trigonometric functions functions)
| 1.2 Exercises 1, 2, 3, 4, 17. |
| Sept. 12 |
1.1 Four ways to represent a function (the graph of a
function, the vertical line test, increasing and decreasing functions).
1.2 Mathematical Models: A Catalog of Essential Functions (linear,
polynomial and rational functions)
| 1.1 Exercises 28, 30, 33, 34, 36, 40, 42, 44, 52, 58.
1.2 Exercises 5, 6, 7, 8, 9, 13. |
| Sept. 09 |
1.1 Four ways to represent a function (functions,
domain, codomain, range, graph). | 1.1 Exercises 1, 2, 3,
4, 11, 12, 22, 23, 24, 25. |
| Sept. 07 |
1.1 Four ways to represent a function | |