MATH 142,  CALCULUS II

July 6 - August 13

M,T,W,R   9:00-11:15

Hylan 105

Prerequisites: MTH141 or MTH161

Textbook: Calculus - concepts and contexts, by James Stewart

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.

Schedule and Homework assignments

Practice midterm: Distributed in class

Midterm: CONGRATULATIONS! All of you did it very well, most of you even extremely well!

Practice final: Distributed in class

Grading policy:
Attendance 20%
Homework 30%  (Weekly homework will be due Thursday of each week)
Midterm 20%  (July 26)
Final 30%  (August 13)

Instructor: Maria Voloshina
Office: Hylan 805
Office hours: M 16:00-17:30, W 11:30-13:00 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.html


Schedule

July 6 .... 4.2. Maximum and Minimum Values (absolute maxima, absolute minima, absolute extrema, local maxima, local minima, local extrema, extreme value theorem, Fermat's theorem, critical numbers, closed interval method)

July 7 .... 4.3. Derivatives and the Shapes of Curves (mean value theorem, increasing/decreasing test, first derivative test, concavity, points of inflection, concavity test, second derivative test)

July 8 .... 4.4. Graphing with Calculus and Calculators (change scale, large scale to see asymptotes, small scale to see roots, critical points, points of inflection, graph list and second derivatives to help see critical points and inflection points). Exercises.

July 12 ... 4.5. Indeterminate Forms and L'Hopital's Rule (L'Hopital's Rule for evaluating two types of indeterminate forms zero/zero or infinity/infinity, indeterminate products zero times infinity via rewriting as quotients, indeterminate differences infinity minus infinity via common denominators, three types of indeterminate powers via logarithms)

July 13 ... 4.6. Optimization Problems (6 step process, first derivative test for absolute maxima or minima).

July 14 ... 4.7. Applications 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 15 ... 4.8. Newton's Method (approximation of roots via successive tangent lines, successive approximation formula)

July 19 ... 4.9. Antiderivatives (definition of an antiderivative, general antiderivatives, table of antiderivatives, direction fields, applications to rectilinear motion)

July 20 ... 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 21 ... 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)

July 22 ... 5.3. Evaluating Definite Integrals (evaluation theorem, proof via the mean value theorem, indefinite integrals, table of indefinite integrals, total change theorem, examples). Review.

July 26 ... 5.4. The Fundamental Theorem of the Calculus (comparison properties of integrals, Parts 1 and 2 of the Fundamental Theorem, proofs). Midterm

July 27 ... 5.5. The Substitution Rule (substitution rules for indefinite and definite integrals, integrals of symmetric functions)

July 28 ... 5.6. 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 29 ... 5.7. 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 2 ..... Appendix F, Integration of Rational Functions (reducing the degree of the numerator by division, integrating by expressing rational functions or irreducible quadratics)

Aug 3 ..... 5.8. Approximate Integration (left or right endpoint approximation, midpoint approximation, trapezoidal rule, Simpson's Rule)

Aug 4 ..... 5.9. Improper Integrals (integrals with infinite bounds, discontinuous integrands, comparison tests for the convergence or divergence of improper integrals)

Aug 5 ..... 6.1. More about Areas (areas between curves, areas enclosed by parametric curves)

Aug 9 ..... 6.2. Volumes (definition of volume via integrals of cross sections, volumes of revolution by slicing into disks and by cylindrical shells)

Aug 10 .... 6.3. Arc Length (arc length formula in parametric form and standard function form)

Aug 11 .... 6.4. Average Value of a Function (definition of the average value, mean value theorem for integrals). Review.

Aug 12 .... 6.5. 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)

Aug 13 .... Final exam


Homework assignments

Assignment 1, due July 15
4.2. p.279-280: 4, 17, 25, 38;     4.3. p.292-293: 6, 10, 19, 22; (extra credit: 35);    
4.5. p.308-309: 4, 10, 14, 24

Assignment 2, due July 22
4.5. p.308: 16;     4.6. p.316-319: 2, 9, 30;     4.7. p.325-326: 2, 13;    
4.8. p.331: 4, 5, 13;     4.9. p.338: 2, 10, 14; (extra credit: 34)

Assignment 3, due July 29
4.9. p.338: 20;     p.341-342: 26; (extra credit: 59); 5.1. p. 359-360: 2, 12;    
5.2. p.370-371: 6, 27;     5.3. p.380: 4, 8, 22, 28; (extra credit: 40);     5.4. p. 390: 4, 12

Assignment 4, due August 5
5.5. p.400-401: 2, 8, 10, 18; (extra credit: 47);     5.6. p.407: 4, 18, 37;    
5.7. p.413-414: 1, 5, 10;     Appendix F, p.A50: 5, 13;

Assignment 5, due August 12
5.9. p.435-436: 2, 5, 10, 23;     p.439: 20, 23;     6.1. p. 453: 2, 6, 16;    
6.2. p.462: 1, 4;     6.3. p.468: 5; (extra credit: 18)


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