Textbook: Single Variable Calculus, by James Stewart, fourth edition
Topics to be covered:
Applying the derivative to problems of maxima and minima (optimization problems), to l'Hopitals rule for evaluating certain limits, to Newton's method for estimating the roots of equations.
The notion of antiderivative, definite integrals. The fundamental theorem of calculus. Using the integral to evaluate areas, distances, volumes, arc lengths, and the average value of a function. We also learn various techniques for evaluating integrals, among them substitution, integration by parts, and partial fractions.
Examples and applications to Physics, Engineering and Economics.
A "Catalog Description" is available at
http://www.math.rochester.edu:8080/courses/catalog/MTH142.html
Practice midterm (also distributed in class)
Practice final (also distributed in class)
FINAL: August 11, Hylan
1101, you can come any time between 8am and
11pm, but please let me know when you are going to come (approximately)
Also, August 11 is the last day you can submit your homeworks and
extra credit problems.
Grading policy:
Attendance 10% [20 points] (If you are going to miss a class, please
send me an email (preferably in advance) explaining
your reason. You will not lose any points in case of illness, family emergency, or other serious reason)
Homework 35% [70 points] (Weekly homework will be due Monday of each
week)
Midterm 20% [40 points] (July 25)
Final 35% [70 points] (August 11)
Total: 200 points.
Instructor: Maria Voloshina
Office: Hylan 818
Office hours: M W 11:30-13:00, T R 16:00-17:30, and by appointment
Email: voloshin@math.rochester.edu
Webpage: http://www.math.rochester.edu/u/voloshin/
Webpage for Math 142: http://www.math.rochester.edu/u/voloshin/math142-00.html
Week 1
June 26 .... Review of 4.1 - 4.4. Maximum and Minimum Values. The Mean Value Theorem. How Derivatives Affect the Shape of a Graph. Indeterminate Forms and L'Hopital's Rule.
June 27 .... 4.5, 4.6. Summary of Curve Sketching. Graphing with Calculus and Calculators. (domain of a function; itercepts; symmetry (even, odd, and periodic functions); horizontal, vetical, and slant asymptotes; intervals of increase or decrease; local maximum and minimum values; concavity and points of inflection)
June 28 .... 4.7. Optimization Problems (6 step process, first derivative test for absolute maxima or minima).
June 29 ... 4.8. Application to Economics (cost functions, average cost functions, marginal cost functions, minimum average implies equality of marginal and average cost, demand or price functions, revenue or sales functions, marginal revenue functions, profit functions, marginal profit functions, maximum profit implies equality of marginal revenue and marginal cost)
July 3-7 .. NO CLASSES
Week 2
July 10 ... 4.9. Newton's Method (approximation of roots via successive tangent lines, successive approximation formula)
July 11 ... 4.10. Antiderivatives (definition of an antiderivative, general antiderivatives, table of antiderivatives, direction fields, applications to rectilinear motion)
July 12 ... 5.1. Areas and Distances (estimating areas via upper and lower rectangles, areas as limits of thinner and thinner rectangles, sigma notation, determining distances from velocities)
July 13 ... 5.2. The Definite Integral (definite integrals via limits of Riemann sums, application of three summation formulas to evaluating definite integrals, midpoint rule, fundamental properties of the difinite integral)
Week 3
July 17 ... 5.3. The Fundamental Theorem of the Calculus (comparison properties of integrals, Parts 1 and 2 of the Fundamental Theorem, proofs)
July 18 ... 5.4. Indefinite Integrals and the Total Change Theorem (indefinite integral as a family of functions; applications: the total change (in the amount of water in a reservoir or in the concentration of a chemical), or the increase in population, or displacement, etc, is the definite integral of the rate of change)
July 19 ... 5.5. The Substitution Rule (substitution rules for indefinite and definite integrals, integrals of symmetric functions)
July 20 ... 6.1. Areas between Curves (the area of the region enclosed by 2 curves or by 2 curves and 2 straight lines, integrating with respect to y instead of x, splitting the region in 2 or more pieces)
Week 4
July 24 ... 6.2, 6.3. Volumes (definition of volume via integrals of cross sections, volumes of revolution by slicing into disks and by cylindrical shells) . Volumes by Cilindrical Shells.
