Section | Subject | Problems |
1.2 | Coordinates | 1,13,15,16 |
1.3, 1.4 | Increments, Slope of a line | |
1.5 | Equation of Straight lines | 10,11,15,19 |
1.7 | Slope of a curve | 1,2,12,13 |
1.8 | Derivative of a function | 1,2,3,6,8,12, 14, 22 |
1.9 | Velocities and rates | 1 (see Pblm12, § 1.8), 2, 8, 19, 20 |
1.10 | Limits | 1,2,4,6,7,9,12,15,16,17,18 |
2.2 | Derivatives of polynomials | 1,3,10,11,13,25,27 |
2.3 | Product and Quotient rules | 2,3,6,7,8,9,14 |
2.4 | Inverse functions | 1,2,3 |
2.5 | Implicit Functions | 1,2,3,7,19 |
2.8 | Chain rule | 6, 7, 9 |
2.9 | Trigonometry review | |
2.10 | Derivatives of sin, cos and tan | 1,2,3,4,7,23,24,26,29,35,39 |
2.6 | Increments (we skip differentials) |
6,7,10 |
3.2 | Related rates | 1,2,3,7,8,9 |
3.3-3.4 | Convexity and Concavity | 1,2,3,5,7,8 |
3.5-3.6 | Maxima and Minima | 1,2,3,4,5,6,7 |
3.7-3.8 | Rolle's and Mean Value Theorems | (3.7) 4, (3.8) 1,7 |
3.9 | l'Hôpitals's rule | 1,3,6,7,8,9 |
3.10 | Taylor's formula | A hand out with problems will be provided |
4.2 | Indefinite integral and differential equations | 1,2,3,6,9,10,14—24 |
4.3 | Interpretations of the indefinite integral | 1,3,4,6(!), 7,8,13,14 |
4.4 | Integrals of trigonometric functions | 1—10,25 |
4.5 | Area under a curve | 1,2,4,6,9 |
4.6 | Area as a limit | — |
4.7 | Area and calculus | 1—4,9,10,12—15 |
4.8 | The Fundamental Theorem of Calculus |
6—14 (Sketch the region
whose area is represented by each of these integrals) 18,20,22,23 |
4.9 | Approximating integrals | |
5.2 | Plane areas | 1(b),2,3,4,6,8,9,10,11 |
5.3 | Distance traveled | 1,3,4,10,11,14 |
5.4 | Volumes (in general) | 1,2,3,5,9,10,11(a&b!),13(!),17 |
5.5 | Volumes by shells &washers | 1,3,6,8,10,12 |
6.1 | Trig functions again | 37 (no computations required!) 34, 38, (related rates review) 40, 45,46,47,48 49 50,51,52 |
6.2 | The inverse trig functions | 1,2,3,8(abcd)(no calculator) 6,9 On your graphing calculator look at the graph of y=sin^{-1}(sinx). Explain. |
6.3 | Derivatives of inverse trig functions. | 5,6,8,9(!),11, 16,17,18,20 |
6.4,6.5, 6.6, 6.7,6.8 |
Natural Logarithm, the exponential function and exponential growth. |
We deviate significantly from the textbook. Notes will be handed out. |