July 25 ... 6.4, 6.5. Work. Average Value of a Function (definition of the average value, mean value theorem for integrals). Midterm (covers chapters 4 and 5)
July 26 ... 7.1. Integration by Parts (two notations for integration by parts, stripping powers of x, introducing multiplication by 1 , switchback integration, reduction formulas for trigonometric powers)
July 27 ... 7.2. Trigonometric Integrals (integrating powers of sin, cosine, and tangent; using trigonometric identities for integration; recursive formulas)
Week 5
July 31 ... 7.3. Trigonometric Substitution ("inverse substitution" effective for radical expressions, the area enclosed by an ellipse)
Aug 1 ..... 7.4. Integration of Rational Functions by Partial Fractions (reducing the degree of the numerator by division, integrating by expressing rational functions or irreducible quadratics)
Aug 2 ..... 7.5, 7.6. Strategy for Integration. Integration using Tables and Computer Algebra Systems (using division, reduction formulas, and completing the square to reduce integrals to results in tables, doing integrals with Maple or Mathematica, not all integrals can be computed by elementary functions)
Aug 3 ..... 7.7. Approximate Integration (left or right endpoint approximation, midpoint approximation, trapezoidal rule, Simpson's Rule)
Week 6
Aug 7 ..... 7.8. Improper Integrals (integrals with infinite bounds, discontinuous integrands, comparison tests for the convergence or divergence of improper integrals)
Aug 8 ..... 8.1. Arc Length (arc length formula in parametric form and standard function form)
Aug 9 ..... 8.2. Area of a Surface of Revolution (areas of circular cylinders and cones, a formula for the area of the surface obtained by rotating a curve y=f(x) about the x-axis or about the y-axis)
Aug 10 .... 8.3.Applications to Physics and Engineering (work problems with a given force, Hooke's law and applications to springs, work done in lifting or pumping, hydrostatic pressure and force, moments and centers of mass, symmetry principle). Review. Practice final.
Aug 11 .... Final exam (covers chapters 6, 7, and 8)
Each problem is worth 1 point.
Assignment 1, due July 10
4.4. p.311: 8, 50
4.5. p.321: 10, 36, 40, 44, 50
4.6. p.328: 12, 16
4.7. p.335: 10, 18, 25, 31, 52
4.8. p.344: 4, 8, 22
Assignment 2, due July 17
4.9. p.349: 16, 34
4.10. p.356: 4, 34, 40, 42, 62
5.1. p.376: 4, 20
5.2. p.389: 16, 30, 36, 46, 52, 64
Assignment 3, due July 24
5.3. p.398: 6, 14, 26, 52, 58
5.4. p.407: 8, 26, 30
5.5. p.416: 2, 28, 58, 78
6.1. p.438: 4, 16, 28
Assignment 4, due July 31
6.2. p.448: 2, 12, 46
6.3. p.454: 4, 39
6.4. p.458: 2, 12
6.5. p.462: 2, 10, 14, 22
7.1. p.474: 4, 22, 42
7.2. p. 482: 4
Assignment 5, due August 7
7.3. p.488: 2, 14, 30
7.4. p.498: 12, 16, 28
7.5. p.504: 2, 36, 44
7.6. p.509: 2, 12, 42
7.7. p.521: 8, 24, 46
Assignment 6, due August 11
7.8. p.531: 20
8.1. p.546: 14
8.2. p.552: 5, 28
8.3. p.563: 20
The following problems are not required. They are optional. You may do them if you want to get some extra points (1 point for each problem).
p.364-365: 1-24
p.430-431: 1-19
p.465-467: 1-14
p.538-539: 1-12
p.578-579: 1-10